4713 | 12.3 | .38 4781 | 11.8 | .48 4793 | 12.4 | .20 4808 | 12.6 | +0.34 4995 | 11.8 | +0.36 5005* | 11.1 | .70 5012 | 11.9 | .43 5033* | 11.8 | 0.78 5194* | 7.4 | 1.08 5204 | 12.8 | 0.59 5236 | 10.4 | 1.00 5247 | 13.3 | 0.70 5248 | 11.5 | .50 5290 | 12.5 | .48 5297 | 12.6 | .60 5364 | 13.3 | .60 5395 | 12.8 | 0.30 5457 | 9.9 | 1.34 5474 | 12.0 | 0.60 5585 | 12.3 | .60 5676 | 11.8 | .48 5678 | 11.8 | .41 5832 | 13.1 | 0.56 5907§ | 11.9 | 1.04 6181 | 12.5 | 0.30 6217 | 12.1 | .25 6503 | 9.9 | .70 7448 | 11.8 | + .30 7671 | 13.3 | – .15 +-----------+--------- Mean | 11.75 | +0.537 ----------+-----------+--------- Peculiar Spirals (Unclassified) ----------+-----------+--------- 972 | 13.3 | +0.17 2537 | 13.3 | .0 4900 | 11.8 | +0.23 ----------+-----------+--------- RELATION BETWEEN LUMINOSITIES AND DIAMETERS Among the nebulae of each separate type are found linear correlations between total magnitudes and logarithms of diameters. These are shown in Figures 2–5 for the beginning, middle, and end of the sequence of types and also for the irregular nebulae. In Figures 2 and 3 adjacent types have been grouped in order to increase the material, and in Figure 5 the Magellanic Clouds have been added to increase the range. The correlations can be expressed in the form $m_{T} = C - K \log d,$ (1) where K is constant from type to type, but C varies progressively throughout the sequence. The value of K cannot be accurately determined from the scattered data for any particular type, but, within the limits of uncertainty, it approximates the round number 5.0, the value which is represented by the lines in Figures 2–5. When K is known, the value of C can be computed from the mean magnitude and the logarithm of the diameter for each type. This amounts to reading from the curves the magnitudes corresponding to a diameter of one minute of arc, but avoids the uncertainty of establishing the curves where the data are limited.