TABLES OF PHASE 877 



line segment since the Aa; interval has been halved) of comparable order of 

 magnitude to the 8iB error for the original interval selected and therefore 

 small in comparison to the 52^ error for the original Ax interval. This 

 technique was therefore used in checking the adequacy of the intervals in 

 so far as 52^ errors are concerned in the region Xc = .9 to Xc = 1.0. 



Using the procedure outlined above the phase associated with the semi- 

 infinite unit slope of attenuation of Fig. 1 was computed for values of /less 

 than /o and is given as a function of ///o in Table I in degrees and in Table 

 III in radians. For values of/ greater than/o the phase was computed as a 

 function of /o// utilizing the odd symmetry behavior of the phase char- 

 acteristic of Fig. 2 on opposite sides of ///o = 1, and this phase is tabulated 

 in Table II in degrees and in Table IV in radians. For the other type of 

 semi-infinite unit slope of attenuation in which the attenuation slope is 

 constant and equal to unity at all frequencies below /o and the attenuation 

 is constant for all frequencies above /o (with the constant slope of attenua- 

 tion intersecting the /o axis at the same point as the constant attenuation 

 line) the same tables can be used by reading the values of phase for///o < 1 

 from the/o// tables and the values of phase for/o// < 1 from the ///o tables. 



The intervals over which the straight line approximation to the true phase 

 was assumed are given below: 



.02 from .00 to .40 



.01 " .40 " .70 



.005 " .70 " .92 



.002 " .92 " .98 



.001 " .98 " .996 



.0005 " .996 " .998 



.0002 " .998 " .999 



.0001 " .999 " .9998 



.00005 " .9998 " 1.0000 



The points at which the cumulative sum of the straight line increments 

 of phase was corrected to the phase as determined from (1) above are listed 

 below : 



A study of the errors based on the error analysis discussed above indicates 

 that the computed values of B in degrees are accurate to ± .0005 degree and 

 since there is an additional possibility of ± .0005 degree error in dropping 

 all figures beyond the third decimal place, the over-all reliability of the degree 

 tables is d= .001 degree. Similarly the computed values of B in radians are 

 accurate to ± .00001 radian and since there is an additional possibility of 

 ± .000005 radian error in dropping all figures beyond the fifth decimal 



