26 Prof. J. Joly on Scientific 



a knot. This is the danger rate of approach ; and is the 

 same as 24 knots per hour as given above. 



We have incidentally found also the danger bearing. The 

 arm c in fact points from A to B ; that is, it' we moved it 

 parallel to itself til! it crossed the centre of the divided com- 

 pass circle, then it would read the bearings required. It is 

 easy to arrange for the attachment of a parallel motion to c, 

 which can be moved so as to cross the centre of the divided 

 circle and read the bearings. In the example chosen, for 

 instance, it shows that B bears NNE. from A, and A 

 SSW. from B if collision is threatened. We here use the 

 instrument as a means of constructing a triangle of displace- 

 ments rather than of velocities : which is obviously legitimate. 

 Thus the navigator by merely setting the limbs on this 

 instrument to the courses, and setting the arm c to the 

 speeds, obtains the danger rate of approach and the clanger 

 bearing. 



It may be helpful to some to consider a quite simple case. 

 Suppose the courses of the ships are directed exactly oppo- 

 site. Suppose X is going due south and Y is going due 

 north. Let the speeds be 20 and 10 knots respectively. 



Now the fact of the courses being opposed does not involve 

 collision. The bearing of X from Y or of Y from X may be 

 anything at all so far as courses are concerned. For instance, 

 the ships might be passing abeam of one another. But there 

 is one particular bearing of X from Y and one of Y from 

 X which denotes collision: — whenX bears north from Y and 

 Y bears south from X. The ships are then approaching end 

 on and collision is threatened. These are in this case the 

 danger bearings of ship from ship. 



Again, the rate of approach of X and Y may be anything 

 at all, within certain limits, so far as courses and speeds are 

 concerned. Thus the distance between the vessels would be 

 shortening quite slowly supposing Y bore somewhere for- 

 ward of the beam of X ; or, it might be, actually increasing 

 if Y bore aft of the beam of X. It is evident that only when 

 the vessels are approaching end on is the distance decreasing 

 at the maximum rate : that is, the relative velocity is a 

 maximum ; and it must amount to 20 + 10 = 30 knots. This 

 is the danger rate of approach, and it is evidently associated 

 with collision. If observations of distance are taken every 

 two minutes this rate would involve the distance between 

 the vessels diminishing at each observation by one knot. 



We see then that there is a danger bearing and a danger 

 rate of approach peculiar to collision. The Collision Pre- 

 dictor applied to the above case would give the danger 



