January 14, 1904] 
NATURE 
249 
gases, which under great pressure have the properties of 
a fluid, move with various velocities, and along more or 
fess curved lines toward the opening. 
That component of the resulting momentum which acts 
at right angles to a diameter through the point of rupture 
causes an excess of pressure along this diameter; this 
excess, in the nature of a reaction, acting on a surface 
already strained to near the breaking point, finally causes 
a second rupture at the diametrically opposite part of the 
body. 
The ejected masses will not all have the same velocity ; 
those parts near the outer boundary of each stream will 
be deviated and retarded through side currents and friction 
at the aperture; the central parts of the stream will, in 
general, acquire the highest velocity, sufficient to carry the 
lighter matter in a radial direction far beyond the sphere 
of sensible attraction of the parent mass, where it finally 
attains a uniform velocity. The heavier masses and those 
near the borders of the opening will form secondary streams 
having various inclinations and velocities which, if there 
were no rotation, would be incomplete arcs of hyperbolas, 
parabolas and ellipses, in all of which the lighter masses 
would continually be outstripping the heavier ones. 
Through the rotation, however, the outer parts of every 
Stream are left behind the parts nearer the origin, so that 
each stream falls into a spiral curve of a more or less com- 
plicated form, resulting in an increase in the confusion of 
detail with diminishing distance from the centre. 
If the orifices are on the equator, the radially ejected 
streams will be plain spirals. If the line joining the two 
orifices is inclined to the equator the streams will be of 
double curvature, each producing a spiral in the form of a 
helix* (conical). This class of nebulas not being confined 
fo a single plane will, as a rule, exhibit much confusion 
of detail in projection. 
In general a practically straight line drawn from the 
origin to any part of the plane spiral represents the actual 
path traversed by the matter in that particular part of the 
spiral, and the angular length of any given mass, measured 
ia the direction of increasing distance from the origin, re- 
presents the corresponding arc through which the parent 
body rotated, in the opposite direction, while this particular 
mass was being cast out. 
The two principal factors which operate to produce the 
observed form of any particular spiral are :—(1) internal 
pressure ; (2) velocity of axial rotation. 
The decrease in pressure, after the surface has been 
ruptured, may in some cases be so rapid that the orifices 
close up before the body has completed a single rotation; 
such a body will, later on, repeat the process, the orifices 
remaining open for a longer period; later still the surface 
will have reached such a condition that the orifices remain 
open for an indefinite period, finally reaching a stage re- 
presented (on a small scale) by the earth’s present con- 
dition.* 
If the earlier conditions were such that at the time of 
the first great eruption long ages were required for a single 
rotation of the body, the observed form indicates that the 
internal pressure remained nearly constant, and that the 
angular velocity was continually being accelerated. (Owing 
to the removal of heated matter from the interior the con- 
traction was much more rapid than that which would 
have resulted from simple loss of heat at the surface.) 
According to this theory, then, the spiral nebulas reveal 
to us the past history of the forces operating at the mouths 
of the two opposing volcanoes.* The fluctuations in the 
forces and in the relative amount of matter belched forth 
simultaneously by each crater are faithfully recorded in the 
1 Photographs of these objects can be found in various astronomical 
publications. The most complete work in this line has been done by Isaac 
Roberts, D.Sc., F.R.S. See his ‘‘ Photographs of Stars, Star Clusters and 
Nebulz,” vols. i. and ii. 
alte worthy of notice, in this connection, that the two most disturbed 
terrestrial regions are diametrically opposite to each other and near the 
equator. The deep-seated character of these disturbances is shown quite 
conclusively by tke observed phenomena. Martinique belongs to one region 
Krakatoa to the other. i 
3 Spectroscopic and photometric changes in the light of certain fixed 
stars, when considered in connection with the phenomena which would be 
produced by two radially moving columns of matter (incandescent at the 
orifices and rotating about a fixed axis inclined at a given angle to the line 
of sight), might in some cases lead to more satisfactory explanations of the 
observed data. 
