Weber-like interactions and energy conservation

Velocity-dependent forces varying as k((r) over cap/r)(1 - mu(r) over dot(2) + gamma r(r) double over dot) (such as Weber force), here called Weber-like forces, are examined from the point of view of energy conservation and it is proved that they are conservative if and only if gamma = 2 mu. As a consequence, it is shown that gravitational theories employing Weber-like forces cannot be conservative and also yield both the precession of the perihelion of Mercury as well as the gravitational deflection of light.