TABLE IV Irregular Nebulae ==========+===========+========= N.G.C. | m_{T} | log d ----------+-----------+--------- 2968 | 12.6 | +0.08 3034* | 9.0 | .85 3077 | 11.4 | .48 3729 | 11.8 | .17 4214* | 11.3 | .90 4449* | 9.5 | .65 4618 | 12.3 | +0.40 4656§ | 11.5 | +1.30 4753 | 11.4 | +0.43 5144 | 12.8 | – .30 5363 | 11.1 | +0.20 ----------+-----------+--------- Mean | 11.34 | +0.469 ----------+-----------+--------- NOTES TO TABLES I–IV * Magnitude from Hopmann. † N.G.C. 524 and 3998 are late elliptical nebulae in which the equatorial planes are perpendicular to the line of sight. They might be included with the E6 or E7 nebulae. § Absorption very conspicuous. ‡ N.G.C. 3607, 4459, and 5485 appear to be elliptical nebulae with narrow bands of absorption between the nuclei and the peripheries. The progressive change in the value of C throughout the sequence may be expressed as a variation either in the magnitude for a given diameter or in the diameter for a given magnitude. Both effects are listed in Table VII and are illustrated in Figure 6, in which magnitudes and diameters thus found are plotted against types. With the exception of the later elliptical nebulae, for which the data are wholly inadequate for reliable determinations, the points fall on smooth curves. In the region of the earlier elliptical nebulae, the curves should be somewhat steeper in order to allow for objects of greater ellipticities which are probably included. REDUCTION OF NEBULAE TO A STANDARD TYPE The slope, K, in the formula relating magnitudes with diameters, appears to be closely similar for the various types, but accurate determinations are restricted by the limited and scattered nature of the data for each type separately. With a knowledge of the parameter C, however, it is possible to reduce all the material to a standard type and hence to determine the value of K from the totality of the data. The mean of E7, SBa, and Sa was chosen for the purpose, as representing a hypothetical transition-point between the elliptical nebulae and the spirals, and was designated by the symbol “S0.” The corresponding value of C, in round numbers, is 13.0. Corrections were applied to the logarithms of the diameters of the nebulae of each observed class, amounting to $\Delta \log d = 0.2 (13.0 - C)$ where C is the observed value for a particular class.[17] When the values of C are read from the smooth curve in Figure 6, these corrections are as shown in Table VIII. TABLE V Frequency Distribution of Types =========+==========+==============+=========== Type | Number | Percentage | Mean Mag. ---------+----------+--------------+-----------