566 Scientific Proceedings, Royal Dublin Society. 
to AS, (owing to the great distance of the star), and hence the 
angle at the vertex of the triangle ASB will be equal to the angle a 
(the horizontal angular separation of the two stars as seen from 
A). Now, the triangle ASB is isosceles, for BS is equal to AS. 
Hence the angles (b) at its base are equal and evidently 
a+2b=180 or 2b=180-a and b= 90-5. 
The Rule for shaping the course from A is then as follows :— 
With the bearing AS lay off the complement of 5 and sail till S82 
is over S, when make the second observation ; a being the difference of 
the bearings of S, and S, as observed from the place of first observa- 
tion. Of course S,is over S when the angular elevation is the 
least. In fairly calm weather a plumb line may be used to assist 
in placing the ship for the second observation. ‘This is not per- 
fectly accurate owing to the shift of the celestial objects in the 
interval required to run the distance AB. 
For example, suppose S, bears HOS, and S, NHDEZE; the 
5 19° 40’ nearly. The 
complement of this is 70° 20’ or 64 points. The bearing of S, 
being HOS, we lay off 61 points to the south of HDS. The course 
is therefore S2#; and this course is held till S, is over the signal. 
The data now obtained are the altitudes of S, and S, above 
the horizon, the times of observation and the “run” over the dis- 
tance AB, and made in the direction A to B, between the observa- 
tions. ‘This distance will have been measured by log, or, of course, 
it may be computed as the necessary elements of the triangle ASB 
are known. It may be that the run is negligible if the degree 
of accuracy required is not considerable. In the usual manner 
two latitudes are assumed between which or near to which we 
know the ship to be, and using the altitude and polar distance of 
S;, we compute the longitudes corresponding to the assumption that 
the ship is actually in either of these latitudes. Secondly, using 
the altitude and polar distance of S., we again calculate two longi- 
tudes corresponding to the two latitudes. After plotting the results 
one of the “ lines of position ” is shifted for the run (if necessary), 
and the intersection of the two final lines of position gives the 
position of the ship. 
angle a is then 39° 20’ approximately, and 
