You realize that the link you provided is for the 1915 version of RROR. I might be mistaken but I REALLY think that the language style and the some of the text has changed since then.
If your bylaws indicate the principal is a member of your Exec board, seems s/he has voting privileges unless the bylaws specifically indicate otherwise. If your bylaws are silent on tie-breaking votes, and you follow parliamentary procedure, the president casts the tie breaker.
Roberts Rules of Order Revised the 10th edition (gold color looking book) You can get it at your bookstore or have them order it. E-bay, Amazon.com... Usually the principal should refrain from voting. In our by-laws, in case of a tie our secretary casts the deciding vote. Good luck!!
Any larger bookstore should carry a copy. If you read it carefully, it will guide you thru what to do. Chapter 14 is where to start.For your problem I suggest NOT getting the BRIEF version. If your bylaws don't mention that parliamentary authority then no one HAS to abide by the book. Common sense might prevail and your people will at least accept the notion that some form of written structure is better than chaos.