Hi, I am a dog trainer. Despite most Jack Russels having this natural instinct to bark, it is their way of making up for their lack of size! However mos annoying for their owners! When he is in mid rant, DO NOT bend down to him and say "NO", as this only gives dog the idea that you are pleased (any attention to a dog is good attention), all dogs behave much worse when they are on a lead, as they feel constrained! When your dog is barking at another dog, do not tighten your grip on the lead, keep it lose, as any tention from you can be felt through the lead to the dog, buy a water spray bottle, fill with water and take this out with you, when he is barking, losen your grip on the lead (taking care not to let go completely) spray the water at your dog, but say NOTHING!!
Keep spraying and walking at the same time, all the while saying nothing. After a few attempts at this the dog will realise that he isn't getting any attention for his behaviour and that you are not stressed at him barking, as the lead is not tense.
This may take a few trips to the park, but persevere, as dogs are persistent and hope that you will give in first.
Good luck