612 REPORT— 1895. 



when plotted on a map of oscillation frequencies, as disposed sj-mmetrically on 

 either side of a common centre, this indicates that the periodic time continues 

 unchanged during the shortening of the amplitude. 



This suggests the cause of the width of spectral lines in general, so far as their 

 width is not merely apparent, i.e., due to the Doppler effect of the translational 

 motions of the molecules, or to the breadth of the slit of the spectroscope. The 

 rest of the Avidth of the line, as seen, is its true physical width, and seems to be 

 due to the interchange of energy between the molecule and the rether. This 

 leads to diminished amplitude ; and this reduction of the amplitude maybe accom- 

 panied by either a reduction, or an increase, or a persistence unaltered of the 

 periodic time, according to the way in which the motion of the electron is 

 dynamically associated with the rest of the events which go on within the 

 molecule. If the periodic time decreases, this gives rise to a ruling fading out 

 towards the red ; if there be an increase of the periodic time, the shading is towards 

 the violet ; while if the line fades out both ways symmetrically, there is no change 

 in the periodic timp. The relative intensities and the spacings of the lines of the 

 ruling depend on the law which connects the escape of energy and the shorten- 

 ing of the semi-amplitude, and in its turn this law depends on the dynamical 

 relations in which the parts of the molecule stand to one another. The excessively 

 fine rulings of which the widths of individual lines consist can probably not be 

 seen otherwise than as a shading, unless perhaps in some very few exceptional 

 instances, owing to their being blurred together by the Doppler effect. 



We have attributed these very fine rulings to the interchange of energy with 

 the sether. On the other hand, the more conspicuous rulings, such as those we 

 have been studying in oxygen and carbon, seem to be associated with the trans- 

 ference of energy from one motion within the molecule to another. This may be 

 briefly described by saying that the widths of the individual lines and their being 

 in various ways shaded off' are due to radiation, while that they are arranged in 

 Eeriea is due to conduction. 



SATURDAY, SEPTEMBER 14. 

 The Section was divided into two Departments. 

 The following Papers and Reports were read :— 



Department 1. Mathematics. 



1. On the Translational and Vibrational Energies of Vibrators after 

 Impacts on fixed Walls. By Lord Kelvin, Pres. R.S. 



2. On Bicyclic Vortex Aggregates. By Professor W. M. Hicks, F.R.S. 



The author showed that in any case of a vortex aggregate in which the motion 

 takes place in planes through an axis, and symmetrical about this axis, another 

 state of motion was possible with the same current and vortex sheets, but in which 

 the motion was in circles round the axis, and in which the fluid external to the 

 aggregate remained at rest. These two motions can be superposed with a result- 

 ing steady motion, and the two cyclic constants independent of each other. 



3. On Hill's Sx>herical Vortex. By Professor W. M. Hicks, F.R.S. 



The author showed that it is possible to build up a compound spherical vortex, 

 consisting of shells in which the rotation is oppositely directed in successive shells. 



