Crossing one anothers Track. 287 | 
cedure which creates disasters, and then triumphantly ascribes 
them to a wrong cause. No wonder, then, if the number of 
_ disasters is diminished by three-fourths, when the weather 
is so thick and foggy as to prevent the natural courses of the 
ships being meddled with. . And now we come to speak of 
the discovery itself, and to illustrate it with a diagram 
which we conceive will satisfactorily establish all that has 
been written on the subject, both in the treatise and in this 
paper. 
The writer discovered that a grand yet sublimely simple 
mathematical principle, easily distinguishable, always 
developes itself in every casein which the danger of collision 
is involved in the courses of two approaching ships, and 
that the principle never can be developed unless that danger 
exists, so that being once known, it can never mislead, and 
the principle itself may be thus stated : 
“Whenever the danger of collision pervades the courses of 
“two approaching ships, each vessel maintains unalterably 
“one line of direction, or ‘ bearing,’ from the other through- 
“out the progress of the ships towards the point of contact,” 
so that if the light of an approaching ship in the night 
time is seen, after a moderate interval of time, to continue 
on the same “ bearing” as was first observed, as in the case 
of the “Penola” and “City of Launceston,” it is a certain 
indieation that the danger of collision is involved in the 
courses of the ships; butif the second observation shows the 
approaching ship to be upon a smaller angle with the course 
than that which was at first observed, it indicates that she 
will pass “ahead; but if upon a larger angle, that she 
will pass “astern ;” any alteration therefore in the angle or 
“bearing” is a sign of safety ; but a continuance of the same 
angle, whether it be two, three, four or five points on the 
bow, is an infallible token of danger, as the accompanying 
illustrative diagram clearly proves :— 
ILLUSTRATIVE DIAGRAM BY C. J. PERRY. 
To prove that whenever the danger of Collision pervades 
the courses of two approaching ships, each vessel maintains 
unalterably one line of direction, or bearing from the other 
throughout every stage of their progress towards the point 
of contact. 
Let A represent a ship when she sights the lights of three other vessels in 
various directions, and at different distances, as at the positions C, D, P, the 
thin lines shewing their bearings from A. And let it be assumed that all the 
