358 
The Great Nebulae 
[ch. xm 
For these reasons ejection of matter ought to occur symmetrically at two 
antipodal points on the equator of the nebula, and the ejected matter ought 
to form two symmetrical streamers or arms in the equatorial plane of the 
nebula, branching out from two opposite points of the equator*. 
The typical nebula shews precisely such arms. Plate XIV shews two 
nebulae in which the arms are closely coiled around the central mass, while 
Plate XV shews two others in which the arms are much more open. 
329. Van Pahlenf, GrootJ and Reynolds § have measured the curves 
formed by these spiral arms and find that in normal cases they approximate 
to the equiangular spirals 
r = A(T 6 (329T), 
where A and a are constants, the value of a determining the degree of openness 
or closeness of the spiral. 
N.G.C. 4321. N.G.C. 1232. ' M.101 
Fig. 59. The curves formed by the spiral arms of six nebulae (Reynolds). 
The agreement is not at all close. Van Pahlen measured the three spirals 
M 33 (Plate XI), M 51 (Plate XV) and M74>, and found substantial de 
partures from the strictly spiral shape in each. Groot found that in eight out 
of nine spirals considered, the curve was tolerably close to a true equiangular 
spiral. Reynolds measured six other spirals which he regarded as typical and 
found substantial deviations from the spiral form in each. Fig. 59 shews the 
* For a fuller and more precise discussion, see M.N. lxxxiii. (1923), p. 453. 
f Ast. Nach. clxxxviii. (1911), No. 4503. X M.N. nxxxv. (1925), p. 535. 
§ Ibid. p. 1014.