POTENTIALS AND STRESS FUNCTIONS 147 



In fact of whatever scalar form P be, if V*T = V/>, VT P, a pure scalar. 

 Multiply this by dp (a pure vector) and you get a pure vector dpVr = dpP. 

 Hence your expression 



sl V (dpV)T = SJdpP = o 



because if it is anything at all it is the integral of a vector multiplied by a scalar 

 and that is a pure vector and the scalar part of it is o. I suppose this is nonsense 

 arising from our being barbarians to one another. Will you therefore be so kind 

 as to give me a code by which I may interpret the symbol VdpV, that is to say, 

 tell me what these symbols, thus arranged, ask me to do.... 



Note the Vector <r as determined above is such that SV<r = o so that we may 

 truly say V<r = V/ > . 



In electromagnetism P is the magnetic potential and VP is the magnetic force 

 outside the magnet or inside it in a hollow tube whose sides are parallel to the 

 magnetization. 



V<7 = V/ > outside 



but inside Vcr = V/> + 47r3 

 where 3 is the magnetization. Va- is the magnetic force in a crevasse x 3>. 



I have not been able to make much of your T. I coloured some diagrams of 

 lines of force Blue and red but I must study the astronomer to define the magnetic 

 tints and softness. Sir W. Hamilton (Edin h ) was partial to redintegration, an 

 operation you should get a symbol for. Among other scientific expressions I would 

 direct your attention to the salutary influence of Demon-stration and Deter-mination, 

 and to two acids recently studied, Periodic and Gallery Thronic acids. The 1st you 

 will find use for. The 2nd is for the L d High Commissioner. 



Yours J C M 



In another letter, of which the opening paragraph has already been 

 given (page 1 1 7 above), Maxwell refers to Tail's quaternionic investigations 

 in the stress function. The letter is on a half sheet of note paper and is 

 undated, but was probably written towards the end of 1872. The 

 continuation is as follows: 



" I return your speculations on the (f> ( Uv) ds. Observe that in a magnet placed 

 in a magnetic field the stress function is not in general self-conjugate, for the elements 

 are acted upon by couples. But the = n of = m is very properly got as you get it 1 . 



" Search for a physical basis for 



5 . V'aVo- 



as a term of the energy developed in a medium by a variable displacement <r. 

 When found, make a note of, and apply to oil of turpentine, eau sucre"e, &c., for it 

 brings out the right sort of action on light of all colours. But the mischief is FV<r, 

 which it is manifest, can be produced without making any physical change inside 

 a body. The very rotation of produces it. Now VV is a vector. Turn it 

 alternately in the direction of FV<r and oppositely and you have increase & diminu- 



1 See Tait's Note on the Strain Function, Proc. Jt. S. E. 1872 ; Sci. Pap. Vol. i, pp. 196-7. 



192 



