Please forgive the long post. I am probably reading too much into this - however...

Contaminated Runways

Sec. 2.6.3 of CAP 698 seems to state that:

(1) Enter table with the current limit (be it FLLTOM or CLTOM), and find the mass reduction. Subtract this off, and this is the new limiting take off mass.
(2) If in the shaded area, go to the bottom table to find the V1 = Vmcg limit.
(3) The new limiting mass is the lower of (1) and (2) above

Fine. It then says to enter with the actual TOM (which is hopefully lower than the limit found above) to find the actual V1 reduction to be applied to the actual V1 speeds calculated for this mass. Again, fine.

However, I'm a bit confused by the example given in the CAP. They provide a TOM mass of 50,000kg, and enter the table to find the mass reduction. However, given the procedure above, I thought one only applies the mass reduction to the maximum mass (be it FLLTOM or CLTOM) to find the new limiting maximum, and then just check that your actual mass is below this. You don't apply the reduction to your actual mass?

So did they mean that 50,000kg is the FLLTOM? Because if it's the actual, I'd argue you need to be given the FLLTOM/CLTOM (whichever the lower), apply the reduction, and then check whether your actual mass is lower than this. I mean, why would you apply a reduction to your actual mass if it's already below the contaminated maximum?

Ignoring this, I then calculate the V1 using the density sub-graph and their (contaminated) maximum to be 118 kt with a Vmcg of 114 kt. I get a V1 reduction (after interpolation) of 12kt. So 118-12 = 106kt which is below Vmcg. According to 2.6.3, 'take off is not allowed' - However, the person writing the example appears to have just made V1=Vmcg which seems to contradict this.

Anti-Skid Inoperative

Again, I'd just like to check here - Am I correct in thinking one reduces the maximum allowed mass by 7700kg, calculates the V speeds for this reduced mass, reduces V1 by the amount shown in the table, and then checks whether the actual is below this?

Item (d) in sec 2.9.1 of CAP 698 then says:

"If the actual TOM is already less than the anti-skid inoperative limited TOM, ensure V1 does not exceed the anti skid operative V1"

The anti skid operative V1 comes from the density sub graphs (i.e. the normal way), not reduced by any value. Does it therefore mean 'ensure that it doesn't exceed the anti skid inoperative V1' (i.e. calculated using the method described in (a), (b), (c)), as this is indeed reduced. It doesn't seem to make sense as-is.

Phrased differently, the way I read (d) is 'Calculate V1 for your actual mass. Use this as the V1, unless it's above the reduced V1 calculated earlier, in which case use the lower V1(?)'

TLDR

I guess my confusion here stems from the fact that the CAP seems to imply you apply these mass and V1 reductions to the maximum mass (i.e. the current FLLTOM or CLTOM), and then check whether your actual mass and V1 is below these. Yet, in the example given for contaminated runways, they appear to use the procedure described for the maximum mass on the given 'TOM' (which to me is the actual mass).