Transactions . ruments. * Trans., xxix., 1001, 1899. f The system is explained in the book of Nonius entitled De Crepusculis. X Alee Seu Scalce Mathematical, Thomas Digges, London, 1573. [See also Trans.,xxix., 986 and 987, for an illustration and the history of this method of subdivid-ing angles, the so-called diagonal scale, or method of transversals.] g Universal Biography, Mackenzie, p. 854. [Brahes great quadrant of 14 cubits,about 19 feet, in radius, was built at Augsburg in 1569. See Dreyers TychoBrahe, 1S91, p. 32.] REMARKS ON MINE-SI RVEYING INSTR1 Ml Om Vernier or Two.—The m- double
Transactions . ruments. * Trans., xxix., 1001, 1899. f The system is explained in the book of Nonius entitled De Crepusculis. X Alee Seu Scalce Mathematical, Thomas Digges, London, 1573. [See also Trans.,xxix., 986 and 987, for an illustration and the history of this method of subdivid-ing angles, the so-called diagonal scale, or method of transversals.] g Universal Biography, Mackenzie, p. 854. [Brahes great quadrant of 14 cubits,about 19 feet, in radius, was built at Augsburg in 1569. See Dreyers TychoBrahe, 1S91, p. 32.] REMARKS ON MINE-SI RVEYING INSTR1 Ml Om Vernier or Two.—The m- double vernier described byMessrs, W^ttstock is much leaa satisfactory than two singleverniers placed n opposite Bides of a circle: simply becausetlic latter plan affords the means of taking an average of read-ings from two parts ol the pircle at tin- same time, so as to re-duce the effecl of eccentricity and errors of graduation. Butwith one vernier, although double, as proposed by Messrs. Fig. Cookes Theodolite. Wittstock, such errors, if they exist, must remain without cor-rection. Possibly, however, this objection may be met by thestatement that such refinement is not required for best English mathematical instrument-makers, writersand other scientific men have long since recognized the prin-ciple just noted, and have provided means for the reduction ofsuch errors to a minimum. Generally, therefore, three equi-distant verniers are provided for the horizontal circle of theo- * IVans., xxix., 1003, 1899. 80 REMARKS ON MINE-SURVEYING INSTRUMENTS. dolites from 6 to 8 inches in diameter. As far hack as 1858three verniers were attached to the vertical circle of the minerstransit-theodolite. Fig. 74;* and the same plan has been con-tinued and applied to the horizontal circle of Pig. 75,f also withthe addition of double readings to the vertical semicircles. Leveling-Screws.—With reference to the mode of leveling-upsurveying and spirit-level instruments, Mr. Sta
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