  Eisenstein Loeb and Turner (ELT) have recently proposed a method for
estimating the dynamical masses of large-scale filaments, whereby the filament
is modeled by an axisymmetric, isothermal cylinder, for which ELT derive a
global relation between the (constant) velocity dispersion and the total line
density. We first show that the model assumptions of ELT can be relaxed
materially: an exact relation between the velocity and line density is derived
for any cylinder (not necessarily axisymmetric), with an arbitrary constituent
distribution function (so isothermality need not be assumed). We then consider
the same problem in the context of the modified dynamics (MOND). After a brief
comparison between scaling properties in the two theories, we study idealized
MOND model filaments. A preliminary application to the segment of the
Perseus-Pisces filament treated by ELT, gives MOND M/L estimates of order 10
s.u., compared with the Newtonian value of about 450, which ELT find. In spite
of the large uncertainties still besetting the analysis, this instance of MOND
application is of particular interest because: 1. Objects of this geometry have
not been dealt with before. 2. It pertains to large-scale structure. 3. The
typical accelerations involved are the lowest so far encountered in a
semi-virialized system.
