1877.] 



On the Motion of Vibrating Bodies. 



157 



be the case with the light from the enveloping surface formed by the 

 gaseous envelopes. The light from this envelope received on a slit in the 

 focus of an object-glass would be sensibly constant, because the contri- 

 buting area would be increased in the same proportion that the light 

 received from each part is diminished. The result would be that at some 

 definite distance, and all greater distances, the preponderating light 

 received from such a cluster would be derived from the gaseous envelopes 

 and not from the isolated stellar masses. The spectrum of the cluster 

 would therefore become a linear one, like that from the gaseous sur- 

 roundings of our own sun. The linear spectrum might, of course, under 

 certain circumstances, be seen mixed up with a feeble continuous spec- 

 trum from the light of the stars themselves. 



It should be noticed that, in this view of the subject, the linear spec- 

 trum can only appear when the resolvability of the cluster is at least 

 injuriously affected by the light of the gaseous envelopes becoming 

 sensibly proportional to that from the stellar masses, and that in the 

 great majority of such cases it would only be in the light from the irre- 

 solvable portions of the cluster that bright lines could be seen in the 

 spectrum. 



The changes in form which would be presented to us by such a nebula 

 might be expected to be small. These changes would depend chiefly 

 upon changes in the distribution of the stellar masses constituting the 

 cluster. It has always appeared to me difficult to realize the conditions 

 under which isolated irregular masses of gas, presenting to us sharp 

 angular points, could exist uncontrolled by any central gravitational mass 

 without showing larger changes in form than appear to have been the 

 case with many of the nebulae. In my view of the nature of nebulae this 

 difficulty no longer exists. 



Royal Observatory, Cape of Good Hope, 

 February 9, 1877. 



III. " On some Figures exhibiting the Motion of Vibrating Bodies, 

 and on a New Method for determining the Speed of Machines." 

 By Herbert M'Leod, F.C.S.. Professor of Experimental 

 Science, and George Sydenham Clarke, Lieut. R.E., In- 

 structor in Geometrical Drawing in the Royal Indian En- 

 gineering College, Cooper's Hill. Communicated by Prof. 

 Duncan, F.R.S., Pres.G.S. Received April 5, 1877. 



If the image of a point of light or of a black dot on a white ground be 

 observed in a vibrating mirror, the motion of which may be produced by 

 a tuning-fork or reed, the point, in virtue of the retention of the image 

 on the retina, will appear as a straight line. If, however, the luminous 

 point be moving in a direction at right augles to the plane in which the 



