= 485\, $nm (top data set). Using $t=4\,\sunit$ for the same data systematically underestimates the motion of larger beads (green circles). The curves are empirical polynomial fits to the datasets(see Table \[tab:fit\]). ](bitmaps/cali-curve-eq4sclean1.eps "fig:"){width="4truein"}

   Time \[s\]   Diameter   $a\times10^{-5}$        $ b$               $c$
  ------------ ---------- ------------------ ----------------- -----------------
       5         200nm     -2.58 $\pm$ 0.68   0.17 $\pm$ 0.02    -4.5$\pm$14.8
       10        490nm     -3.37 $\pm$ 0.47   0.19 $\pm$ 0.01    57.3$\pm$ 7.2
       20        970nm     –3.49 $\pm$0.46    0.20 $\pm$ 0.01   109.5 $\pm$ 8.7
       4         200nm     -2.60 $\pm$0.69    0.17 $\pm$0.02    -4.75$\pm$14.7
       4         490nm     -3.17 $\pm$ 0.41   0.18$\pm$ 0.01    58.05$\pm$ 6.6
       4         970nm     –3.31 $\pm$0.48    0.18 $\pm$ 0.01   107.7 $\pm$ 8.7

Theoretical predictions
-----------------------

![\[calibrplot\] 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 