I wonder if Coffey's logic book was worse than most of the time. I have not read it, but it's available: https://archive.org/details/thescienceoflogi01coffuoft I have strong feelings about the usefulness of this sort of logic despite its flaws, and would have been interested to know his thoughts on W.S. Jevons' book.
That sort of logic is of really limited usefulness. It does not even allow, strictly speaking, to take "Horse is an animal" and derive "a horse's head is an animal's head". That's is why mathematicians tended to disregard logic as useless for the maths up until the late XIX century when they actually bothered to invent the mathematical logic -- that's when the modern delusion that "logic is a part of mathematics" app…
> It does not even allow, strictly speaking, to take "Horse is an animal" and derive "a horse's head is an animal's head".
This is because it doesn't permit relations in a systematic way. In FOL, you would express "head of" as binary relations (one for horse, one for animal since you cannot quantify over predicates; you would need a HOL for that). But traditional logic can be extended with relations as Sommers has done in term functor logic.
Interestingly, Veatch argues that FOL cannot tell you what a thing is. If predicates are modeled after relations—and Russell also includes the unary predicate here as a relation between subject and property instead of multiple subjects—then you cannot say what a thing is because relations don't say what their relata are. So you're left with a peculiar situation where individuals are bare particulars which brings up all sorts of other questions.
Sommers and Englebretsen have interesting things to say in response to Russell and Frege as well as their defenders (like Geach and Dummett).