NO. 1785, VOL. 69] 
often twisted, broken, serrated and irregular aspect of the 
masses which make up the general outline of the main 
hyperbolic spiral curves. This history covers the period 
from the first great catastrophe, represented by a distant 
large mass at the extreme outer limit of one branch, telling 
us which of the two orifices was the first to relieve the 
internal pressure, down to the time when the outer portions 
of the numerous inner streams having less initial velocity 
but the same angular length—or perhaps the outer portions 
of the main streams of a later eruption—reached to such 
distances from the centre as to produce too much confusion 
of detail for further trustworthy analysis of the form seen 
in projection.* 
The generally more dense and more luminous inner 
boundary of the main spiral curves plainly indicates that 
after all these ages the lighter more swiftly moving but 
later ejected particles are still bombarding the earlier 
slower moving masses. Every time either orifice came 
nearly in line with, say, a particular distant previously 
ejected mass, the more swiftly moving particles were sent 
oa their invisible course, many on the way transferring 
part of their energy of motion to other particles and to the 
production of the accompanying phenomena of heat and 
light; others to find free passage, leaving far behind those 
masses ejected in the same direction at previous rotations 
(thus crossing in radial directions the space between the 
main spiral arcs), finally to overtake, some to bombard the 
particular mass, thus helping to keep it luminous, others, 
like all parts of the main spiral, to continue their out- 
ward journey indefinitely, or until some other obstruction 
changes their energy of mass-motion into a different equiva- 
lent. Through the action of gravity the particles ejected 
by one body—aided by those coming from other sources— 
play their part to re-create the conditions leading to a re- 
petition of the parental experiences.* 
Isolated or heavier condensations on the spiral arcs will 
generally take on a cometary form indicating the direction 
from which the particles come. I would suggest that a 
long nebulous mass, as, for instance, H.V. 14 Cygni, may 
be a part of some great spiral (perhaps approaching and 
relatively near to the earth); if this is so, the general direc- 
tion of the parent mass is plainly indicated in the visible 
structure of this nebula. 
When the eruptions are periodic and of very short dura- 
tion, the heavy surface-matter ejected at each re-opening of 
the craters will not be carried beyond the limits of the 
system. Certain results I have recently obtained seem to 
show that the masses forming star-clusters are the inner- 
most parts of spiral structures similar to those considered 
in the present paper. 
In the case of the great cluster in Hercules, the star- 
like masses are found to be connected by nebulous streams 
which first leave then return towards the centre of the 
cluster, showing that the initial velocity of ejection was 
insufficient to carry these masses (which can hardly be 
called stars in the ordinary meaning of the word) beyond 
the sphere of central attraction. A similar arrangement is 
found to exist among the stars near y Cassiopeia. The 
two known nebulas near this star (first photographed by 
Barnard and Wolff) are but the more condensed parts of 
a broad spiral-like nebulous band (made up of similar con- 
densations) which can be traced from near the middle of 
the second quadrant up to within a few minutes of arc of 
the naked eye star in the fourth quadrant. More complete 
details have been sent to the Astronomical Journal for 
publication. 
In conclusion, it may be permitted once more to direct 
attention to a unique case in solar observation, bearing, as 
it does, directly upon the subject of the origin of spiral 
nebulas. How much, or rather how little, importance has 
been attached to this particular phenomenon, and to the 
‘* mechanical theory of comets ’’* put forward at the time, 
1 Through irregular variations in the pressure at the orifices, and through 
differences in the amount of matter ejected at different times, an endless 
variety of forms can be produced. 
2 Readers acquainted with Lockyer’s views will notice that I adopt the 
theory of the meteoric constitution of nebulous matter. ‘I he evidences in 
favour of this theory are fully set forth inthe work entitled ‘‘ The Meteoritic 
Hypothesis,” by Sir Norman Lockyer, K.C.B., F.R.S. 
3 See ‘‘ Contributions from the Lick Observatory,”’ No. 4, p. 118 ef seg. 
This theory calls for justsuch crucial, seemingly abnormal but really typical 
phenomena as were presented by Borrelly’s last comet. 
