METHODS OF PERIODIC ANALYSIS. 



91 



Now, taking analyzing lines aa 1 and bb l in figure 31 as horizontal, and 

 letting the sweep be inclined as a small angle 5 with the analyzing 

 lines, the number of lines required to cross the sweep in the direction 

 ab perpendicular to analyzing lines will be increased and hence the 

 value in years between two analyzing lines will be decreased; hence 



cos 5 = years per line from a to 6. 



If the fringe is perpendicular to the analyzing lines, its period is the 

 distance ab in years and we have for this special case: 



ys ,, 

 p\= cos o. 



i 



FIG. 31. Diagram of theory of differential pattern in periodograph analysis. 



If, however, the fringe takes some other slant, as the direction ac, 

 making the angle 6 with the analyzing lines, then the period desired 

 is the time in years between a and c. That equals the time between 

 a and 6 less the time from b to c. Now be in years would equal ab cot 6 

 except for the fact that the horizontal scale along be is greater than the 



vertical scale along ab in the ratio - ' an d therefore a definite space 



sin o 



interval along it means fewer years in the ratio of !!E_. Hence we have : 



cos d 



be (in years) = ab (in years) tan 5 cot 6 



or 



P = pi(i tan 5 cot 6) 



which is the period required. 



The separation of the fringes needs to be known at times in order to 

 find whether one or more actual cycles are appearing in the period 

 under test. In figure 31 



ab = 



ad = 



sin 5 



s sin (05) 

 ae = 



sin d 



which is the width required. 



