Q:

What is a bootless oath?

In Book X (10) of The Illiad Hector (edition: Britannica Great Books of the Western World (The Illiad and The Odessey together), rendered into English prose by Samuel Butler) swears the following oath

"May Jove the thundering husband of Juno bear witnes that no other Trojan but yourself shall mount those steeds, and that you shall have your will with them for ever."

He swears this to Dolon, son of Eumedes, who agrees to, in return for Peleus's chaiot and steeds when and if they should be captured, spy on the Achaeans and try discover their plans of battle for the next day. 
The oath is followed by the following sentence:

The oath he swore was bootless, but it made Dolon more keen on going.

Why is the oath bootless? Is it because Jove only has to witness (instead of may jove take my children, juno give me no sons etc). 
It can't be because the oath gives him no 'booty' (treasure/loot) because the horses are the boot...
Edit: There seems to be no reason (at this point) to think Hector would go back on his word, and the horses do exist, so presuming the Trojons win (which they are at this point in the story [the Achaeans are in retreat]) there is every reason to presume that Dolon will at some point recieve the horses. 
Is the oath 'bootless/useless' because the promised reward is not certain, i.e. it cannot immediately be bestowed on him? If so why is Dolon more eager to go?

A:

The specific Butler passage you reference can be found on Perseus
 line 272-348. 
An alternate 1924 translation by  A.T. Murray may also be found there.
The Murray is quite distinct from the Butler in these passages, which got me wondering about the Greek because

The use of "bootless" is undoubtedly wordplay referencing Achilles' famous heel.

Murray's translation, by contrast, merely reads:

"So spake he, and swore thereto an idle oath, and stirred the heart of Dolon.."

The Greek can be found here, line 332:

ὣς φάτο καί ῥ᾽ ἐπίορκον ἐπώμοσε, τὸν δ᾽ ὀρόθυνεν:

There is nothing in the Greek overtly relating to footwear or feet—The Ancient Greek word for "boot", here anglicized as "cothurnus" bears no relation to any of the words in the passage, but 
the use of ἐπίορκον ("epiorkon") made me think of a pun per the "pee" sound--πούς ("poos") is the Greek word for foot, which becomes, among other things, "pie" (pee-ay) in Spanish.  Butler is said to have been influenced by Cervantes, so it is quite possible the same thought would have occurred to him.  
(Puns regarding feet are a staple of Oedipus Rex, for instance.  Oedipus was pierced through his ankles when his father had him exposed him in the wilderness, and that "Oedipus" actually means "swollen foot" greatly increases the irony of the irony of revelation of his identity, which turns out to be hilariously obvious in retrospect;)
Thus, while the use of "bootless" in this passage appears to be an invention of Butler he is in very good company.  Butler's choice of bootless is not only consistent with the spirit of Ancient Greek literature, but quite brilliant imo. 

A:

From the Merriam-Webster Dictionary:

useless, unprofitable
a bootless attempt

So we can replace the word bootless like this:

The oath he swore was useless, but it made Dolon more keen on going.

The oath didn't mean anything, but it made him more keen anyway.
The way I'm understanding it, it's saying that it won't be kept. As Rand said, I'm not explaining why it won't be kept, because I'd need to actually have the book with me ;). But from what you quoted, it appears that the text - whoever the narrator is - is saying that the oath won't be kept. Perhaps it wasn't a strong enough oath; perhaps the person making it doesn't have the power to carry it out. But whoever the narrator is doesn't think that the oath will carry any weight. But, despite this, it makes whoever it was directed to more confident in what they are doing.

