For a topic as covered and re-covered and re-re-covered as the Norman Conquest, I (as a teacher) would absolutely not accept a secondary source from 1902. My honest thought would be, My student just found this on Google Books and was too lazy to go to the library in person.

That's not to say that historical scholarship from the turn of the 20th century is without merit. I have some sources from the late 19th in my dissertation! But if I cite them for more than basic facts (like "this sentence in primary source is a reference to this other primary source"), I have to be very, very careful to contextualize them properly. And more importantly, I need to demonstrate that no one since 1892 has developed the idea further or offered evidence to support/contradict it. I need to show that positivist, political, confessional, nationalist 1900s historical methodology still holds up to a critical reading of its use of the primary sources.

I would absolutely not expect this in a high school or undergraduate paper.

I would expect you to find a more recent source that does that work for you. :)

I'd use it, but I would bear in mind at all times that the age of the book means it will pre-date anything we have learned in the last 114 years. It's probably devoid of any input from archaeology, anthropology, cross-disciplinary research, newly discovered primary documentation, modern economic theories, or current thinking on how the environment shapes events. It might also be steeped in some of the intellectual fads of its time --especially when it comes to race and nationalism. For all that, it might be a truly excellent summation of primary documents and well-understood events. Victorian and Edwardian academics were no slouch when it came to the history of their own country!

Why not use this resource to familiarize yourself with the period and cite it in your paper when referencing contextual points that other books could also cover. When you read the other three books, be on the lookout for where they differ from your first book. Why do they differ? What new information or school of thought has shaped that more recent book? I expect you will get a lot out of the experience if you approach it that way.

I would talk to the professor about it, explain why you think the source is useful, and ask if that will be ok for the assignment. We here can't predict how your work will be graded (and I say this as a college instructor myself) - you'll have to go to your prof for that information.

In general terms, anything from 1902 would be very suspicious. The way we read sources has changed a lot in the past century. Scholars 100 years ago were excellent, but their methods and questions were different, and I would only trust them if I could check their claims against their sources. And at that point, why not just cite the primary sources themselves?

In some cases, however, old scholarship really does speak well to modern questions. But determining whether or not it does often requires detailed knowledge of the historiography - something that your professor may have, but (at this stage) you yourself likely do not. Which brings me back to where we started: you should stop by your professor's office hours and ask.