Overall I'm liking the story. The writing is okay, though you need to use spell check and get a beta, and the idea is something new and I really like it. For this particular chapter a few things jump out at me as odd though:
1) You spend a paragraph talking about how record breakingly hot it was, including details about the grass and trees, etc. and in the next paragraph you have Harry go outside because it was such a nice day. You could just delete the whole 'it was hot' paragraph.
2) What the hell kind of library can ANYONE go into and not find any reference to MERLIN?? Sure, not the details I'm sure you could find in the Wizarding World, but there are hundreds of books with Merlin in them.
3) You spend about a paragraph explaining that Harry wasn't going to try anything until he had finished the book because it said to make sure you knew it all first, and then a few paragraphs later you have him trying to manipulate Petunia just because it is his birthday, and only getting a measly box of crackers out of it (which you then seemed to forget were in a box since you said he put several of them (implying single crackers and not hiding the box itself) in his cupboard).
4) I could be wrong, but I'm fairly sure that in the first chapter you mentioned mind magics. I know the book wasn't going to be ABOUT legilimensy/occlumensy, but the way you have it written and who is doing the writing, it is HIGHLY likely that they would be mentioned. Even if they weren't it isn't very likely that nothing magical (aside from a few names) would be mentioned either; it was written BY a wizard FOR a wizard after all.
Overall... well, I AM following this story since I really do like the idea, but I'm hoping you clean up the writing a bit in future chapters.
Thanks for the review! You've pointed out a lot of things which I'll definitely try to fix in the future. I realize that there are quite a few mistakes, but I'll go over the stuff a couple more times the next time I write a chapter to ensure that this doesn't happen anymore.
Addressing point number 4 (because that's the only one I even SLIGHTLY disagree with), this book that was written by Potter's ancestor was focused entirely on the art of manipulation, not mind magics (legillimancy, in my humble opinion, is not actually changing a person's memories/emotions, but rather taking a look at them and seeing what they consist of).
As for there being nothing magical mentioned, please take note of Harry not knowing all of the words and having a difficult time understanding some things. ;)
Anyway, thank you very much for your critical review (I value one critical review over one-hundred reviews filled with praises)!
Hope you continue to read and criticize in the future,