Burrard weighed a lot of birds, then plucked them traced their outlines onto graph paper & checked their volumes. He found their volume to wt being actually a curve with smaller birds have a larger volume per ounce than larger ones. Birds below a lb had a volume of approximately 1 sq/in per ounce as I recall. By doing all the math his formula of 1760/oz gives an average pattern of about 2½ shot per bird.
Many years ago I read an article in the "Rifleman" concerning loads for doves which went into much the same type of reasoning as Burrard, in fact as I recall it used many of his formula. The main thing I recall from it was that the author concluded that #8 shot was in most cases the best size for "Mourning" Dove. I think that I would tend to agree.