PREFACE TO THE FIRST EDITION. THE SOURCES from which the following Exercises have been taken are sufficiently indicated by the Table of Contents. This collection differs, in two respects, from any with which the author is acquainted; in the first place, the questions are arranged in such a manner that most of the papers embrace various subjects; secondly, "book-work' is introduced, in order to assimilate the papers to those set at Examinations. WOOLWICH COMMON: August 1864. PREFACE TO THE SECOND EDITION. THIS EDITION contains about 900 additional Examples, selected from Examination Papers which have been set since the publication of the first Edition. The greater part of the new matter will be found in the Appendix; but the fresh questions in Mixed Mathematics commence at Considerable pains having been taken in correcting errors, it is hoped that they now amount to a comparatively small number. page 287. WOOLWICH COMMON: January 1867. CONTENTS. PAGE 1 2 4 . . Tables of Weights and Measures . Numbers of frequent occurrence, Squares, Cubes, etc. Formulæ in Spherical Trigonometry Formulæ in Co-ordinate Geometry Formulæ in Differential Calculus Civil Service Papers (ARITHMETIC) 191 193 194 198 . 201 208 211 219 MATHEMATICAL EXERCISES. TABLES, FORMULÆ, ETC. TABLES OF WEIGHTS AND MEASURES. LINEAL MEASURE. 12 inches (in.) - 1 foot (ft.) 3 ft. =l yard (yd.) 2 yds. or 6 ft. =l fathom. 53 yds. or 162 ft. =) pole (po.) 40 po. or 220 yds. =1 furlong (fur.) 8 fur. or 1760 yds. = 1 mile (mi.) 3 mi. =1 league (lea.) 697 mi. =1 degree (1°). I chain=22 yds.=66 ft. = 100 links. 1 hand -4 inches. 1 line =of an inch. SUPERFICIAL MEASURE. 144 square inches=1 square foot CLOTH MEASURE. 24 in. =l nail (n.) 4 n. =l quarter (qr. ) 4 qrs. =1 yd. 3 qrs. 1 Flemish ell. =1 English ell. o grs. = 1 French ell. (sq. ft.) 9 sq. ft. =1 square yard (sq. yd.) 302 sq. yds. =1 sq. pole (sq. po.) 40 sq. po. =1 rood (ro.) 4 roods, or 4840 sq yds. =) acre (ac.) 5 qrs. B d S do. T = •7853986; log -=1.8950899; :·5235988; log 1.7189986 4 4 6 Unit of Circular Measure 570.2957795; log 57.2957795=107581226. Do. = 206264:"8; log 206264.8= 5•3144251. : •43429448 ; log10 M=1:6377843. e=base of Napierian system of logarithms=2.718281828; log100 =°4342945. g=force of gravity = 32.19084 ft.; log g=l•5077323 ; 1 log =2.4922677. 9 M10 |
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