TRANSACTIONS OF SECTION A. 451 



electric currents traversing conductors in various circumstances, and finds that 

 from the figures alone nearly all the recognised electrodynamic, magneto-dynamic 

 and magneto-electric relations can he deduced or verified. 



The series of figures now presented illustrate amongst other matters the 

 following actions : — 



(1.) The attraction (or repulsion) of magnets by magnets. 



(2.) The attraction (or repulsion) of currents by currents. 



(3.) The attraction (or repulsion) of magnets by currents. 



(4.) The rotation of magnets by currents. 



(5.) The rotation of currents by magnets. 



(6.) The rotation of a magnet round its own axis under the influence of a current. 



(7.) The repulsion by a current of its own parts. 



(8.) The mutual inductive action of solenoids and magnets, and of magnets and 

 magnetic matter. 



(9.) The flow of currents in conductors and conducting media. 

 (10.) The action on magnets of magnetic media. 



(11.) The action of magnetic instruments, magnetometer, galvanometer, electro- 

 dynamometer. 

 (12.) The action of magneto-electro machines. 

 (13.) The magnetic properties of cobalt and nickel. 



The figure illustrative of the lines of force surrounding a current has been 

 previously given by Faraday, Guthrie, and Barrett. Those illustrative of the 

 attraction and repulsion of parallel currents by Faraday, but imperfectly. Those 

 illustrative of flow of currents in conductors by Kirchhoff, Guthrie, and Carey 

 Foster and Lodge. Those illustrating the action of the galvanometer and the 

 Gramme machine were suggested to me respectively by Mr. C. W. Cooke and 

 Mons. A. Niaudet. The photographs have been executed directly from the filing- 

 figures by Mr. Robert Gfllo, of Bridgwater, of the firni of F. York and Co., of 

 Notting Hill, the eminent manufacturers of photographic transparencies for the 

 lantern. 



9. On Dimensional Equations, and on some Verbal Expressions in Numerical 

 Science. By Professor James Thomson, LL.D., _D.Sc, F.B.S. 



In recent years attention has been given, more than before^ to relations among 

 standard quantities of variable things, to be taken as units for use in giving nume- 

 rical expression to various quantities of those things. The quantity of each dif- 

 ferent variable thing selected as a unit might be, and often has been, arbitrarily 

 chosen, independently of the quantities chosen for units of other things. But 

 great advantages as to convenience and facility are attainable by making a 

 methodical connection among the quantities to be selected for the units of the 

 various things, so that when some of the units are arbitrarily selected, the others 

 will be derived from them in some good systematic way. 



The units thus arbitrarily selected are called fundamental units ; and the others 

 obtainable from them by the systematic method are called derived units. 



Teaching on this subject is given in the early pages of Professor Clerk 

 Maxwell's 'Treatise on Electricity and Magnetism,' and in Professor Everett's 

 'Treatise on the Oentimetre-Gramme-Second System of Units.' The subject is 

 important ; but much of the nomenclature and notation hitherto used is very con- 

 fusing and unsatisfactory. 



I now wish to propose some amendments, or new modes of expression, which 

 appear to be commendable. 



Instead of saying, as is done in Professor Everett's very useful treatise, 



" The unit of acceleration varies directly as the unit of length, and inversely 

 as the square of the unit of time ;" 

 I would propose to say 



The change-ratio of the unit of acceleration is the product of the change-ratio of 

 the unit of length and the inverse second power of the change-ratio of the unit of 

 time. 



GO 2 



