1871.] Sir W. Thomson on Approach caused by Vibration* 271 



were given off from the lower part of each internode, but above the 

 node, and were apparently epidermal. 



There is also considerable doubt respecting the fructification of Calamites. 

 Some of the Volkmannise have evidently belonged to this group ; but only 

 one example retaining its minute organization has yet been found in which 

 the structure of the central axes corresponded with that of the Calamites. 

 The relationship to Calamites of the fruits figured by Binney, under the 

 name of Calamodendron commune, which are identical wth the Volkmannia 

 Binneyi of Carruthers, is more than doubtful, because of the anomalous 

 structure of their central axes. 



After a careful comparison of the organization of Calamites with 

 that of the recent Equisetaceae, the author prefers constituting the former 

 an independent order, distinct from, though allied to, the Equisetums, 

 under the name of Calamitacece, and characterized by cryptogamic fructifi- 

 cation and verticillate foliage, associated with an exogenous axis. The 

 latter feature probably involved the existence of something resembling a 

 cambium layer, furnishing the material for the new tissues. 



It is further proposed to divide these plants into two generic groups, 

 viz. Calamites and Calamopitus ; the former to comprehend those un- 

 provided with infranodal canals, and the latter those which possess them. 

 The existing specific distinctions appear to have little or no scientific 

 value. 



III. " On Approach caused by Vibration." A Letter from Prof. Sir 

 W. Thomson, LL.D., F.R.S., &c. to Prof. Frederick Guthrie, 

 B.A. Communicated by Sir W. Thomson. Received November 

 17, 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 experiments you describe constitute 

 very beautiful illustrations of the established theorem for fluid pressure in 

 abstract hydro-kinetics, with which I have been much occupied in mathe- 

 matical investigations connected with vortex-motion. 



According to this theorem, the average pressure at any point of an in- 

 compressible 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 im- 

 mediately explains the attractions demonstrated in your experiments ; for 

 in each case the average of square of 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 that the average of the square of 

 the velocity must be greater on the surfaces of the tuning-fork next to the 



