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2. THE 1934-1936 N(m) COUNT CAMPAIGN

2.1. The observational data from the 1934 campaign

Building on the work of Fath (1914) as analyzed by Seares (1925), work that was based on galaxy counts using 60-inch reflector plates taken for The Mount Wilson Catalogue of Photographic Magnitudes in Selected Areas 1-139 (Seares, Kapteyn, & van Rhijn, 1930, hereafter the Mount Wilson Catalog), Hubble (1926b) used all existing data to show that the "white nebulae" increased in number as log N(m) ~ 0.6m. This is the requirement for a uniform (homogeneous) distribution in depth in Euclidean space, regardless of any form of the distribution of absolute magnitudes (the luminosity function) as long as the integral of that function over luminosities is finite and if there are no effects on the magnitudes with distance (absorption, redshift, etc.). It is also the expected form in the limit of zero redshift, even using the modern (Mattig) equations that correctly describe the distribution (section 4).

The observational data available in 1926 was spotty and not well calibrated in magnitudes. Beginning in 1927, Hubble undertook a major survey with the Mount Wilson 60 and 100-inch telescopes to carry the survey of galaxies at increasing distances by extending the magnitude coverage beyond mpg = 16.7 which was the effective limit of his 1926 study.

Hubble (1934) completed the massive observational program in 1934 in which he counted 44000 galaxies in an area of 650 square degrees on 1283 plates in a systematic sampling in both Galactic hemispheres. The result was a definitive study of the average properties of galaxy distribution, both in depth (for homogeneity) and around a significant fraction of the sky (for isotropy). In this major paper, Hubble (a) confirmed that galaxies continue to increase in numbers to the faintest limits surveyed (the ultimate organizational hierarchy appeared to have been reached), (b) there is a strong latitude effect showing absorption by the Galaxy, (c) the "zone of avoidance" is mapped in greater detail than was possible by Seares (1925), (d) the frequency distribution of the numbers of galaxies per square degree, when the counts on each of the 1283 plates were reduced to standard conditions (for the latitude effect, for different exposure times for the plates, for different seeing, for distance-to-center of each plate due to coma, etc), shows a normal error (Gaussian) distribution in log N, not in N itself (his Fig. 7, 1934).

This last discovery was one of the first indications of the tendency of galaxies to cluster, and was so noted by Hubble. In the 1934 paper he wrote:

[The log normal, rather than a straight N normal distribution is] "the feature [that] serves as a description and a measure of the tendency to cluster. It is clear that the groups and clusters are not superposed on a random (statistically uniform) distribution of isolated nebulae, but that the relation is organic."

While it is not clear what he meant by the last phrase of being organic, it is known (his comment once to me) that he knew that the distribution of the growth of bacteria in petri dishes in the laboratory show a log normal distribution of counts, and that after some time, clusters or colonies describe the mature distribution across the face of the dishes. (See Saslaw 1989; Saslaw and Hamilton 1984; Crane and Saslaw 1986; Coleman and Saslaw 1990; Karasev 1982, for modern discussions of the importance of a log normal rather than a direct normal distribution for the question of clustering).

Important as the 1934 paper was, no reliable apparent magnitudes could be attached to the counts. Indeed, the data were given as log N(E) (Hubble's Fig. 2), where E are the various exposure times of the photographic plates taken in the program.

As a final step, approximate conversion to magnitudes was then made by considering the reciprocity failure "Schwarzschild p exponent" in I ~ Ep for the intensity (I) and exposure time (E). In this way Hubble could assert that the galaxy counts continued to increase approximately as would be required as N(m) ~ 0.6m if galaxies are distributed homogeneously in Euclidean space in the absence of all effects of redshift.

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