400 Intelligence and Miscellaneous Articles. 



It is, I think, unnecessary to insist on the extreme importance 

 which attaches to the confirmation of the theoretic views of M. 

 Mendeleef respecting the density of the new element. — Comptes 

 Rendus de V Academic des Sciences, vol. lxxxiii. pp. 611-613. 



HARMONICS. 

 The value of </>(m, n) is stated inaccuratelv in the long footnote at 

 pp. 302,303. If (2^ 



1.3.5 ...(2i-l) 

 and R = V 1 — 21.hJi . f + 27i 2 . lh"\ t\ 



then I find ( K+V\~ W- 1 ** 



n ' T ) 2m + 2i-l' 

 and accordingly the Bipotential in space of 2i-\-l dimensions is 

 r° aidt^-i 



Also I find that in space of 2i-\-2 dimensions the prospherical 

 Bipotential is 



2tt* f<> cU 



1 . 2 . 3 . . . ij i (1— 2zhh'.t+ 27i\ 2h'\ f)i 



The above results may be extended to general quadric surfaces 

 and prosurfaces. Thus, ex. c/r., if an indefinitely thin ellipsoidal 

 shell be contained between two concentric surfaces, the equation to 

 one of which is Gr(x, y, z) = 1, where G is a general quadric, and if 

 the squared density at x, y, z is the reciprocal of 



G(x—7i, y—k, z—l) . Gr(x — hf, y—k', z— £'), 

 then the mass of the shell divided by its volume is 

 ,0 dt 



f 



s/1-A.f + Bt 4 

 where 



and 



B=>G(h,7c, ^.GcQi'^Tc'J). 

 It is further noticeable that if ~F and Gr are contravariantive 

 forms, each numerator of the fractions expressing the differential 



derivatives of — ==- is nullified by the operator 

 VG-O?, y, z) 



d d_ d\ m 

 dx dy dz J ' 



and conversely, every rational integer function of x, y, z so nulli- 

 fiable is a linear function of such numerators. And so in general 

 the Theory of Spherical and Prospherical merges in a theory of 

 Conicoiclal and Proconicoidal Harmonics. — J. J. S. 

 Steamship * Parthia/ Sept. 8, 1876. 



*G 



