THE work of Humason, Mayall and Sandage1 and the more recent work of Sandage2–5 and Peterson6 show that the dispersion in the absolute magnitude of the first brightest galaxies in rich clusters of galaxies is only 0.3 magnitude. Peebles7 suggested that this small dispersion is simply the consequence of the cluster luminosity function and compared the distribution predicted by the statistical theory with the observations of Humason, Mayall and Sandage1. I have shown8 how the distributions predicted by the statistical theory vary with the richness of the cluster of galaxies and has compared the predicted distributions with the observations of Humason, Mayall and Sandage1, and with his own observations6. But Peach9 considered that the statistical theory is inadequate when he compared the distributions calculated from the statistical theory with new data of Sandage.