﻿Sir W. Thomson on Approach caused by Vibration. 423 



tened by a thread to a stand, and the bottom so loaded with wax 

 fastened to it by a string, that the whole system had a tendency 

 to sink. 



In order to test the theorem further, a large glass cylinder 

 was filled with carbonic acid, and one of the above-mentioned 

 balloons was filled partly with atmospheric air and partly with 

 illuminating gas, so that it floated in the carbonic acid and only 

 exposed its extreme top above the cylinder. The vibrating fork 

 distinctly repelled this balloon. 



Hitherto I have not yet had time to examine the effect of the 

 before-mentioned slit upon this system (see 2). 



I may be allowed to add that the influence of such a slit was 

 exhibited at a distance of 6 decimetres. 



The majority of the above- described experiments may, more- 

 over, be performed with a glass bell-jar such as is commonly 

 used for domestic purposes, and with an ordinary easily move- 

 able magnetic needle. 



A little machine for striking, the hammer of which is set 

 going by an electric current, shows the attraction of a strip of 

 paper in a very regular manner ; so that when the machine has 

 been at work for some minutes, the paper is brought into contact 

 with the bell. 



The above observations furnish a sure means for the explana- 

 tion of the phenomena offered by the so-called sensitive flame. 



Part III. Letters from Professor Sir W. Thomson to 

 Frederick Guthrie. 



Glasgow, Nov. 14th, 1870. 



Dear Sir, — I have to-day received the ' Proceedings of the 

 Royal Society ' containing your paper " On Approach caused by 

 Vibration," which I have read with great interest. The expe- 

 riments you describe constitute very beautiful illustrations of the 

 established theorem for fluid pressure in abstract hydrokinetics, 

 with which I have been much occupied in mathematical investi- 

 gations connected with vortex-motion. 



According to this theorem, the average pressure at any point 

 of an incompressible frictionless fluid originally at rest, but set 

 in motion and kept in motion by solids moving to and fro, or 

 whirling round in any manner, through a finite space of it, is 

 equal to a constant diminished by the product of the density 

 into half the square of the velocity. This immediately explains 

 the attractions demonstrated in your experiments ; for in each 

 case the square of the average velocity is greater on the side of 

 the card nearest the tuning-fork than on the remote side. Hence 

 obviously the card must be attracted by the fork as you have 

 found it to be ; but it is not so easy at first sight to perceive 



2F2 



