452 Intelligence and Miscellaneous Articles. 



be produced, whereby the steady motion might be partially 

 converted into vibratory motion. This effect would be pre- 

 cisely analogous to the generation by the siren of Cagniard 

 de la Tour of musical sounds by means of a succession of in- 

 terruptions of a steady current of air, the pitch of the sound 

 increasing with the velocity of the current. These vibratory 

 motions, being an accession to those produced by the speaker 

 at the transmitting end of the telephone, and having a con- 

 stant relation to them, are attended by an accession of cur- 

 rent, and therefore an accession of effect at the receiving-end. 

 This follows from the analytical formula in the second para- 

 graph of the article in the Phil. Mag. for June 1878, the effects 

 under consideration being all referable to pressures depending 

 upon the squares of the velocity of a steady current of the 

 astherial medium. 



I have now completed all that I am able to say relative to 

 the department of physical science the principles of which 

 were inaugurated by Newton, and which for distinction may 

 be named Theoretical Physics. I must now leave to younger 

 mathematicians the task of correcting and extending, if they 

 think good, the efforts I have made in this direction, and shall 

 only urge the important consideration that Theoretical Physics 

 are as necessary for constituting a complete system of Physical 

 Science as Experimental and Empirical Physics. 



Cambridge, May 15, 1880. 



LXI. Intelligence and Miscellaneous Articles. 



ON THE THEOKY OF INDUCTION-CURRENTS. BY M. MASCART. 



MHELMHOLTZ has shown that, taking as starting-point the 

 • laws of Ohm and Joule, the induction-phenomena produced 

 by the displacement of a magnetic system in the vicinity of a cur- 

 rent might have been foreseen. It has seemed to me that a natural 

 generalization of the results obtained in this particular case permits 

 us to establish the theory of electrodynamic induction-currents so 

 as to connect them simply with a common principle. 



It is known that, according to Ampere's theory, the work neces- 

 sary for displacing a magnetic mass m in the vicinity of a current 

 is equal to the product of that mass by the intensity I of the cur- 

 rent and by the increment of the angle under which the circuit is 

 seen from two points occupied successively by the magnetic mass. 

 The energy of the mass m wdth respect to the current may there- 

 fore be represented by Imw. It will be useful to enunciate this 

 property in another form by employing the notion of Paraday's 

 lines of force. 



If the force exerted by a magnetic system upon the unit of mass 

 situated in a point be considered, and any surface-element whatever 



