Mutt, which part of the FAR's are you reading about the critical engine, because certain FAR parts do not apply to jet aircraft.
There is no definition of critical engine on twin jet aircraft as either engine will have the same effect to controllability, in zero wind conditions. Now what is mentioned earlier by others such as Lancer with reference to the x-wind effects are correct but that is just an external effect.
On 4 engine jets we have a speed called Vmcl-2 which is the lowest controllable speed with loss of both engines on the same side which is the worst case senario.

A340driver,

Sec. 25.107 Takeoff speeds.

(a) V1 must be established in relation to VEF as follows:
(1) VEF is the calibrated airspeed at which the critical engine is assumed to fail. VEF must be selected by the applicant, but may not be less than VMCG, determined under Sec. 25.149(e).
(2) V1, in terms of calibrated airspeed, is selected by the applicant;
however, V1 may not be less than VEF plus the speed gained with critical engine inoperative during the time interval between the instant at which the critical engine is failed, and the instant at which the pilot recognizes and reacts to the engine failure, as indicated by the pilot's initiation of the first action (e.g., applying brakes, reducing thrust, deploying speed brakes) to stop the airplane during accelerate-stop tests.

You are correct in saying that the “defined” critical engine doesn’t apply to twin engined jet aircraft, primarily because the aircraft was tested in perfect conditions with NO WIND.

Are we therefore right in allowing VMCG limited V1 speeds when there is a crosswind ?

Would love to continue, but I have an appointment with a pint of Guinness in the Irish Village.

Mutt.

.. which is why those in the know, when circumstances permit, don't needlessly expose themselves to very low speed schedules in crosswind conditions .... that way, the crosswind related increase in Vmcg can still be kept below the nominated V1 ...

Jhieminga, an aircraft flying straight and Level is at a positive angle of attack, and this only gives a low assymetric blade effect (AKA "P" factor) - you are forgetting about torque reaction, slipstream effect and the gyroscopic effect.