Based on the observations of M giant stars in the north galactic polar objective-prism survey of Upgren (1960) and the data summarized by Blanco (1965) the overall space density of all M-type giants as a function of distance from the galactic plane at the position of the sun can be approximated by,
where z is in kpc and ρ(z) is the number of stars per 106 pc3. This relationship is derived from the observed fall-off in space densities up to a distance of about 2 kpc.
The question arises as to the validity of extrapolation equation (1) to larger z distances so as to predict the number of faint M giants expected per unit area near the galactic poles. Adopting for the M giants a mean visual absolute magnitude of −1.0 (Blanco 1965), one finds that equation (1) predicts that less than one giant fainter than V~12 should be expected in a region of 200 square degrees. This expectation formed the hypothesis of a thesis study (Sanduleak 1965) in which it was assumed that the very faint M stars detected in a deep, infrared objective-prism survey at the NGP were main-sequence stars, since this could not be ascertained spectroscopically on the very low-dispersion plates used.