380 BELL SYSTEM TECHNICAL JOURNAL 



In Table I the virtual heights are deduced from the curves for the 

 assumed hop orders. The calculated relative delay is the delay differ- 

 ence corresponding to these heights. All angles below 60 degrees were 

 considered and all combinations of hop orders were considered for each 

 angle, subject to the experimental knowledge of the sense of the delay. 

 The values shown in the table are the ones which give the best agree- 

 ment with the measured delay. In most instances there was no 

 question concerning the interpretation; in a few doubtful cases two 

 possibilities are presented (December 27 and January 22). 



Examination of the table shows that except near noon, the propaga- 

 tion comprises the first and second reflections from the F region of the 

 ionosphere. Groups A, C, E and G illustrate this. In the majority of 

 instances the agreement is excellent; these cases constitute strong 

 evidence that the MUSA performs correctly. 



The discrepancies in the table between layer heights for the first and 

 second hops and between measured and calculated delay are not 

 entirely experimental error. Assuming errors in measured angles suffi- 

 cient to make the delays agree will, in some cases, increase the dis- 

 crepancy in heights. An interpretation one might make of this is that 

 the ionosphere is not uniform over the circuit and the regular reflection 

 basis of calculating is not strictly in accord with facts. However, there 

 are other theoretical explanations for discrepancies in height. Under 

 usual conditions, the second reflection height should be slightly greater 

 than the first but for certain ionizations in the E region, the first F 

 reflection may be retarded more than the second F reflection in passing 

 through the E region. Thus the heights may differ in either direction 

 without demanding horizontal non-uniformity. The discrepancies be- 

 tween measured and calculated delay may be explained by horizontal 

 non-uniformity in the ionosphere. For an essentially non-dissipative 

 atmosphere of ions having any vertical distribution but no horizontal 

 gradient, and neglecting the earth's magnetic field, the group delay is 

 identical with that calculated from triangular paths coinciding with 

 the initial earth angles. Breit and Tuve showed this in their 1926 

 paper. With horizontal variations in the ionosphere such as tilting 

 layers, no kind of agreement could be expected; the waves might even 

 travel via other than great circle routes. 



During three days of our observations W. M. Goodall made measure- 

 ments of virtual height and of critical frequency which enabled him to 

 predict the results we might be expected to observe. His estimates 

 are shown in the next to the last column of the table. 



The data for December 27 (B) are interesting in that after 11 o'clock 

 the first F reflection apparently disappeared. Instead, a first reflection 



