While Rust’s Modified Azimuth Diagram affords a speedy method of surprising accuracy for finding the azimuth, some people prefer to compute the azimuth. Mr. H. H. Brown of Red Bank, New Jersey, suggested to the writer the use of Ogura’s Table B for the logarithmic computation of azimuth. The same formula that is used in the construction of the Rust’s Modified Azimuth Diagram is used for computing the azimuth by Table B.
By this method those who dislike to use any sort of diagram have at hand an accurate logarithmic solution of the azimuth. Incidentally, the use of this formula for determining azimuth increases confidence in Rust’s diagram.
By computing the azimuth by Table B as it stands, the unexcelled altitude tables of Ogura are left intact. Thus with twenty-seven pages of tables both the altitude and the azimuth are accurately determined by one standard method without tedious rules and for all conditions.
Directions
Enter Table B from the top with declination (d) and take out its log secant. Enter Table B from the bottom with the local hour angle (LHA) and take out its log cosecant. Add these two logs and get their sums. Next enter Table B from the top with the computed altitude (Hc) and take out its log secant. Subtract this from the sum just obtained and get the difference. Now with this difference enter Table B from the bottom and take out the azimuth. The azimuth is named like the quadrant in which the body is found, the same as with the diagram.
Example
Enter Table B at top with the declination (d) 10°-05' and take out................... 676
Enter Table B at bottom with LHA (local hour angle) 49° and take out............. 12222
Sum........................................................................................................... 12898
Enter Table B at top with altitude (H0) 23°-37' and take out............................. 3799
Difference...................................................................................................... 9099
Enter Table B at bottom with difference (9099) and take out the azimuth (S4°-12') S54°-12'E
The Reason Why
Sin Z = sec H cos d sin t (see any book on navigation) in which Z is the azimuth, Hc is the computed altitude, d is the declination, and t is the local hour angle.
We can invert the above equation and write:
Cosec Z = sec d cosec t / sec h and of course,
log cosec Z = log sec d + log cosec t – log sec H
Ogura’s table B is simply a table of log secants when read from the top and of log cosecants when read from the bottom.