areas. This system produces a total of 1,851 charts, illustrated as Figure 1. 
The numbering of these charts begins in the northern polar area and progresses 
to the southern polar area. For convenience, the area above 84° north was 
considered as one chart, a slight deviation from the conventional system. 
Otherwise, each chart covers 4° of latitude with the range of longitudes 
depending upon the latitude. The projection is Mercator between latitudes 
0° and 4°, Lambert conformal between latitudes 4° and 72°, and polar 
stereographic between latitudes 72° and 90°. Each chart containing obser- 
vational data was studied independently, with the results based on those 
data falling within the chart boundaries. 
Data 
The observed variation data used in this study are identical to the 
data used in compiling the recent world chart. These data represent approxi - 
mately 165,000 values measured at land, sea, and airborne locations since 
1900. Airborne values were reduced to sea level and all data extrapolated 
to epoch by applying the appropriate secular change rate. In addition to the 
observed data, the corresponding charted values were computed from the 
mathematical model. Finally, a residual value or difference between each 
charted and observed data point was calculated. The above information was 
then sorted by geographic position into the appropriate World Aeronautical 
Chart. 
ANALY SIS 
Following the preliminary preparation of the data, a FORTRAN 
program was written to perform the analysis. An IBM 7074 computer executed 
all computations and prepared the results in a format suitable for plotting on 
the CalComp Automatic Plotter. The resulting graphics and associated statis- 
tics are presented in Table Il. Definitions and formulae pertinent to the 
analysis are discussed below. 
Histograms 
A histogram was used to depict the frequency distribution of the 
residual values of variation within each World Aeronautical Chart. The 
horizontal axis was divided into thirty-one intervals with the first and last 
interval regarded as "open-ended," i.e., without specific limits. All other 
intervals have fixed boundaries with a range of 0.5°. A mid-point value 
for each interval is indicated and labeled in 0.5° increments with zero 
representing that point where charted and observed data are in perfect 
agreement. Treating the charts independently, each residual value of 
