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Pp. 65-69. These are in the form given in Bégat, Géodésie. They

are sufficiently accurate for our ordinary wants; for

very extended operations, it is not to be presumed

that the officer would make this collection his only guide.

70-71. At the solicitation of several officers I have introduced into this edition examples to explain the application of many of the formula.

72-77. The values of N and R, etc., within the limiting parallels of the territory of the United States, were computed by Lieut. Thom, Corps Topographical Engineers; afterwards by Mr. Downes, and the two carefully compared.

78-80. Bégat, Géodésie.

81-82. Trigonometrical surveying-Lieutenant Frome, Royal

Engineers.

83-86. Baily, Astronomical Tables and Formulæ.

87-94. Abridged from Guyot's Meteorological Tables-prepared for the Smithsonian Institution. 1852.

95. Adapted, from Guyot's tables, to English inches and Fahrenheit's Thermometer scale.

96-98. The first method is from a manuscript of the late J. N. Nicollet, who probably obtained it from Mr. Hassler,

as it is the projection in use at the Coast Survey office. The remaining methods will be found in Francœur, Geodésie.

99-128. The whole of these tables were computed, under my direction, for the Bureau of Topographical Engineers, by Mr. Downes. They were, occasionally, compared with similar quantities (in metres) in the manuscript tables in the Coast Survey office.

Appendix. Magnetical observations-from the Magnetical Instruc129-137. tions prepared by order of the British Government, by Lieut. J. C. B. Riddel, Royal Artillery. 1844. 138. Eighth report of the British Association, 1838, page 91.

B

PART III.

Pp. 141-143. Francœur, Astronomie Pratique-Baily, Ast. Tables and Formulæ.

144-145. Baily, Ast. Tables and Formulæ.

146-157. Downes, U. S. Almanac, 1845. Compared, also, with Baily, Ast. Tables whenever practicable.

158-160. This, with subsequent examples of Sextant observations, was obtained through the kindness of Brevet Lieut. Col. J. D. Graham, Corps Topographical Engineers, from the records of the Northeastern Boundary Survey.

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173. American Almanac; Downes's U. S. Almanac. 174-181. Ivory's Refractions, from Galbraith, Math. Tables and Formulæ. The zenith distances are changed to altitudes, as more convenient for our purposes.

182-184. Baily, Ast. Tables and Form.; Simms on Math. Instruments, London, 1836.

185. Original. This table, and the one on page 188, will be found convenient in setting up a Transit Instru

ment.

186-187. Extracted from some of my own observations whilst attached to the Coast Survey.

189-191. Francœur, Astronomie Pratique.

192-199. Baily, Ast. Tables and Formulæ.

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207-210. Fram a manuscript translation of an article by Prof.

Hanson, Ast. Nach., No. 143. The method of reversals, described by Struve in his notice of the Rhepsold Instrument, Ast. Nach., Vol. 20, is undoubtedly the best; but, for the want of a reversing apparatus, is ill suited to such Transit Instruments as are usually carried into the field.

Pp. 211-214. From a description, by myself, of the use of the zenith and equal altitude Telescope, printed for the

Bureau of Topographical Engineers in 1848.

215-218. Francœur, Ast. Prat.; Simms on Math. Instruments. Reduction to elongation and corrections for level,

R. H. Fauntleroy, U. S. Coast Survey.

218. Correction for Run. Henderson's Edinb. Ast. Obser

vations.

219-221. Downes, U. S. Almanac. Francœur, Ast. Prat.

222-223. Frome, Trigonomerical Surveying.

224-231. Downes, U. S. Almanac; Walker, Trans. Am. Phil. Society, Vol. VI; Prof. Bartlett on Longitude by

lunar culminations, printed for the Bureau of Topographical Engineers.

232-237. Gummere's Astronomy.

238-240. From a manuscript explanation, by Prof. Bartlett, of an article by Encke, translated in Taylor's Scien

tific Memoirs, part VII.

241-242. The authorities are given in the text.

T. J. L.

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