each of the three bead sizes studied, two curves are shown. From top to bottom, each pair of curves assumes persistence length values $47{}$ and $39\,\nmunit$, respectively, a range appropriate for the solution conditions we used [@wang97a]. There are *no fit parameters;* the theoretical model uses values for bead diameter given by the manufacturer’s specification. The bumpiness in the curves reflects the statistical character of the Monte Carlo algorithm that generated them. ](calibrationfigPN/KBT_calib.eps "fig:"){width="3.54truein"} ![\[calibrplot\] Theoretical prediction of equilibrium bead excursion, following a method introduced in [@sega06a; @Nelson2006]. *Dots:* Experimental values (same as red squares in ). Each dot represents $20$–$200$ different observed beads, with the given tether length. Each such bead was observed for about $200\,\sunit$, yielding $(200\,\sunit)/t$ measurements of the RMS motion, which were averaged; here $t=20,\ 10$, and $5\,$s as in . Each data point shown is the average of these averages; error bars represent the variation (standard deviation) among the beads. *Curves:* Theoretically predicted RMS motion, corrected for the blurring effect of finite shutter time. For each of the three bead sizes studied, two curves are shown. From top to bottom, each pair of curves assumes persistence length values $47{}$ and $39\,\nmunit$, respectively, a range appropriate 