It seemed rather odd, however, that the variances should be significantly 
different. Further inspection of the paper led me to believe that the samples 
treated at 65 per cent relative humidity were in fact rectangles 8 inches X 9j, 
inches. Those treated at 50 per cent level were strips 2 inches X 10 inches cut 
lengthwise and crosswise of the films. The differential shrinkage is obtained in the 
first case from the difference of two measurements made on the same piece of 
film; while, in the other case, it was calculated from measurements made on two 
different pieces. The sizes of the pieces used are different in the two cases, as I 
have just pointed out. It is conceivable that these differences account for the 
difference between the variances of the measurements; and that they may also 
affect the general conclusion as regards the significance of the superiority of 
treatment at the higher level of humidity. 
2.22. The next two examples demonstrate a source of error in the more complex 
experiments where the variates which we propose to investigate are not themselves 
observed quantities, but deduced therefrom by analytical or other treatments. In 
such cases it is clearly necessary to examine very carefully the treatment process 
to avoid misinterpretation of the results. 
2.221. The first example illustrates a simple type of error of analysis. The 
experiment (3) was concerned with the estimation of the accuracy of the deter- 
mination of the altitude profile by a certain type of altimeter. The height of the 
air camera was determined by photogrammetric methods, and compared with the 
recordings of the altimeter, at five exposures in each of six short strips. The results 
are reproduced in Table 2 where E is the error in absolute height in metres, and 
V is the ‘variation from true profile in metres’. 
  
  
  
  
Table 2 
Strip 1 | Strip 2 Strip 3 | Strip 4 Strip 5 
Photo | (30000 feet) | (22000 feet) | (20000 feet) | (16000 feet) | (16000 feet) 
Nr En ET IIT TT. | TT E 
E vd. vd = VIE VIE V 
1 —20 0| —14 14. +27 3 | +35 1. 4-30 10 
2 —22 2 + 2 2.1 23 1) +30 6; +18 2 
3 —26 6 0 0 à 1-22 2 | 4-29 7-9 11 
4 —26 6 de 3 3 ; : +44 8.1. +26 6 
5 — 6 14 | +11 11 | +25 1 | +40 4: |. 7-19 ] 
  
  
  
  
  
The point is that the quantity V in which the conclusions were founded had 
been obtained in a peculiar way which does not correspond to the altitude profile 
defined in the paper as ‘the difference in height from one exposure to the next’. 
It appears from the Table that a different quantity was subtracted from each 
E column so as to make the respective V quantities small. A correct assessment 
was obtained elsewhere (4) as follows: Let H,, H.,..., H, be the sequence of true 
heights. The true profile is therefore the sequence of numbers AH, r1 7 H—H, a, 
r7 2,... 4,7. Let H' and 4 H' be the values of the same quantities as determined 
by the altimeter. The variation from the true profile is therefore 
AH'—AH = Hypo Hr - (Hr — Hr) = H,— H, — GT, 3 — H1), 
12