30 PROCEEDINGS OF THE AMERICAN ACADEMY. 



5000 



h = 



COti\"+ COt>S'" 



The values given in column 8 were read directly from the chart 

 referred to above on page 27. A correction of 9 feet has been added to 

 each value, as the sextant base was higher than the middle of the field 

 by that amount. 



Only four crossings were well observed in the ascent and two in the 

 descending spiral. The second observation, however, though incom- 

 plete, served a purpose, as will appear later. Not only the altitudes, 

 but the projections of the crossing points on the ground line are given 

 by the observations, since the distances of the projection from the north 

 and south stations are h cot N and h cot S respectively, and six points 

 in the spiral are thus fixed, making, with the start and finish, eight 

 points in all thus completely determined. 



Observations at the Distant Base. 



As compared with the eight determinations made by the sextants, 

 twenty-one simultaneous observations were made at the Quincy-Milton 

 base. These are shown in detail in Table II. For purposes of com- 

 parison the results of the sextant observations are inserted, unnum- 

 bered but in chronological order. 



The values of the altitudes in columns 5 and 9 are computed as 

 follows : 



Let h be the height of the aeroplane above the center of the field, 

 C, the length of the base line, 6236 feet, 

 q = 128, and m = 11 feet, the heights of Q and M above the 



center of the field, 

 a and /?, the horizontal angles between the aeroplane and base 



line at Q and M respectively, 

 A and B, the angular altitude of the aeroplane at Q and M 



respectively. 



Then k = Ctan A sin /? cosec (a + f3) + g, 



= Ctan B sin a cosec (a -f /?) -f m. 



All effects due to the curvature of the earth and refraction are neg- 

 lected as being less than the errors of measurement which were expected 

 to occur. The accuracy actually attained would seem, however, to 

 justify the application of such corrections. 



