[99] It is well to remember, however, that the laws we have considered are all in the image of Newton’s in that they contain no derivatives of the potentials to an order higher than the second. If this restriction is omitted, a number of alternative laws become possible. Inasmuch as their study presents tremendous mathematical difficulties they have not been investigated; and it is hard to say what might be the nature of their solutions.
[100] There are also the other time-potentials, i.e.,
,
,
. But as, in our mesh-system, the direction of time is perpendicular to those of space, these potentials vanish in the present case, and we are left with
.