THE OPERATOR "NABLA" 145 



It was probably this reluctance on the part of Maxwell to use the term 

 Nabla in serious writings which prevented Tait from introducing the word 

 earlier than he did. The one published use of the word by Maxwell is in 

 the title to his humorous Tyndallic Ode 1 , which is dedicated to the " Chief 

 Musician upon Nabla," that is, Tait. 



The following letter from Maxwell shows how clearly he had grasped 

 the significance of the quaternion notation. 



ARDHALLON, 



DUNOON, 



Jan. 23, 1871. 

 Dr T' 



Still harping on that Nabla ? 



You will find in Stokes on the Dynamical Theory of Diffraction something of 

 what you want, this at least which I quote from memory. 

 I. For all space your eq n 



Vo- = V"(T + 7>) 



where <r is given and T and v are to vanish at oo gives but one solution for r and 

 one for v, the first derived by integration from FVo- and the second from >SV<r by 

 the potential method, and we then get the result in the form 



(because, as Helmholtz has shown (Wirbelbewegung) 5Vr = o). All this is as old 

 as 1850 at least. See Stokes. 



Now we leave all space and consider a region 2 within which VlP = o and therefore 

 V/* has no convergence. Now if a vector function has no convergence it ought to 

 be capable of being represented as the curl of a vector function, or there ought to 



be a vector <r such that 



FVo- = 



The simplest case to begin with is of course the potential due to unit of mass 

 at the origin. Find <r and T for that case ! The difficulty arises from the fact that 

 the region in which V 2 / 3 = o is here periphractic and surrounds completely the origin 

 where this is not true. If we draw a closed surface including the origin then 



Si 



whereas 



1 5 Uv Wads = O, necessarily*. 



Hence to make it impossible for the region to include the origin we must get 

 rid of periphraxy by drawing a line from the origin to oo and defining the region 2 so 

 as not to interfere with this line. 



1 Reproduced partly in facsimile at the end of this Chapter. 

 ' Because \\Sdv VV<r = \\ \ dvSV W<r = o for V'<r is a vector. 



T. 19 



