Plane trigonometry with practical applications, by Leonard E. Dickson.

70

TRIGONOMETRY

[Art. 49

We now apply formula (1) of Parallel Sailing to find diff. long., given
dep. = 167.8 and L = 40~25.6'. Dividing by 3 to get numbers directly within
Table VI, we have dep. = 55.9. From 55.9 = d cos 40~, Table VI gives diff.
long. d = 73. From 55.9 = d cos 41~, d = 74.1. Adding
25.6/60 X 1.1 = 0.5
to the former, we get 73.5. Its product by 3 gives diff. long. = 220.5 miles, or
3~ 40.5' E. This must be subtracted from the given longitude. Hence long.
in = 55011' W.
EXAMPLE 2. A ship in lat. 49~57' N, long. 15~16' W, is bound for a port in
lat. 47018' N, long. 20010' W. Find the course and distance to be sailed.
Solution. diff. lat. = 2039' S = 159 miles,
diff. long. = 4~54' W = 294 miles,
mid. lat. = 49057' - (2039') = 48~37.5' N = L,
dep. = 294 cos L.
Taking L to be 48~ and 49~ in turn, we obtain by Table VI the departures
196.7 and 192.9 respectively. By interpolation, dep. = 194.3. Dividing the
numbers by 3, we have diff. lat. = 53, dep. = 64.8. The course is thus
> 45~. By mental interpolations on lat. in Table VI, we get
C lat. dep. dist.
50~ 53 63.2 82.5
510 53 65.5 84.2
Hence, by interpolation-on dep., C = S 50042'W, dist. = 83.7 X 3 = 251.1
EXERCISES ON MIDDLE LATITUDE SAILING
Find the quantities indicated by question marks.
Ex. Lat. out Lat. in Long. out Long. in True course Dist.
1. 25035' N 27028' N 60~ W 54055' W??
2. 32030' N 34010' N 25024' W 29~ 8'W??
3. 46024' S? 178028' E? S 53026' E 278
4. 20029' N? 179010' W? 2530 333
5. 41038' N 41026' N 59016' W? 101015?
6. 4r19' N 41011' N 57047' W?? 167
7. 46028' N 45~17' N 22018' W 19039'W??
8. 36052'N? 75051' W? N66 E 175
9. 36052' N 38042.2' N 75051' W 71051.6' W??