The phrase "next day in the course of time" can be substituted with several words that carry similar meanings. Firstly, it can be replaced with the word "subsequently," meaning it will happen at a later time following an event or action. Secondly, "eventually" can be used to describe a future event that will occur in due time. Additionally, "ultimately" can be used to signify a definitive outcome or a final decision. Another possible synonym is "eventual," which is used to describe something that will happen at some unknown point in the future. Lastly, the phrase "in due course" can be used to express that something will happen in its proper time and sequence.