METHODS OF PERIODIC ANALYSIS. 91 
Now, taking analyzing lines aa’ and bb in figure 31 as horizontal, and 
letting the sweep be inclined as a small angle 6 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 6=years per line from a to b. 
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 6. 
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Fie. 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 @ with the analyzing lines, then the period desired 
is the time in years between a and c. That equals the time between 
aand b less the time from b to c. Now bc in years would equal ab cot @ 
except for the fact that the horizontal scale along bc is greater than the 
‘ a - cos 6 
vertical scale along ab in the ratio ae and therefore a definite space 
interval along it means fewer years in the ratio of me Hence we have: 
be (in years) =ab (in years) tan 6 cot 6 
or 
P=p,(1—tan 6 cot @) 
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 
a iss ps at sin (0—6) 
sin 6 sin 6 
which is the width required. 
