I have recently been handed a small book entitled “Sumner’s Method for Finding a Ship’s Position,” by Rev. G. M. Searle, Director of the Observatory, Catholic University, and formerly a Professor in the Department of Mathematics at the U. S. Naval Academy. The book is published by D. Van Nostrand Co., New York (price fifty cents). It provides a means of computing the intersection of two Sumner’s lines without solving for each line separately—a method that I have not before seen used and which seems to me to be more simple than any other method of computing intersections with which I am familiar. I believe that navigators who desire to get a fix from two observations with a run between will find this method to be advantageous, and this article is submitted with a view to calling their attention to it.
The author gives first a practical method of working the sights out and follows with a deduction of the formulae involved. I will not endeavor to do more than explain the practical side of the work. The fix may be determined either at the time of the first sight or at the time of the second sight. Inasmuch as the position at the second sight is the one usually desired, the author has developed a form with that in view. The altitude of the first sight is corrected in such a way that it has the value it would have had had the first observation been made at the same time but at the second place, but with the sun’s declination as it was at the other place. The theory involved is rather complicated, but the practical working results are comparatively simple.
The nomenclature and form given by the author differ from the nomenclature and form ordinarily used by officers of the navy. I have therefore changed both to make the method more easily understood.