on the next day but one（but是什么意思）

I saw that she wished me to appeal to his sympathies by every means in my power. She was weeping freely. I was extraordinarily touched. I felt indignant at Strickland's cold cruelty, and I promised to do all I could to bring him back. I agreed to go over on the next day but one, and to stay in Paris till I had achieved something. Then, as it was growing late and we were both exhausted by so much emotion, I left her.

请教老师：I agreed to go over on the next day but one 中，but在这里是什么意思？ on the next day but one 究竟是什么意思？主要是but one怎么理解？顺便问一下老师，这里的the不可以去掉吧？是否因为是从过去的角度谈论the next week的？