The Bible says concerning the eagle:

In the mid 19th century it was commonly believed that eagles found their prey by smell. In Cassell’s Book of Birds (1869-1873) Volume 2 p.9 we read:

In Volume 1 p. 9 of the same series we read the experimental evidence with vultures (which are similar to eagles) demonstrating that sight is the sense used:

"The SENSE OF SMELL in birds has afforded subject-matter for much discussion, and great obscurity still exists with reference to the extent to which they make use of their olfactory organs. It has been generally asserted that birds of prey are gifted with an acute perception of odours, and are thus enabled to discover their food at a distance;  but the rapidity with which vultures are known to assemble round the carcase of an animal too recently killed to attract them by putrefactive exhalations has induced many observers to consider them as being directed entirely by sight

That this latter is the preferable theory appears to be sufficiently established by the experiments of Audubon, which go to show that these birds possess a sense of smell very far inferior to that conferred upon carnivorous quadrupeds, and that, so far from guiding them to their prey from a distance,  it affords them no indication of its presence even when close at hand.

Having procured the skin of a deer, M. Audubon stuffed it full of hay, and after the whole had become perfectly dry and hard, he placed it in the middle of an open field, laying it down on its back in the attitude of a dead animal. In the course of a few minutes he perceived a vulture flying towards and alighting near it. Quite unsuspicious of the deception, the bird immediately proceeded to attack the carcase, as usual, in the most vulnerable points. Failing in this, he next, with much exertion, tore open the seams with which the skin had been stitched, and appeared earnestly intent upon getting at the flesh which he expected to find within, and of the absence of which not one of his senses was able to inform him. Finding that his efforts, which were long reiterated, led to no other result than the pulling out of sundry quantities of hay, he at length, though with evident reluctance, gave up the attempt, and took flight in pursuit of other game.

Another experiment, the converse of the preceding, was then tried:- A large dead hog was concealed in a narrow and winding ravine, about twenty feet deeper than the level of the ground around it, and filled with briars and high cane. This was done in the month of July, in a tropical climate, where putrefaction takes place with great rapidity;  yet, although many vultures were seen sailing in all directions over the spot where the putrid carcase was lying covered only with twigs of cane and light underwood, none of them appeared at all to suspect its presence.

Nevertheless, notwithstanding the apparently decisive result of the above experiments, anatomy teaches us that the olfactory apparatus in this class of animals is largely developed, and indicates by its extent that it is well adapted to investigate the odorous properties of the air taken in for respiration."

Some writers opted for both conclusions. W Nicholson wrote:

Some other ancient sources besides the Bible were also correct. Pliny The Elder (23-79 AD) for example wrote: "There remains the sea-eagle, which has the keenest eyesight…" (Penguin. Translated by J F Healy)

The fact is, such claims in the Bible are usually based upon observational data, and has no relevance to scientific fact. Anyone who has ever seen eagles, hawks and falcons circling and hovering, and then suddenly drop on their prey, would assume that they were using exceptional eyesight to locate their prey.

However, while it seems unlikely that such birds would be able to smell an animal in a field of grass, hundreds of metres below, the fact is we do not really know. It is entirely possible that birds can use both smell and vision in locating prey. We do not know what degree of smell of the animal is carried upwards on air currents, but I can assure you from long experience animals produce a particularly unique odour when frightened, and perhaps birds can pick up traces of that odour.

One must appreciate that different birds of prey lead different life styles; Eagles, hawks and falcons, spend all day searching for food, whereas vultures tend to spend the early hours of the day resting. Relying on thermal currents to a far greater degree than eagles, hawks and falcons, they wait until the land has heated up sufficiently to provide ample thermal updrafts to enable them to glide for miles.

This was outlined in a recent television programme, which studied the vultures of Miami. Large flocks of vultures have settled in that city. They live on the roofs of the high buildings, and they spend the morning waiting for the sun to heat up the bitumen and concrete roads and car parks of the city. In the same programme it was mentioned that vultures can smell dead flesh from a distance of some thirty miles.

Given their life style, and the environment in which they live, it appears that vultures use the thermals to circle seeking to pick up the smell of decaying flesh, and then fly to the site, unlike the other birds of prey which actively seek out living prey with their eyes.

With our extremely limited sense of smell we cannot appreciate the totally hidden olfactory world which animals and birds experience. Furthermore, for a variety of reasons, the olfactory world is the most difficult to study, especially in the wild. As a result I believe that we should refrain from making decisions on what sense is actually used by birds, until we have the equipment which will allow us to study the matter properly.

In the meantime, biblical claims should be taken with a large dose of skepticism; they are no more than glorified folklore, and while they can often be correct, they can also be totally invalid.