23 
1921-22.] On Tubes of Electromagnetic Force. 
and another family of geometrical forms by the same equations with 
Xg and ^2 substituted for \ and /x^. 
When the two conditions of unconditional integrability are satisfied, 
these geometrical forms are families of surfaces intersecting each other 
everywhere at right angles, and resembling the electropotential and 
magnetopotential surfaces previously introduced ; when the conditions 
of unconditional integrability are not satisfied, the geometrical forms 
are curves in the four-dimensional hyperspace. In the former case, the 
tubes of force or calamoids can be introduced in precisely the same way 
as in § 7 ; in the latter case, the problem is somewhat more complicated 
from the geometrical point of view, and will be deferred to a subsequent 
paper. In all cases, the partial differential equations satisfied by the 
calamoids are the same as those found in the special case, namely? 
equations (I7) : and the integral properties found in § 12 are valid in 
the general case just as in the special case. 
(Issued sepai'ately December 27 , 1921 .) 
