Three-halves law in sunspot cycle shape

Annual mean sunspot numbers R(t) since 1700 show evidence of a non-linear effect, first evidenced by the detection of a third harmonic in Rsub(±)(t), the alternating representation of the magnetic (22 yr) cycle of solar activity. The form of the non-linearity proves to be a three-halves law R(t) = 100[|Rsub(lin)(t)|/83]sup(3/2), where Rsub(lin)(t), also an alternating quantity, is a presumed underlying or 'linearized' sunspot number. The non-linearity is of such a nature as to cause strong semi-cycles to be sharper than sinusoidal and to produce the inflexion in Rsub(±)(t) noted at sunspot minimum. The difference R(t) -|Rsub(lin)(t)| is sufficiently like a third harmonic, for semicycles of average strength, to explain the band around 22/3 yr which is noticeable in the spectrum of Rsub(±)(t). (author)