They were wrong

A compound column is inherently stable in respect of the temperature of the reflux returned by the head condenser, so no special precautions need be taken to control the flow of coolant in that condenser, other than keeping it steady at a rate that ensures complete condensation of all vapor reaching it. Many people have spent needless hours worrying and struggling to design systems that avoid cooling the condensate, and all the time they were pursuing the wrong goal. Some time spent up front studying theory can save many hours of fruitless toil.

(If you're using Cooling or Vapor Management (Chapter 4) to control reflux, then of course you don't want complete condensation, but the key point is that the stability of the system ensures that whatever reflux ratio you do impose will remain constant.

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