For each candidate source, a series of likelihood test statistic maps were constructed for the observation (single or summed) which produced the highest 
. It was assumed that the highest signal gives the most likely position of the source. These maps used energy ranges E > 100 MeV, 100 MeV < E < 300 MeV, 300 MeV < E < 1000 MeV, and E > 1000 MeV. Because the EGRET point spread function is narrower at higher energies, the upper energy ranges can give better source position information, but only if adequate statistics are available at those energies. The likelihood test statistic maps for independent energy ranges were also added to improve the signal. Comparing the summed map with the maps from the individual energy ranges, the one which produced the smallest error box was chosen to represent the source position, as long as 
was greater than 4, a level chosen to reflect a reasonable degree of confidence in the detection.
Within each test statistic map, the source position can be determined in a variety of ways. The location with the highest value of 
is the single most probable position for the source. In many cases, however, a range of locations with nearly the same level of confidence can be found. Often the highest test statistic is not at the center of this region. Because the EGRET point spread function is relatively broad, the exact position of a source is rarely defined to the arcmin level. We have chosen, therefore, to present the ``best'' position as the centroid of the region enclosed by the 95% confidence contour, i.e. the statistical confidence is greater than 95% of including the true source position.
Confidence levels calculated by the likelihood mapping reflect only the statistical uncertainty in the position of a single source. Systematic uncertainties can also affect the position determination:
1. The model of the diffuse radiation is assumed to be an accurate representation of the background against which a source is seen. The model is unlikely, however, to be perfectly accurate on all size scales and for all directions in the sky.
2. The presence of nearby sources can change the apparent position of a source. EGRET cannot easily resolve sources within 1
of each other, and sources even 5
away have substantial overlap of their point spread functions at all but the highest energies. Sources in the catalog close to other sources must be considered to have larger positional uncertainties than the statistics alone would indicate. In some cases an excess at a statistical significance level below what would be included in the catalog is seen near a catalog source. Including this excess changes the position of the source, particularly for sources near the catalog threshold. We have included such excesses at a 
level between 4 and 5 near the galactic plane and between 3.5 and 4 at higher galactic latitudes. Sources whose positions are influenced by such excesses are noted in the catalog as possibly source-confused.
Figure 2 shows sample maps of locations of four bright sources. It should be emphasized that these figures are likelihood test statistic contours, not intensity contours. In each case, the contours indicate the 50%, 68%, 95% and 99% statistical probability that a source lies within that contour ([Mattox et al. 1995a]). Because most of the sources lie along the galactic plane or at galactic latitudes less than 45
, the error contours are shown in galactic coordinates. The scales of the figures also vary; brighter sources have smaller error contours. Also shown in some figures are COS-B gamma-ray source positions (whose error boxes are typically 0.5 - 1.0
in diameter) and some other objects which might be associated with the gamma-ray source. The only firm identifications are those pulsars which show gamma-ray pulsations and those radio-bright, flat-spectrum active galactic nuclei (often blazars) which have been identified with EGRET sources (Montigny, et al., 1995).
The 95% contour has been chosen as representative of the EGRET statistical source uncertainties. For all the sources, an elliptical fit to the 95% contour was constructed. This fit is a reasonable approximation to the contour in most cases. The elliptical semimajor axes range in size from 2 arcmin to more than 1
. Four cases in which the elliptical fit was not acceptable are shown in Fig. 3. The complete set of source location figures is available on-line (see note at the end of this article) and in the AAS CD-ROM version of this paper.
As noted above, systematic uncertainties make these contours somewhat optimistic estimates of the EGRET source location capability. We have devised no quantitative way to depict the effect of these systematics on the error contours. Table 2 summarizes some relevant information about sources along the galactic plane whose positions are definitely known: the pulsars and the bright solar flare of June 11, 1991. The table shows the offset of the measured position from the true position and where the true position falls with respect to the confidence contours. The true positions tend to lie in the outer regions of the error contours, with the Vela position outside the 99% contour (although as the brightest source, Vela has the smallest contours). The effect of nearby sources is reflected in the solar flare measurement, since it occurred when the Crab pulsar was only 4.6
distant from the sun. These results indicate that the systematics do not pose a major problem for the source location capability even in these regions of significant diffuse emission or strong nearby sources. The error contours for many of the Active Galactic Nuclei show that the location capability improves for regions away from the galactic plane. Table 3 shows offsets from the true positions for a number of the AGN identified in the EGRET data.