numbered in his catalogue 225. This is probably a mistake, for Fort Pierre is in South Dakota, which will leave the Lytle meteorite as the first recoded in the state.

While this notice was going to press a second meteorite, also turned up by the plow, was procured by the author from southwestern Nebraska. This, too, is a pure iron meteorite weighing 2,783.3 grams (6.13 pounds). When etched the Widmanstätten figures appeared but feebly, due possibly to some derangement consequent to the rough handling to which this excellent specimen has been subjected, it having been pounded and battered by a heavy hammer. See Figs. 6 and 7.

The University of Nebraska,

December 26, 1896.

PLATE VI. Four views of the York county, Nebr, meteorite.

WHAT IS MATHEMATICS?

ELLERY W. DAVIS.

The definition, "Mathematics is the science of quantity," will not stand in the light of modern developments. For example: teacher, p = pupil.

Let t

Then :p the relation of teacher to pupil.

We have the following multiplication table, where the relations at the left are

is pupil of pupil of does not exist. The rule of combination is that two relations give a new relation, that of antecedent of first to consequent of second, if consequent of first is antecedent of second; otherwise they give zero.

Using the same rule of multiplication consider the expressions, -never mind their meaning,—

precisely that of the quaternion units.

Is all this mathematics? Has the idea of quantity for a moment entered in? The example is from Charles Pierce's Logic of Relatives. He has among other algebras expressed all of the two hundred odd of his father's "Linear Associative Algebra" in this notation.

Take another example, this time from the theory of groups.

Let (1h) denote the operation that changes love to hate and hate to love, while (wp) similarly interchanges wealth and penury.

Then (h): = 1, i. e., leaves all as it was.

Likewise (wp)2 = 1.

While (lh) (up) gives both transformations at once.

The similarity to the quaternion table is manifest. In fact, the quaternion units are identity and three quarter-rotations, while here we could take for units identity and three half-rotations.

Any meanings whatsoever may be given to our symbols that are consistent with the purely formal laws of combination. It is not the subject-matter, but the character of the reasoning and the method of carrying it on, that makes the science rather ab

stract. The reasoning is deductive, rather intricate, and generally carried on by an elaborate symbolism. Wherever this is so, whether in physics, chemistry, or biology, economics, logic, or philosophy, we recognize it as mathematics and we know that only the mathematical mind can successfully grapple with it.

I plead, then, that all who have, in any degree, mathematical power should, no matter what their chosen line of work, develop that power. At any time an occasion demanding the use of that power is liable to arise. I would that a large proportion of scientific men, especially, could have what Darwin has called their "sixth sense" developed. I would, too, that all mathematicians could take at least a master's course in some non-mathematical science. It seems to me that no one science can so well serve to co-ordinate and, as it were, bind together all of the sciences as that queen of them all, mathematics.