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Figure IX.E.1 Plot of log (number) versus
log fv for sources
seen with the spectrometer. The number plotted in the ordinate
is the integrated number of sources with flux densities less than
the designated flux density. The flux densities plotted in the
absissca have been obtained from the main point source catalog.
The bottom three curves correspond to individual spectral classes
defined in Section IX.D.
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No sharp flux density limit can be specified above which completeness is strongly guaranteed, because of the stringent rejection criteria (see Section IX.C.3). In general, completeness is much better at high than at low galactic latitudes since most of its selection criteria were meant to discriminate against confused sources. Figure IX.E.1 shows plots of log (number) versus log (fv) where fv, is the flux density at 12 µm. The three most populated main classes have been plotted as well as the total sample. The total number follows a power law with a slope of ~ -1.3, while for sources with flux densities between 15 and 100 Jy the slope of the power law is closer to -1.0. These slopes are consistent with a population of galactic sources. The catalog is obviously incomplete below ~15 Jy. The variation of slope with fv, is rather large for classes 4 and 2, while the slope of the class 1 curve is steeper than any of the others and much more constant. These differences can be understood if the spectral features characterizing classes 2 to 4 become unrecognizable to the classification program for fainter sources. Consequently, the fainter class 2-4 sources tend to migrate into class 1 at lower flux densities, thus causing an over-population of class 1 and an under-population of classes 2-4.
The general shape of the spectra is largely determined by
the wavelength- dependent responsivity correction, the deviation
of which has been discussed in Section IX.B.2. If a considerable
error were made in assuming that the infrared spectrum of 
Tau
was consistent with that of a 10000 K black body, this would show
up as a systematic variation of the ratio of integrated spectral
flux over 12 µm survey flux with spectral index. Some individual
spectra observed from the ground have been compared with the IRAS
spectra. The comparison showed satisfactory results.
A word of caution is due with respect to line spectra. Relative line strength observed in different spectrum-halves (8-13 and 11-22 µm) of spectra with little 01 no continuum, may not be reliably calibrated. This uncertainty is because of the uncertainty in the cross-scan dependent responsivity correction (see Sections IX.B.3 and C.2.e). Without the presence of a continuum in the overlap region of the two spectrum-halves, joining the spectrum-halves is uncertain and has generally not been done. Each spectrum-half may therefore have an uncertainty of up to 20%.