The possibility of obtaining some type of confinement of particles is discussed in a field theory with multipole fields of the N-th order. The limiting case N -+ ~ yields various forros of Jtatic confincment potcntials.1. The d a t a of the c h a r m o n i u m s p e c t r u m seem to fit to experiments quite well [1, 2, 3] when a eonfinement potential between c and ~ is supposed in the form:r F o r e x a m p l e [2] gives the values of ~, A, K as = --0 , 2 , K = ----, a = 0 , 2 f m . a 2T h e value of A is irrelevant (actually A = 0 is taken), it is an additive constant only to the total energy. A great v a r i e t y of theoretical considerations predicts the forro (1). We quote two r a t h e r conservative field theoretical approaches only [4,5] (similar to ours [61), where other referenees can be found.In a previous work [6] we have ealled the attention to multipole fields as possible sourees of some kind of particle confinement. There the free L a g r a n g i a n has been proposed to possess the forroand it has been shown t h a t the fields A, B, C interacting vŸ ah interaction L a g r a n g i a n L I in the form L i = -~cq~, q~ = glA + g2B + gaC, * On leave of absence from the Institute of Theorctical Physics, Roland E6tv6s University,