The observations point to very large values for the rotational components of velocity, although the necessarily small scale of the instruments employed in their study renders the measuring difficult. Pease has determined the velocity of rotation for N.G.C. 4594 with some degree of accuracy. At 120″ from the nucleus it amounts to 300 km and varies linearly with the distance outward. V. M. Slipher reports that for the Andromeda nebula the angular rotation is fastest near the nucleus, and that this type of rotation promises to be the more common.
Assume a typical spiral 400″ in diameter, with the ratio of the axes of figure as β/α = 0.1, and with rotation perpendicular to the line of sight at a velocity of, say, 200 km at the periphery. These figures are apparently not very different from the average of the two dozen brighter spirals. [Table VII] gives the dimensions in terms of distance.
The velocity of escape is 280 km/sec.
At the lower limit of average distance of spirals the typical nebulae would be fifteen light-years in diameter, forty-five million times as massive as our sun, and 3 × 10¹³ as dense as our atmosphere. On the other hand, if the typical spiral nebula is placed at a suitable distance, its dimensions assume the same order of magnitude as those of our own stellar system.
The conception of our galaxy set forth by Eddington in his book Stellar Movements and the Structure of the Universe is that the Milky Way forms a ring around a central, slightly flattened cluster. This ring is supposed to rotate in equilibrium so that the stars may remain concentrated in the configurations they now form. Assuming the ratio of the two radii as one to five, and using Eddington’s figures of 2000 parsecs for the distance of the Milky Way, and 10⁹ suns as the mass of the inner cluster, the period and density may be computed and compared with those of the typical nebula placed at a distance such as will make the diameter the same as that of our system. The results are given in [Table VIII].
TABLE VII
| d | α | Mass | Period | Density |
|---|---|---|---|---|
| 10² | 10⁻¹ | 2.7 × 10⁵ | 9 × 10² | 1.4 × 10⁹ suns per cu. LY |
| 10⁴ | 10¹ | 2.7 × 10⁷ | 9 × 10⁴ | 1.4 × 10⁵ |
| 10⁵ | 10² | 2.7 × 10⁸ | 9 × 10⁵ | 1.4 × 10³ |
| 10⁶ | 10³ | 2.7 × 10⁹ | 9 × 10⁶ | 1.4 × 10¹ |
TABLE VIII
| Distance | Radius | Mass | Period | Density | |
|---|---|---|---|---|---|
| Nebula | 6 × 10⁶ LY | 6 × 10³ LY | 1.6 × 10¹⁰ S | 5.4 × 10⁷ year | 5.6 × 10⁻¹ |
| Galaxy | 6 × 10³ | 10⁹ | 2.5 × 10⁸ | 1.2 × 10⁻² |
The velocities of escape would be about 280 km for the nebula and 170 km for the galaxy. Considering the problematic nature of the data, the agreement is such as to lend some color to the hypothesis that the spirals are stellar systems at distances to be measured often in millions of light-years. The computations by O. H. Truman[8] and by R. K. Young and W. E. Harper[9] of the motion of our system with respect to the spirals, based on the radial velocities of the spirals, are another and stronger argument for the hypothesis.