69 



queiitly, a direct line which cuts one meridian at any angle cannot cut 

 any other meridian at the same angle. Now, supposing that either of 

 the audience and myself were at equal distance from the North Pole, 

 the pole between us, and in sight of each other, we should then be 

 both north of each other, because each would be situated in the direc- 

 tion in which the North Pole was situated. Thus it must be when 

 the principles of great circle sailing are admitted ; but, according to 

 Mercator's principles, we should be east and west of each other, being 

 both on the same parallel, which on the chart is represented as a 

 straight line, running east and west. Then, we find that the great 

 circle course is the direction we see any object — the course the crow 

 flies; it is the real direction of the object, if in sight ; it is the direction 

 iu which is situate the base of a mountain, when we discern its summit 

 in that position. It is also the position of any place at which a 

 heavenly body is vertical, at the time in which that heavenly body is 

 seen from any other place. For instance, the island of St. Salvador, 

 or Cat Island, has, at a certain hour of the sidereal day, a star, called 

 Alpha Aiietis, nearly vertical, or overhead. Liverpool has also another 

 star, called Beta Draconis, nearly vertical, at a certain time of each 

 sidereal day. Now the position in which we, at these times, see 

 these stars is the real position of the place over which it is vertical at 

 the time. If, then, we sail from Liverpool for St. Salvador, we should 

 see Alpha Arietis bearing west; as we proceeded on our voyage, its 

 position with regard to the ship's place would veer round to the south, 

 till at length we reached our port at last by a course S.W. by S. 

 During the whole of this voyage, we should see the vertical star of St. 

 Salvador right before us ; and the vertical star of Liverpool right 

 astern ; and in returning, by great circle sailing, we should observe the 

 vertical star of Liverpool right a-head, and the vertical star of St. 

 Salvador right astern ; so that it is evident that though we were obliged, 

 in adopting great circle sailing, to alter continually our course by 

 compass, still we sailed directly from one port to the other. Not so, 

 however, if we adopted Mercator's sailing. We should then start from 

 Liverpool, with the position of the vertical star of St. Salvador to the 

 right 28°. The difference between the position of our port and our 

 course would daily decrease, until we arrived at our destination. Thus, 

 again, we find that, by Mercator's sailing, we sail one course by 

 compass throughout the voyage ; but, by great circle sailing, we 

 constantly vaiy our course ; still it is by great circle sailing we steer 

 directly to our port, while by Mercator's sailing we arrive at our 

 destination bv a circuitous )'outo. 



