<527 
NAVIGATION. 
make TH i*oo miles, the diff. of Ion. join H and M; 
then will the angle TMH be the cou. S. 4i°oi' W. and 
OM the dift. 1165 miles. 
By Calculation. 
To find the Courfe, it will be, 
As mer. diff. of lat. 1080, co. ar. 
is to rad. 90 0 - 
So is the diff. of Ion. 1200 - 
6*96658 
IO'OOOOO 
3-07918 
to tang, of cou. 48° 1' - 
10-04576 
To find the Diftance, it will be. 
As cofine cou. 48-1 co. ar. - - 
is to p. diff. lat. 779 - 
So is rad. •.«•*■«*• 
0-17463 
2*89154. 
0*00000 
to the dift. 1165 " - 
3-06617 
Of OBLIQUE SAILING. 
Oblique Sailing is the application of oblique-angled 
plane triangles to the folution of problems at fea. This 
failing will be found particularly ufeful in going along 
ftiore, and in furveying coafts and harbours, &c. 
Ex. At nh. A. M. the Girdle Nefs bore W.N.W, and 
at zh. P. M. it bore N.W.&N. the courfe during the in¬ 
terval S.f>W. five knots an hour. Required the diftance 
of the fhip from the Nefs at each ftation ? 
By Conftru&ion. —Defcribe the circle NESW, fig. 8. 
and draw the diameters NS, EW, at right angles to each 
other : from the centre C, which reprefents the firft Na¬ 
tion, draw the W.N.W. line C F; and from the fame point 
draw C H, S.&W. and equal to 15 miles the diftance failed. 
From H draw HF in a N.W.ftN. direction, and the point 
F will reprefent the Girdle Nefs. Now the diftances CF, 
HN, will meafure 19-1, and 26-5 miles refpedtively. 
By Calculation. —In the triangle FCH are given the 
diftance C H 15 miles, the angle FCH equal to 9 points, 
the interval between the S.6W. and W.N.W points, and 
the angle CHF equal to 4 points, being the fupplement 
of the angle contained between the S.bW. and N.W.6N. 
points; hence CFH is 3 points. To find the diftances 
CF, HF. 
To find the Diftance C F. 
As the fine of C F H 
is to the fine of CIIF 
So is the diftance C H 15 
3 points 
- 4 points - 
miles 
974474 
9-84948 
1-17609 
to the diftance C F « 
<■> 19-07 
1-28083 
To find the Diftance F H. 
As the fine of CFH - 3 points 
is to the fine of FC H - points 
So is the diftance C H - 15 miles 
974474 
9 ' 99 I 57 
1-17609 
to the diftance F H 
26-48 
1*42292 
Of WINDWARD SAILING. 
Windward Sailing is when a fhip, by reafon of a con¬ 
trary wind, is obliged to fail on different tacks in order to 
gain her intended port; and the obje£t of this failing is 
to find the proper courfe and diftance to be run on each 
tack. 
Ex. A fnip is bound to a port 48 miles diredlly to wind¬ 
ward, the wind being S.S.W. which it is intended to 
reach on two boards ; and the fliip can lie within fix points 
of the wind. Required the courfe and diftance on each 
tack ? 
By Conjlrufiion. — Draw the S.S.W. line C B, fig. 9. 
equal to48 miles. Make the angles ACB, ABC, each 
equal to 6 points. Hence the firft courfe will be W. and 
the fecond S.E. alfo the diftance CA, or AB, applied to 
the fcale, will meafure 62g miles, the diftance to be failed 
on each board. 
By Calculation. —From A draw AD perpendicular to 
B C ; then in the triangle ADC are given C D, equal to 
24 miles; and the angle A C D, equal to 6 points : to find 
the diftance AC : 
As radius - - io'ooooo 
is to the fecant of C - 6 points - 10-41716 
So is C D - - 24 miles - - 1-38021 
to C A 
627 
1 ‘7 9 7 3 7 
Of CURRENT-SAILING. 
The computations in the preceding fedlions have been 
performed upon the aflumption that the water has no mo¬ 
tion. This may no doubt anfwer tolerably well in thofe 
places where the ebbings and flowings are regular, as then 
the effeft of the tide will be nearly counter-balanced. But, 
in places where thereis aconftant current or fetting of the 
fea towards the fame point, an allowance for the change 
of the fhip’s place arifing therefrom tmift be made; and 
the method of refolving thefe problems, in which the 
efteft of a current, or heave Of the fea, is taken into con- 
fideration, is called current-failing. 
In a calm, it is evident a Ihip will be carried in the di- 
reflion and with the velocity of the current. Hence, if a 
fhip fails in the direction of the current, her rate will be 
augmented by the rate of the current; but, if failing di- 
reftly againft it, the diftance made good will be equal to 
the difference between the (hip’s rate as given by the log 
and that of the current. And the abfolute motion of 
the fhip will be a-head, if her rate exceeds that of the 
current; but, if lefs, the fhip will make ftern-way. If the 
fhip’s courfe be oblique to the current, the diftance made 
good in a given time will be reprefented by the third fide 
of a triangle, whereof the diftance given by the log, and 
the drift of the current in the fame time, are the other 
fides ; and the true courfe will be the angle contained 
between the meridian and the line actually deferibed by 
the fhip. 
Ex. A fhip failed N.N.E. at the rate of 8 knots an hour, 
during 18 hours, in a current fetting N.W.ftW. z\ miles 
an hour. Required the courfe and diftance made good ? 
By Cotiftruclion. — Draw the N.N.E. line C A, fig. 10. 
equal to 18 X 8 =2 144 miles ; and from A draw AB pa¬ 
rallel to the N.W.iW. rhumb, and equal to 18X24=45 
miles ; now B C being joined will be the diftance, and 
NCB the courfe. The firft of thefe will meafure 159 
miles, and the fecond 6° 23'. 
B 'J Calculation. — In the triangle ACB are given 
AC =144 miles, AB=45 miles, and the angle CABzrj 
points ; to find B A C and B C. 
To find the Courfe made good. 
Dift. AC - 144 Ar 
lg. BAC=q pts.= 
101 0 15' 
Dift. AB - 45 
■- 
B+C 
78 45 
Sum - 189 
B+C 
Diff. - - 99 
——- 
39 22I 
As the fum of the fides 
189 
2-27646 
is to the difference of the fides 
99 
I-qq 163 
So is the tan. of half fum angle; 
5 39 224 
9-91417 
to the tan. of half diff. angles 
23 154 
9-63334. 
Angle ACB 
16 7 
Angle A CN 
22 30 
Courfe made good 
N 6 23 
To find the Diftance. 
As the fine of ACB 
16 0 7' 
9-44341 
is to the fine of C A B - 
101 15 
999157 
So is the diftance A B 
45 
1-65321 
to the diftance C B 
1 59 
2-20137 
Of 
