What was the important rule of survival Brian learned in either Chapter 7 or 8 of Hatchet?
The most important rule of survival Brian learned in Chapter 8 was that
"feeling sorry for yourself didn't work..It wasn't just that it was wrong to do, or that it was considered incorrect. It was more than that - it didn't work".
Brian has a couple of difficult experiences in his first few days alone. He gorges himself on gut berries, and becomes violently sick, and he panics when he finds a porcupine in his shelter and is slapped painfully on the leg by the animal's tail full of quills. After both experiences, Brian gives into self-pity, curling up into a ball and crying desperately. He discovers, however, that such a reaction is futile -
"When he sat alone in the darkness and cried and was done, was all done with it, nothing had changed...he was still alone and the self-pity had accomplished nothing" (Chapter 8).
Brian finds that it is much more productive to be calm and observant. He finds that when he does act and react in this way, he learns much about his environment and picks up a good many bits of knowledge and skill that will help ensure his survival. By picking only the ripest berries and eating in moderation he can hold off starvation and avoid becoming ill. By staying calm when approached by a bear, he learns that the bears are not out to hurt him, and do not even seem to mind sharing the delicious raspberries found nearby. And by noticing the sparks that fly when he throws his hatchet against the rocks, Brian realizes that he has at his disposal a way to provide himself with that most essential element - fire (Chapters 7-8).