N. W. Point of the Lake of the Woods. 41 



AiRT. V. — The Report of J, L. Tiarks, Astronomer on the 

 part of his Britannic Majesty under the sixth and seventh 

 Articles of the Treaty of Ghent : on his Astronomical Ob- 

 servations for ascertaining the most northivestern point of 

 the Lake of the Woods. 



(Communicated by Prof. Renwick, for insertion in this Journal.) 



In order to explain the operations by which I have endea- 

 voured to ascertain the most northwestern point of the Lake 

 of the Woods, it will be necessary that I should give a defi- 

 nition of the term " most northwestern," and explain the 

 property, which a point of a lake must possess, in order to 

 entitle it to the appellation the " most northwestern," In so 

 doing, I hope I shall not overstep the province of the astron- 

 omer, who is supposed to be qualified to give definitions of 

 terms connected with his science. If there should be a dif- 

 ference of opinion on the meaning of the words " most north- 

 western," I shall humbly offer that definition which appears 

 to me to be the true one, with due deference to the judg- 

 ment of the Honorable Board of Commissioners, in order to 

 render intelligible the operations which I have performed, 

 and the conclusions at which I have arrived, on this subject. 



The most northwestern point of a Lake appears to me to 

 be the point which has the following property, viz : that if a 

 loxodromic fine be drawn from it, intersecting every meridi- 

 an in the direction from southwest to northeast, at an angle 

 of forty-five, and such loxodromic line be continued, both 

 ways if necessary, to its intersection with the meridian of the 

 extreme eastern and western points of the lake, this line shall 

 touch no other water of the lake. It is well known, that on 

 Mercator's projection, all loxodromic fines become straight 

 lines, and the solution of the problem conformably to the 

 definition here given, becomes, therefore, more simple by 

 projecting the lake, the most northwestern point of which is 

 to be ascertained, in this manner, on a plain surface. On 

 such a projection, that point of the lake from which a north- 

 east and southwest course can be drawn, without touching' 

 or intersecting any other point of the lake^ is the most north- 

 western one ; and in order to ascertain which of two given 

 pomts is the more northwest, it will be sufficient to connect 



Vol. XV,— No»l. 6 



