examinations of the rock and the locality by the senior author show it to have been injected and through lower cretaceous beds. Its mineral composition and structure show it to belong to the new type of peridotites, picrite porphyry, or kimberlite of H. C. Lewis. This is the third occurrence of this rock reported in the United States, the first having been that of Elliott county, Kentucky, described by Mr. Diller; the second that of Syracuse, New York, described by Dr. G. H. Williams. It differs somewhat from the rocks of either of the other localities. It contains no enstatite like the Kentucky rock, its pyroxenic constituent being augite. It contains no ilmenite, but has perofskite in great abundance. It has less fresh olivine than that from Kentucky. There is a total absence of rhombic pyroxene.

THE DISTRIBUTION OF THE GRANITES OF THE NORTHWESTERN STATES AND THEIR GENERAL LITHOLOGIC CHARACTERS. By Prof. C. W. HALL, Uni

versity of Minnesota, Minneapolis, Minn.

[ABSTRACT.]

THE paper mentions the following as the situation of the granites occurring in Michigan, Wisconsin, Minnesota and Dakota : in Michigan frequently throughout the Marquette and Menominee iron-bearing districts; in Wisconsin in various localities within the so-called Laurentian area of that state, an area which comprises much of the northern central portion with a few outliers in the Huronian and Keweenawan areas; in Minnesota (1) in several belts along the Canadian boundary projecting southwesterly into the state; (2) quite prominent masses, whether connected with those along the boundary or not, around Vermillion, Snowbank and other lakes; (3) the great Mesabi; (4) the exposures of central Minnesota in Stearns, Sherburne, Benton, Morrison and Mille Lacs counties; in Dakota in the southerly and southwesterly portions of the Black Hills.

These granites are either intrusives or granitic veinstones. The veinstones constitute a very insignificant part of these rocks unless it be in the Black Hills where, as Crosby has recently pointed out, there are vast quantities of this material. In Minnesota and Wisconsin granitic veins seldom exceed a few feet in width.

The intrusives which make up the remainder of this great class of rocks have as a group the following general characters:

(1) A coarseness of texture when the Concord or the Barre granite of New England is taken as a type. This frequently passes into a porphyritic structure.

(2) An excessive proportion of the feldspars in their composition; orthoclase, microcline and a plagioclastic feldspar, sometimes oligoclase and sometimes labradorite, are always present.

(3) The presence of quartz in two modifications: (a) in segregated areas composed of very large individuals and (b) in streams and clusters of minute granules sometimes forming a cement between the quartz, feldspar and other constituents and sometimes saturating these minerals as a secondary product.

(4) The almost universal presence of hornblende as one of the basic constituents and from which the biotite is shown in many instances to be derived.

(5) The presence of a pyroxenic constituent, augite or diallage, in many of the fresher granites situated as a core within the hornblende areas and concluded to be the source of the hornblende which mineral is doubtless wholly secondary.

So far as the question of age can enter into the discussion of the paper it is the writer's opinion that being intrusive the granites have been intruded at various times between the formation of the Laurentian floor of the continent and the close of the agnotozoic era. They as a rock species may be regarded as the product of one of the three or four grand periods of eruptive activity which the intrusive rocks of the northwestern states represent.

ON THE INTENSITY OF EARTHQUAKES, WITH APPROXIMATE CALCULATIONS OF THE ENERGY INVOLVED. By Prof. T. C. MENDENHALL, of Rose Polytechnic Institute, Terre Haute, Ind.

As an exact science, seismology is in its infancy. Although great progress has been made during the past ten years, and especially in the development of instruments and methods for a more precise study of seismic phenomena, the results thus far have served rather to reveal the complicated nature of the problems involved; and while encouraging the seismol. ogist to renewed effort they warn him that his labors are not to be light. The recent advances of the science have been, and properly, toward the study of the phenomena at hand, the nature and extent of the motion of the earth particle together with the rate at which the disturbance is propagated, in the expectation and hope that in time the location and character of the original cause may be revealed through these.

In the early growth of an exact science one of the obstacles met with is the absence of an exact nomenclature, and seismology furnishes no exception to this rule. Whenever it becomes desirable or necessary to incorporate the meaning of a word in a mathematical expression it is imperative that the necessary restrictions be placed upon its use. It has long been customary to speak of the intensity of an earthquake without any special effort to give the word an exact meaning. Generally it is applied to the destructiveness of the disturbance on the earth's surface, and

But

sometimes to the magnitude of the subterranean cause of the same. modern seismology proposes to measure the intensity of an earthquake and to express its value numerically. It is worth while, therefore, to inquire in what sense the term may be used with precision and what may be accepted as its mathematical equivalent. Evidently it may mean, and in fact it has been made by different writers to mean, the measure of the surface destruction; the energy per unit area of wave front of a single earthquake wave; the rate at which energy is transmitted across unit of area of a plane parallel to the wave front; and the total energy expended in the production of the original disturbance. The use of well constructed seismographs has furnished us, within a few years, a good deal of fairly reliable information relating to certain elements of earthquake motion, notably the amplitude and period of vibration and the velocity of transmission, by means of which, and aided by a few not very violent assumptions, some of the above quantities may be calculated. They are not identical, numerically or otherwise, and it is manifestly improper to apply the word intensity to all of them.

