are possible, and their validity domain.

The main characteristics of the considered colour transformations are summarized in Table 2. Two of them are illustrated in Figs. 2 and 3. The analytical forms of the transformations are given below, sorted by categories. Though some formal error bars are smaller, we did not indicate uncertainties smaller than 0.001 mag in the relations given below.

Solar composition main sequence stars
-------------------------------------

### ($U-u$) vs ($u-b$)

$4000$ K $\leq~T_{\rm eff}~\leq~5500$ K (K7V - G8V)

($u-b$) $\in~[0.20;1.50]$\
$U-u =  0.049 + 0.002 (u-b) - 0.097 (u-b)^2 \pm 10^{-3}$

$5500$ K $\leq~T_{\rm eff}~\leq~10500$ K (G8V - B9V)

($u-b$) $\in~[-0.15;0.20]$\
No possible transformation.

$10500$ K $\leq~T_{\rm eff}~\leq~35000$ K (B9V - 08V)

($u-b$) $\in~[-1.40;-0.15]$\
$U-u =  -0.016 - 0.268 (u-b) - 0.043 (u-b)^2 \pm 10^{-3}$

### ($U-u$) vs ($uvw1-u$)

$3500$ K $\leq~T_{\rm eff}~\leq~7250$ K (M3V - F0V)

($uvw1-u$) $\in~[0.35;1.75]$\
$U-u =  -0.009 + 0.212 (uvw1-u) - 0.183 (uvw1-u)^2 \pm 4. 10^{-3}$

$7500$ K $\leq~T_{\rm eff}~\leq~10500$ K (A8V - B9V)

($uvw1-u$) $\in~[-0.10;0.30]$\
$U-u =  0.001 - 0.158 (uvw1-u) + 0.860 (uvw1-u)^2 \pm 2.10^{-3}$

$10500$ K $\leq~T_{\rm eff}~\leq~35000$ K (B9V - O8V)

($uvw1-u$) $\in~[-0.75;-0.10]$\
$U-u =  -0.019 - 0.485 (uvw1-u) - 0.128 (uvw1-u)^2 \pm 2.10^{-3}$

### ($B-b$) vs ($b-v$)

$4000$ 