116 Transactions of the Royal Canadian Institute 



the Gulf of St. Lawrence and the Atlantic, striking land in Morocco, 

 traversed Africa passing near the Cape of Good Hope, passed within 300 

 miles of the South Pole, entered the Pacific south of Cape Horn, c^me 

 northward in the Pacific striking the American continent at Manzan- 

 illo Bay, Mexico, entered the United States in Texas and passing through 

 the States of Arkansas, Indiana and Ohio returned to Canada and 

 Toronto. 



At two o'clock this afternoon in Toronto, the sun's altitude was 

 22° 34' 15". The circular locus of equal altitude passed through New 

 York then southward in the Atlantic, through the eastern portion of 

 Brazil and on ne^arly to the South Pole. Swinging northward, it passed 

 through New Zealand, the Fiji Islands, westward of Hawaii, struck the 

 continent again near Vancouver and so back to Toronto. Each of 

 these circles contains an infinite number of points, but they intersect 

 each other in but two, Toronto and a point in the southern hemisphere 

 only 300 miles from the South Pole. 



From a single time sight, as it is called, namely, the determination of 

 the altitude of a heavenly body at a known time, the navigator can 

 determine a locus upon which he must be. A second time sight at a 

 second known time determines a second loqus which crosses the first. 

 It is this principle which is largely relied upon by the modern navigator 

 and, with his astonishingly accurate instruments for recording time, he 

 can determine his position with great accuracy providing he can see the 

 heavenly bodies. Unfortunately, as we know, this is not always 

 possible. A recent development of science has enormously facilitated 

 accurate navigation, particularly in the vicinity of land where accuracy 

 of navigation is most important. By means of radio apparatus the 

 direction of a ship from each of two radio stations ashore can be deter- 

 mined, and hence the position of the ship herself. This is being done 

 day by day off our coasts. I am betraying no secrets when I state that 

 one very valuable means used in coping with the German submarines 

 during the late war was the determination of their positions, approx- 

 imately, through receipt of their radio signals at shore stations of the 

 British Isles. 



But to return to the question of the various sciences. Of course 

 mathematics are essential and the science of naval architecture finds use 

 for many of its branches. To instance a simple case, accurate calcula- 

 tions are of the greatest importance in connection with shipbuilding. 

 The displacement of the ship is the capital upon which the naval architect 

 hjas to work and it is necessary that he calculate this displacement with 

 the utmost accuracy. The mathematics of mensuration are neither 



