32 PROCEEDINGS OF THE AMERICAN ACADEMY. 



To find the horizontal distances Dq and D^ from Q and M, we have, 

 with Httle extra work and from the same data of computation, 



i)j = CsinyScosec (a + ft) and D^ = Csinacosec(a + /3), 



and by use of these two distances the points are easily plotted with 

 reference to the base line. It is sufficiently accurate, however, and 

 more convenient, to determine the points graphically by drawing lines 

 at the proper angles with the base by means of a protractor and 

 straight edge, and marking their intersection as the position of the 

 aeroplane. 



The computations were quickly made on mimeographed forms fol- 

 lowing the scheme shown on page 33, which gives the original computa- 

 tions for observations 5 and 6 of Table II, using, of course, the 

 uncorrected data. The discrepancy of these results pointed out at once 

 the faulty observations. 



The general agreement of the values at the two stations seems to 

 show that the height is fixed by each observation with an error of less 

 than five feet ; but observations 5 and 6 at Quincy and Milton, as 

 computed from the recorded data, show differences too large to be 

 ascribed to error of observation. The sextant observation at 6*^ 0™ 49^, 

 although the angle was too great to be measured at the north sextant 

 station (the spiral being far out beyond the course), still shows that 

 the observations at the Quincy station give the correct value, and 

 there seems to be good reason for assuming that the vertical angles 

 were read 1° too large in each case at the Milton station. It appears 

 in the discussion of all the flights that the error most frequently made 

 was in reading the vertical angles. In the whole series of observations 

 but two errors are indicated in the reading of the horizontal angles, 

 one of which will be referred to later. 



Time-Altitude Curves. 



By plotting the successive values of k, given in Table II as abscissas, 

 with the corresponding times as ordinates, we have the curve given 

 below. Figure 2 (right), the slope of which gives the rate of ascent in 

 feet per minute. The points corresponding to transit observations are 

 indicated by circles, the sextant observations by crosses. The rate of 

 ascent is about 100 feet per minute, and the descent nearly ten times 

 as rapid. 



