SPIRAL NEBULJS WIRTZ 139 



body from the observer. It is possible by combination in a mathe- 

 matical discussion of all the motions of the various bodies to find 

 the motion of the observer relative to the " centroid " (center of 

 mean positions) of the moving bodies. When we seek this datum 

 from the motions of the spiral nebulae we reach an unexpected result. 

 The "' apex," or goal of the motion of the sun, has no apparent rela- 

 tionship with that found from a similar discussion of the motions 

 of the stars. This apex, determined from the nebular motions, lies 

 not far from the pole of the earth's orbit. There is a further and 

 not less unexpected result. The velocity of the sun relative to the 

 centroid of the spiral nebulae is no longer the commonly found value 

 from various discussions of stellar motions, 20 kilometers (12 miles) 

 per second, but about 700 kilometers (435 miles) per second. It can 

 not be the sun alone which is thus moving relatively to the spiral 

 nebulce. For such a great velocity would have its image in the sur- 

 rounding stars (parallactic motion) ; such is not present, 



3. We are therefore forced to the conclusion that our whole galaxy 

 of stars, the milky way family as a body, is moving with this great 

 velocity relative to the centroid of the spiral nebulae. A further 

 conclusion results: The milky way system and the spiral nebulae 

 must be considered as related systems — that is, the spiral nebulae are 

 distant galaxies and our galaxy or milky-way system, viewed from 

 the spiral nebulae, would have the appearance of a cosmical nebula. 



There is another surprise. If we eliminate the known motion 

 of the sun from the observed motion of the spiral nebulae we would 

 expect to find, according to the underlying assumptions of the pro- 

 cedure, that in the mean they would be zero. But that is not at 

 all the case. We find that the system of spiral nebulae tends to 

 scatter outwards into space. Literally stated, the spirals are moving 

 outwards from the present position of the observer with a velocity 

 of about 800 kilometers (497 miles) per second. 



We can obtain another measure of the distance of these nebulae, 

 although of small accuracy. The goal of the solar motion may be 

 found not only from a discussion of the movements of the nebulae 

 in a radial direction but also from their movements at right angles 

 to this, their angular displacements. The natural lack of sharpness 

 in the outlines of these hazy objects militates against the accuracy of 

 position determinations, so that the proper motions of any individual 

 nebula can not be indicated with any accuracy. But that does not 

 exclude the determination of a statistical mean indicating the part 

 of movement of all of them, which is produced by the motion of the 

 observer himself. If we combine this uncertain l)ut at any rate too 

 o-reat value of the angular motion with the surer value of the 



