of the genera. Perhaps it may be discovered, that the whole family of vultures are altogether indebted to the eye in their search after food; indeed this may yet be found true in regard to the whole feathered tribe. It is, I believe, a common practice in England, for persons who attend on the decoys for wild ducks, to carry a piece of burning peat which they hold near their mouths, to prevent the birds from smelling them, as it is also customary in America to burn gunpowder in various portions of the cornfields, under an impression that the smell of the powder will frighten away the crows. The powder manufacturers can have no great objection to this latter practice, and it must be confessed, that it is among the most innocent ways that powder can be wasted. But I fear that this will not benefit the crops of the farmer. These birds, together with the raven,* and even the wild turkey,† can be approached under cover of a bank or tree, and if they do not either see or hear you, it will, I apprehend, be a difficult matter for them to find you out, by their olfactory powers. Indeed I am of opinion that while to quadrupeds (particularly carnivorous ones) the faculty of scent is their peculiar province, this organ is but imperfectly developed in birds. As it does, however, exist, (although in an inferior degree), I am not disposed to deny to birds the power of smell altogether, nor would I wish to advance the opinion that the vulture does not possess the faculty of smelling in the slightest degree, (although it has not been discovered by our experiments). All that I contend for is, that he is not assisted by this faculty in procuring his foodthat he cannot smell better, for instance, than hawks or owls, who, it is known, are indebted altogether to their sight, in discovering their prey. If our vultures had to depend on their olfactory powers alone, in procuring food, what would become of them in cold winters, in Kentucky and other of our western states, where they remain all the year, and where the earth is bound up with frost for months at a time, and where consequently, during that

* Corvus Corax,

Meleagris Gallipavo.

period, putridity does not take place? And if they depended alone on tainted meat for food, how soon would the whole race (at least in our temperate climates) die of hunger?

How easily error may be perpetuated from age to age, we may learn from a thousand other visionary notions, which the careful observations of recent travellers and naturalists have exploded. At this day, the belief is very general in this country, that immediately after a deer has been killed, the vultures, at the distance of many miles, are seen coming in a direct line, against the wind, scenting the slaughtered animal. This may be accounted for, with a little observation, upon rational principles. When a deer* is killed, the entrails are immediately taken out; these, together with the blood which covers the earth to some extent, are seen by some passing bird-he directly commences sailing around the neighborhood-he is observed by those at a distance; the peculiar motion of his wings, well known to those of his own species, communicates to them the intelligence that something good for them is perceived. These, hastening to the place, give information to those who are still further off, and in the course of an hour, a very great number are guided to the spot. But it will scarcely be argued, that this great concourse of vultures has been attracted by the effluvium of putrid flesh, since the animal has been killed but an hour before.

In the prosecution of our experiments, we discovered that the powers of sight in our vultures were not as great as those possessed by the falcon tribe. A dead fowl was discovered by them at the distance of 70 or 80 yards; a sheep at 100 or 120 yards. These, however, were stationary objects, lying on the ground. One of their own species, however, flying in the air, is no doubt observed by them at a much greater distance. It may easily be conceived why the sight of the vulture is less acute than that of hawks or cagles. The latter prey upon birds, quadrupeds, &c., for which they have to hunt, the former feed chiefly upon dead birds, quadrupeds or reptiles, and fre

*Cervus Virginianus.

quently those of a large size, which it requires no extraordinary powers of vision to discover. An argument much relied upon by those who advocate the doctrine of the olfactory powers of vultures, is the circumstance of their usually flying against the wind, as if to discover and follow some current of tainted air. This practice, it may easily be perceived, is not more common to the vulture than to that of any other bird. It is a mistaken idea, that birds in their migrations, or on any other occasion, prefer flying with the wind. This is inconvenient and uncomfortable to them, and the careful observer of the flight of birds, is well convinced that all birds-the vulture among the rest, prefer facing the wind, not to enable them to smell their food, but to render their flight more easy and pleasant.

