192 Mr. C. Coleridge Farr. Some Expressions for 



Argon Thermometer. 



Temperature. Pressure. Volume. K. 

 C. mm. 



100-1 1414-9 1-0026 3-8095 



0-0 1040-0 1-0000 3-8022 



-182-7 353-2 0-9953 3*8930 



Xo correction has been made for the unheated or uncooled stem of 

 the thermometer ; but it is obvious that although the lowest tempera- 

 ture lies close to the boiling point of argon, the ratio of the values of 

 PV/T of hydrogen and argon at that temperature, as well as the 

 others, is practically constant. 



" On some Expressions for the Eadial and Axial Components of 

 the Magnetic Force in the Interior of Solenoids of Circular 

 Cross-section." By C. COLERIDGE FARR, B.Sc., formerly Angas 

 Scholar, University of Adelaide. Communicated by Professor 

 H. LAMB, F:RS. Eeceived June 7, liead June 16, 1898. 



In the present paper, certain expressions are arrived at, in terms of 

 .zonal spherical harmonics and their first derivatives, by which the 

 values of the two components of the magnetic force may be calculated 

 for any point in the interior of a coil, and hence the total force may be 

 found both in magnitude and direction. The resulting series suffer 

 from the well-known defect in the spherical harmonic method, in that 

 they are not very rapidly converging for points near the boundary 

 of the space for which they apply. A table of the values of the 

 first derivatives of the first seven zonal harmonics is added. This 

 table, in conjunction with that calculated by Messrs. Holland, Jones, 

 and Lamb, and published in the ' Philosophical Magazine/ Series 5, 

 December, 1891, will facilitate the numerical use of the expressions 

 arrived at. 



Let Qda be the magnetic potential at any point within a solenoid 

 whose depth of winding da is indefinitely small. If a be the radius 

 of this " solenoidal sheet," and the axis of z be the axis of the coil, 

 the axis of x being along a radius of the circular section of the coil, 

 and the origin at the centre of the equatorial section of the coil, we 

 have, neglecting the insulating covering of the wire, 



where X = the radial component of the magnetic force, 

 Z = the axial component, 

 S = radius of the outside winding of the coil of finite dimen- 



sions, 

 T = radius of the inside winding. 



