=====+=================================================
| Diameter
List +-----+-----+------+------+------+-------+--------
| 4″ | 6″ | 15″ | 25″ | 60″ | 200″ | >200″
-----+-----+-----+------+------+------+-------+--------
3 | 205 | 322 | 291 | 280 | 195 | 36 | 6
4 | | 1 | 69 | 153 | 19 | 6 | 1
5 | | 6 | 99 | 106 | 23 | 1 | 3
6 | | 14 | 114 | 72 | 2 | 2 | 1
7 | | 9 | 103 | 156 | 35 | 4 | 12
8 | | 80 | 372 | 243 | 34 | 3 |
9 | | 48 | 174 | 160 | 19 | |
10 | | 3 | 31 | 26 | 2 | |
11 | | | 13 | 60 | 19 | 1 |
12 | | 14 | 61 | 162 | 27 | 10 |
13 | | | 20 | 61 | 26 | 3 |
14 | | 3 | 160 | 296 | 43 | 1 | 1
-----+-----+-----+------+------+------+-------+--------
The evidence, while far from conclusive, appears to indicate the
existence of actual clusters of these small nebulae in the sky. If this
is true, it is natural to suppose them physically connected, as is the
case in star-clusters. It is not possible to form a conception of this
state of affairs until some idea of their distance is acquired. Suppose
them to be extra-sidereal and perhaps we see clusters of galaxies;
suppose them within our system, their nature becomes a mystery.
[Illustration: FIG. 2.--Distribution of size of nebulae in Wolf’s
Perseus and three Yerkes fields]
The question of nebular distances is of first importance, for it is in
terms of this quantity that the various dimensions may be expressed.
The dark nebulosities, by their very nature, and the great diffuse
clouds, some obviously connected with even naked-eye stars, may safely
be considered as galactic, and this view is in accord with their low
radial velocities with reference to our system.
The planetaries have repeatedly been measured for proper motion, with
negligible results. Taking a value of 40 km/sec. for the average radial
velocity, and an assumed lower limit of 0.02″ for the average annual
proper motion, a tentative lower limit for the average distance of the
largest, and hence probably the nearest, is found to be about 2000
light-years. There is thus no reason on this ground for placing them
outside our system, especially in view of their decidedly systematic
galactic distribution.
Rotation of these nebulae, as detected by the spectroscope, furnishes
a means of relating mass and average density with distance. Assume
an axis perpendicular to the line of sight, the mass as concentrated
in the nucleus and the individual distant particles as rotating in
equilibrium; let α be the radius, _P_ the period of rotation, _M_ the
mass, and suppose the rotation to be circular. Then α³/_P²M_ = _C_, a
constant. Let the unit of distance be the light-year (LY); of time,
the year; of mass, that of the sun (S), then _C_, as computed from the
earth-sun system, is about 4 × 10⁻¹⁵.