It may next be inquired, for what purpose are the wide nostrils and olfactory nerves given to the vultures, if they are not intended to assist them in procuring their food? To this I answer, that the olfactory nerves of our vultures are not larger than those of many other birds, and their nostrils are less even than those of the hooping crane, * which discovers its food, (as I strongly suspect every bird does), by the eye alone. The wide orifice in the beaks of vultures, and which is generally considered as the true nostril, is probably a wise provision of nature to enable a bird which from its filthy habits of feeding, is continually exposed to have its nostrils closed up-to blow out any substance calculated to obstruct them. The same may be said of the hooping crane, which, from the manner of its digging for roots in the earth, is liable to the same inconveniences. Several heads of the vultures are now in the hands of individuals connected with our medical colleges for dissection. A satisfactory elucidation of the subject will require time, patience, and an extensive knowledge of comparative anatomy in regard to the various species of birds. The result of these investigations will probably be communicated to the public in the course of a few months.

After having resorted to the means detailed above, to satisfy myself of the accuracy of the statements of Audu

*Grus Americanus Temm.

bon, as regards the habits of the turkey buzzard detailed in Jameson's Journal, I once more carefully read over his remarks on the subject, and I now feel bound to declare, that every statement contained in that communication, is in accordance with my own experience, after a residence of twenty years in a country where the vultures are more abundant than any other birds-and I have reason to hope from the characters of the writers who have doubted his veracity, that when they have read a detail of these experiments, they will either repeat them to the satisfaction of their own minds, or place confidence in the statements of those who have taken this trouble; and that they, with that generosity of feeling so distinctive of those who are engaged in liberal and kindred pursuits, will be gratified to assign to Audubon, that meed of praise which he so undoubtedly merits.

Charleston, Jan, 18th. 1834.

[Furnished for the Tracts and Lyceum.]

FURTHER OBSERVATIONS ON THE QUADRATURE OF THE
CIRCLE.

HAVING Sometimes reflected on the quadrature of the circle, though I have never attempted the solution of this long celebrated problem, and my ideas being excited afresh upon this subject by the reading of some articles in the Tracts and Lyceum relating to it, I have undertaken to commit some of my cogitations to paper.

I have long been convinced of the inanity of all the pretended solutions of the question, which so frequently intrude themselves on the public. I have, however, permitted fancy to intrude itself into the field of mathematics, and consequently, have imagined things concerning the solution of this irreducible. I am inclined to think it not only true, but actually demonstrable, that the expression of the quadrature, or in other words, the ratio of the diameter and circumference of a circle, to the determination of

which this question reduces itself, is not merely incommensurable in numbers, but inexpressible by any algebraic formula, other than an irreducible infinite series. That is, that it is not expressible in terms of surd roots of any kind, or at least, of the second degree.

The expressions of surd roots are, it is well known to mathematicians, capable of actual geometric developement, the square root of 2 being involved in the expression of the diagonal line of a square, for instance. Now though a portion of the numerical developement of the ratio of the diameter and circumference of the circle has been actually obtained, yet no geometrical process has ever been discovered, of which we could avail ourselves, actually to develope this ratio. Now the expression of the dimensions of a curve would seem, in the nature of things, to be of a different kind from the expressions of rectilineal quantities. No part of a circle, unless we take an arc infinitely small or a circle infinitely large, can be compared with a right line. Then, since surds of the second degree are expressions of right lines, I think we may conclude, that the ratio sought cannot be expressed in terms of surds of the second degree. This is by no means a demonstration, but it may serve to show how remote we are from being able to form a conception of the kind of quantity of which curved lines are the expression.

If this question ever meets with a true geometrical solution, I am convinced that it will be in no other way than the following: that some curve of the higher orders may be discovered, whose relation to the circle shall be such, that it, or some of its dependent lines, may cut the circle at such points, as that if a square were made to intersect the circle in those points, its area would be that of the circle. But after all, if any curve be discovered which will give the true section of the circle, let it be remembered, that it will not render the area of the circle less incommensurable; and that this intersecting curve will and must be as incommensurable as the circle itself.

A method has been discovered, or is in progress, as your correspondent is informed, of solving the problem by constructing spherical logarithms which are to give the