Chree's method of investigating recurrence phenomena in international magnetic character-numbers has been applied to the daily mean cosmic-ray intensities, as given by the Carnegie Institution's Model C cosmic-ray meter at Teoloyucan, Mexico, somewhat more fully than in the study reported previously by Mr. P. S. Gill. The five days of highest cosmic-ray intensity (high${I}_{0}$) were selected from each of seventeen calendar months, and to each of these days was assigned the number $n=0$. The ${I}_{0}$ for each of these 85 high ${I}_{0}$ days was tabulated, also the ${I}_{0}'\mathrm{s}$ for the consecutive days following (and preceding) each of these selected days, up to $n=+131$ and $n=\ensuremath{-}132$ The average of the 70 to 85 ${I}_{0}'\mathrm{s}$ tabulated for each $n$ value, when plotted against $n$ gives a curve analogous to Chree's "positive pulses." A similar "negative-pulse" curve was obtained by selecting the five lowest ${I}_{0}$ days per month to be the "zero" days. Chree's material (20 years' data) gave sharp pulses at $n=\ifmmode\pm\else\textpm\fi{}27,\ifmmode\pm\else\textpm\fi{}54,\ifmmode\pm\else\textpm\fi{}81,\ifmmode\pm\else\textpm\fi{}108$ with the curves relatively flat between pulses, and pulse-amplitudes decreasing with increasing $n$. The cosmic-ray curves have maxima (or minima) at intervals of 27 to 29 days and an amplitude of about 0.3 of one percent. Unlike Chree's curves, however, they are markedly sinusoidal, the maxima being much less sharp and showing very little damping, if any. Somewhat sharper maxima are shown by the difference-curve (positive-pulse minus negative-pulse), and these average between 27 and 28 days apart.This high correlation, on the average, between the intensity of cosmic-ray ionization at one time and that about one synodic rotation of the sun later is, from this evidence, a recurrence or interval phenomenon, not necessarily a true periodic phenomenon. The possibility that the latter, or at least a quasi-periodicity, is involved is suggested by the persistence in pulse-amplitude.