34 



PROCEEDINGS OF THE AMERICAN AC.\DEMT. 



Representation of the Spiral. 



From the observations of Table II we may plot the ground plan of 

 the spiral described in the ascent, and, with somewhat less certainty, 

 that of the much more rapid descent. Each of the sextant observa- 

 tions, too, fixes a point on the spiral, although taken alone they would 

 give little information as to the actual path of the aviator. 



!e500 



sooo- 



3CJS 



,,000-^ 



o« 



1500 ' 



* \ 



::t^ 



cP' 



c^' 



.oP 



1000 ■ 



500' 



# 



f) 10 



l.J 



20 



30 



6 O 



10 



Figure 2. Time-altitude curves of Grahame- White (left) and of Brookins 

 (right), September 12. 



In Figure 3 are plotted the points as thus determined, each being 

 numbered to correspond with the observation of Table II on which it 

 depends. The points of crossing the base line are determined by the 

 sextant observations of Table I. 



The elevation of the path, as shown in the lower half of the figure, 

 is determined by combining the altitudes from Table I and II with the 

 projections of the observed points of the spiral above. 



It is noteworthy that the spiral serves to give with some accuracy 

 the height at the point of the crossing at 6^ 0™ 49^ where the angle 

 was too great to be measured at the north end of the base. The figure 

 shows that the projection of that point, which is marked by the dot 

 between points 5 and 6 of the spiral, is about 900 feet north of that 

 station, or 5900 feet from the south station, at which the vertical angle 

 was measured as 8° 56'. This gives a height of 940 feet (assuming the 

 elevation of the station as 13 feet), and a little further investigation 

 shows that the angle at the north station was about 134°, and confirm.s 

 the record of the observer that it was not measurable, as the sextant 

 reads only to 128°. The error in position of the projected point is 



