For practice in natural and logarithmic Sines, Tangents, and Secants, Page 58. I. " 9. 2° 40' 10" IO. I 2 18 2. Nat. sine '432651, its common log. is 9.636138, which is the log. sine required. Nat. tang. 3, its common log. is 10'477121, which is the log. tang. required. 3. Log. 9°236713, its corresponding nat. no. is 172470, the nat. cos. required. 4. The given log. tang. 9.850593, being subtracted from 20, gives 10'149407, cotang. the log. 5. The nat. sine of 68° 45′ 24′′ is '932050, the log. of which, or 9°969439, is its log. sine, which, being subtracted from 20, leaves 10'030561 for the log. cosec. 6. The log. sec. 11'024680 subtracted from 20 leaves 8.975320, the log. cosine, the nat. no. corresponding to which, or '094476, is the nat. cosine sought. 7. I. The quantity 9'450981 is found in the tables to be the log. cosine of the aro 73° 35′ 31′′. 2. The nat. no. corresponding to the given log. is 282476, which is the nat. cos. of 73° 35' 31", the arc A sought. 8. I. The square of radius, or 1, divided by the nat. sec. 2·005263, gives '498688, the nat. cosine of A, which is found in the tables of nat. cosines to correspond to 60° 5' 12", the value A. 2. The common log. of the nat. sec. 2.005263 is 0.302171, which is found to be the log. sec. of 60° 5' 12", the arc A sought. NOTE.-A natural sine can be taken out of a table of nat. versines with the most minute accuracy. Or the natural sine of an angle is taken out of the table of versines, by taking out the versine of the angle increased by 90°, and dropping the initial 1. DIFFERENCE OF LATITUDE, Page 79. TRAVERSE SAILING, Page 120. NOTE. In the following key the first line for each question is explained by the titles at the top of the page. The second line contains the courses and distances sailed. The third line contains the D). Lat. and Dep. corresponding to each course and distance; their names are not given because they are easily seen from the course in the second column. NOTE.-In question 3 below, 375'8 N. means 375.8 by NORIE, and 375.6 R.. means 375:6 by RAPER. N84° W 18 N 89° W 30' 4 N 67° W 29'9 N 39° W 33'9N 8° W 25'9 N 73° W 34'9 N 86° W 44 7 8 65° 56' 19 1790''5 304 117 275 253 213 257 3'6 10 2 334 3'1 446 237 50°8 PARALLEL SAILING, Page 125. 4. Dep. 2439 miles; Course S. 84° 52′ 15′′ W.; Dist. 2450 miles. 5. True course N. 61° 53' E., distance 2101 miles. 6. True course N. 80° 2' 30" E., distance 2018 miles. DAY'S WORKS CORRECTED FOR LEEWAY, VARIATION, AND DEVIATION, Pages 149-154 NOTE. In the following key, the first line for each day's work is explained by the titles at the top of the page. The second line contains the True Courses and Distances. The third line contains the Diff. Lat. and Dep. corresponding to each course and distance; their names are not given because these are easily seen from the courses in the second line. |