ASTRONOMY: R. E. WILSON 
183 
out properties of the differential equations (3) and (4). For example, 
it is very easy to determine, when the type of the vector is known, 
whether these equations can be solved by quadratures. Again, it ap- 
pears that the most general equation (4) never corresponds to the 
vector function of the most general type, but to a sHghtly restricted type. 
A consideration of the details of these normal forms would carry the 
discussion beyond the limits of the present paper. 
^ W. R. Hamilton, Lectures on Quaternions, p. 480. 
2 Arthur Cayley, London, Phil. Trans. R. Soc, 48, 17 (1858). 
3 Hermann Grassmann, Gesammelte Werke (Die Lineale Ausdehnungslehre, 1844, § 172). 
* Gibbs-Wilson, Vector Analysis (1902). A dyadic is a sum of dyad terms, where each 
dyad is a product of two vectors. When multiplied into the vector p by dot, i.e., scalar, 
multiplication, a single dyad is equivalent to a Hamiltonian term of the form /SSap. 
^W. Voigt, Die fundamentalen Eigenschaften der Krystalle (1898). 
« Hamilton, loc. cit., Lecture VII. A Hamiltonian invariant is a function of three vec- 
tors which is unaltered when these vectors are varied. 
^ Darboux, Memoire sur les Equations Differentielles Algebriques, Bui. Sc. Math., 
Paris, 13, 83 (1878). 
^ Clebsch, LcQons sur la Geometrie (Tr. Benoist), t. 2, p. 113; Vorlesungen liber Geometrie, 
Bd. 1, 390, 1001. 
^ Hamilton, Elements of Quaternions, Art. 415. 
10 F. L. Hitchcock, Phil. Mag., Ser. 6, 3, 576 (1902) ; Ibid., 4, 187 (1903)."^ 
ON THE RADIAL VELOCITIES OF FIVE NEBULAE IN THE 
MAGELLANIC CLOUDS 
By Ralph E. Wilson 
In the course of observations on the velocities of approach and re- 
cession (radial velocities) of southern nebulae whose spectra contain 
bright lines, made with spectrographs attached to the 37-inch reflecting 
telescope of the D. O. Mills Expedition from the Lick Observatory, 
at Cerro San Cristobal, Santiago, Chile, we have found that the follow- 
ing five nebulae have high radial velocities. The results depend upon 
the observed positions of the H/3 hydrogen line and the nebulium lines 
at 5007A and 4959A, in each case. The velocities are not corrected for 
the solar motion. 
UCK OBSERVATORY. UNIVERSITY OF CALIFORNIA 
Presented to the Academy. February II, 191 5 
Radial velocity 
Nebula 
Right ascension 
Declination 
-73° 44' 
-67 06 
-69 33 
-69 21 
-69 09 
Number of plates 
N. G. C. 1644 
N. G. C. 1714 
N. G. C. 2111 
N. G. C. 1743 
N. G. C. 2070 
Ih 6.2m 
4 52.0 
5 52.6 
4 54.6 
5 39.4 
3 
2 
2 
1 
1 