An earthquake wave is generally assumed to be the result of an harmonic vibration, while this supposition is not strictly correct, it is probably not so far erroneous as to materially vitiate the results which follow. If then,

V

=

d

=

velocity of wave transmission.

density of material through which transmission occurs.

The following are easily obtained:

22a2d V
t

(4) Energy of wave per unit area of wave-front

=

(5) Energy per second across unit area of plane parallel to wave-front (rate of transmission):

=

22a2d V
t2

It is well known that Mallet and others of the earlier seismologists attempted to find a mathematical expression which should represent the so-called "intensity" of the shock, by means of the velocity of projection of loose bodies as determined by their range, and also through the dimensions of bodies which would be overturned by the shock. The maximum velocity of the earth might be ascertained by the first method with fair accuracy; the second method is nearly, if not quite worthless in practice, and both are decidedly inferior in design and operation to the modern seismograph which gives the principal elements of the motion directly.

In a paper by Professors Milne and Gray, Philosophical Magazine, Nov.

1881, the following occurs: "The intensity of a shock is evidently best estimated from the maximum velocity of translation produced in a body during an earthquake. This is evidently the element according to which the destructive power is to be measured, it being proportional to the maximum kinetic energy of the bodies on the earth's surface relative to that surface during the shock." Now this statement is inconsistent with that which immediately follows and with their mathematical expression which is

equivalent to the second expression given above. This inconsistency was doubtless quickly and first detected by the authors and in a copy of the paper received from them I find interlinear corrections in the paragraph quoted above in virtue of which the words " rate of change of” are substituted for the word "maximum" where it first occurs, and “acceleration" for the words "kinetic energy," thus bringing it into agreement with the remainder of the discussion, and at the same time unquestionably better representing the opinion of the authors, who in all subsequent publications have used the maximum acceleration to represent the intensity as shown in the overturning, shattering and projecting power of the shock. The same expression, 212, is used as a measure of intensity by Professor Holden in his paper on "Earthquake intensities in San Francisco," where he defines it as "intensity of shock defined mechanically = destructive effect = the maximum acceleration due to the impulse." He asserts that "the researches of the Japanese seismologists have abundantly shown that the destruction of building, etc., is proportional to the acceleration produced by the earthquake shock itself, in a mass connected with the earth's surface." This statement is hardly justifiable, at least up to the present time. In the Report of the British Association for 1885, the committee appointed by the association for the purpose of investigating the earthquake phenomena of Japan, consisting of Messrs. Etheridge, Gray and Milne, describe among other seismic experiments one which consisted in determining the quantity to be calculated from an earthquake diagram which would give a measure of the overturning or shattering power of a disturbance. The result of this investigation seemed to show that the acceleration, which by calculation from the dimensions of the columns was necessary for overturning, was somewhere between the mean acceleration, represented by 4 and the maximum acceleration, "1.

t

The actual destruction caused by an earthquake wave is undoubtedly a function of many variables, but it seems tolerably certain that maximum acceleration is the leading factor and at the present time no better measure can be found. It appears to me, however, that it is unwise to apply the term "intensity" or "intensity of shock" to this quantity, which might be called the "destructiveness" of the wave, or perhaps, its "destructivity" as indicating a little more clearly the power to destroy.

1 Am. Journ. Science, Vol. XXXV, page 427.

Dutton and Hayden in their "abstract of the results of the investigation of the Charleston earthquake" presented to the National Academy of Sciences on April 19, 1887, define intensity as the "amount of energy per unit area of wave-front," but in the subsequent discussion use it almost continually as a measure of surface destruction. Upon the first definition they have based a very interesting and novel method for determining the depth of the focus; but in the application of the method to the Charleston earthquake they have used the word in its other and very different sense. A reference to the formulæ given above will show that one of these quantities is inversely as the square of the distance from the origin, as assumed by them in the development of their method, while the other, used in its application, is not so proportional and this must be admitted to be fatal to their deductions.

In the discussion of a somewhat analogous case, Lord Rayleigh says,' "the rate at which energy is transmitted across unit of area of a plane parallel to the front of a progressive wave may be regarded as the mechanical measure of the intensity of the radiation." The algebraic expression for this quantity, as shown above, is, of course, similar to that of the quantity last considered, differing from it only in the power of "t "" in the denominator. Both are very important expressions; neither is very closely related to "surface destruction" and the latter is unquestionably a suitable measure of the "intensity of an earthquake" in the most important sense.

It thus appears that at least four measures for earthquake intensity are and have been in use, which are expressed mathematically in terms of amplitude, period, velocity of transmission and density of medium in formulæ (1) (2) (4) (5) above. To show more forcibly the necessity for placing some restrictions upon the use of the word, I have compared the "intensities" of two earthquakes, using each of the four expressions. The disturbances compared are those of May 6 and May 11, 1884, at Tokyo, Japan, the observations being made by Professor Milne. The same instrument, located in the same place, was used in both and the interval of time between the two is so small as to forbid any important change in the conditions. That of May 6 is called "A" and that of May 11 "B." The results are as follows:

from which it is evident that much depends on the measure of intensity adopted.

As stated in the beginning of this paper, the more recent work of seismologists has been in the study of individual disturbances for the purpose of determining the principal elements of motion, amplitude, period, direction and speed of transmission. In this study much has been learned. From the nature of the case we are almost absolutely restricted to an investigation of surface phenomena and we are soon forced to admit that