June 19, 1914] 



SCIENCE 



913 



■works dealing with the problems of navigation 

 and member of various learned societies, has 

 devoted part of his time since his retirement 

 to producing tables from which a " line of 

 position" (Sumner line) can be worked and 

 the ship's position thereon approximately 

 •determined with the least labor and in shortest 

 time. 



The tables are preceded by a condensed ex- 

 planation for the benefit of those who wish to 

 understand their mathematical development; 

 but the many practical and efficient navigators 

 who bother little with theory will be inter- 

 ested to know what Captain Guyou does, with- 

 out having to concern themselves as to how he 

 does it. 



Gird up your imagination and conceive the 

 world and the heavenly bodies as standing 

 still; suppose, further, that your ship is con- 

 nected with a heavenly body not directly over- 

 head—the sun, for instance — by a steel rod 

 having a universal bearing where attached to 

 the ship and another where attached to the 

 sun. Start up your engine and let the wheel 

 alone! The ship will be so controlled by the 

 rod that she must describe an enormous circle 

 on the face of the waters, having for its 

 center that point on the earth's surface at 

 which the sun is then in the zenith. Mean- 

 while, the rod describes an enormous cone 

 with the sun at the apex, and when we con- 

 sider that the sun's altitude, or height, is 

 measured by the angle enclosed between the 

 rod and the base of the cone (roughly), we can 

 realize that an observer on board, taking the 

 sun's height with a sextant at frequent inter- 

 vals, will get the same height all the way 

 around the circle. 



The foregoing must be qualified in practise 

 because the world does not stand still and the 

 ship is not going to sail on a circular course; 

 true, she is on the circumference at the mo- 

 ment of observation, but she may be crossing 

 it at any angle because the position of the 

 center of the circle and the direction in which 

 the circumference trends depend upon the sun 

 and not upon the ship. 



If the ship be at rest, the observed altitude 

 of the sun will change continually from hour 



to hour because of the apparent motion of 

 the sun in his diurnal course. If the ship be 

 in motion, the observed altitude of the sun 

 will likewise change from hour to hour not 

 only because of the sun's apparent diurnal 

 motion, but also, although by a comparatively 

 small amount, because of the fact that the ship 

 is under way pursuing a certain course and 

 making a certain rate of speed. It is evident 

 that she, may be considered to be crossing a 

 circumference at any moment and that all suji 

 observations taken at that moment from ships 

 on different parts of that circumference will 

 show the same altitude. 



Two problems present themselves ! 



Pirst: To find the circumference. 



Second : To find the point at which the ship 

 was crossing it when the observation was 

 taken. 



They have been dealt with in various ways. 

 An able French admiral, Marcq de Saint- 

 Hilaire, evolved an admirable solution by 

 working out the distance from the dead- 

 reckoning point — almost always more or less 

 erroneous — to the circumference; his method 

 may be outlined as follows: the navigator 

 measures the height with a sextant, notes the 

 time, then calculates the height he would have 

 gotten at the dead-reckoning point at the 

 moment of observation. If the two heights 

 agree the dead reckoning may be accepted as 

 correct, for it coincides with the circumfer- 

 ence; this occurs but rarely; as a usual thing 

 the dead-reckoning point falls several minutes 

 (of distance) outside the circle or within it, 

 two heights result, and the difference between 

 them enables the navigator to work out the 

 error in distance from dead reckoning to cir- 

 cumference. This solves the first problem! 



The solution of the second is simpler be- 

 cause the dead reckoning is sufficiently reli- 

 able to limit to a few sea-miles that portion of 

 the circumference at some point in which the 

 observation must have been taken. Since the 

 circle is very large this small portion of cir- 

 cumference may be accepted as a straight line. 

 It is the navigator's " Line of Position " and 

 the ship's crossing point thereon is closely 

 approximated by the direction of the center 



