teeth are not distinctive, except M2, which is very small, oval, and situated about medially with respect to M1. The inferior canine is recurved and the tooth row is continuous, with no diastemata. The ramus is slender; masseteric fossa very deep and large; angle prominent; and coronoid wide, thin, and high. The condyle is situated on a line with the dental series. There are three mental foramina in the same horizontal line. FIG. 5.-Oligobunis darbyi, sp. nov. Holotype. Inferior view, right half of skull. Nat. size. In so far as comparable parts are present of both the type of the genus, O. crassivultus Cope, and O. darbyi, sp. nov., the latter differs chiefly in (1) smaller size, (2) much greater degree of dolichocephaly, (3) a continuous inferior and superior tooth row, (4) larger size of infraorbital foramen, (5) different size and shape of masseteric fossa, (6) different proportions of anterior zygomatic pedicle, (7) much less prominent angle of ramus, (8) considerably smaller deuterocone of P4, and (9) different geographical locality and geological horizon. Many minor differences may also be noted. The new species differs from the type of O. lepidus Matthew, No. 12865, A. M. N. H., in (1) larger size and (2) different proportions. The paratypes of the latter species, Nos. 12866 and 12867, are figured, but not the type. In comparison with the paratypes, O. darbyi, sp. nov., differs in (1) somewhat larger size, (2) possession of P1, (3) greater crowding of the premolars, (4) much larger size of P1, (5) smaller size and different shape of M2, (6) less curvature of the inferior tooth row, (7) greater degree of recurving of C1, (8) straighter inferior outline of the ramus, and (9) greater depth of ramus below the tooth row. These paratypes Matthew designated in his table of measurements as a new variety, robustior, although I think that additional material would elevate them to the rank of a new species, more advanced in development than any of the others. Another paratype of the same species, No. 12868, may well be a male of O. lepidus, as it agrees with the type except in being of larger size. REFERENCES. De Blainville, M. H.-M. D. 1839-1864. Ostéographie. Paris. pl. 14.) (Subursus, Cope, E. D. 1884. The Vertebrata of the Tertiary formations of the Kaup, J. 1832. Vier neue Arten urweltlicher Raubthiere, etc. Archiv für Mineralogie, Geognosie, etc., 5, 150-152, pl. 2, figs. 1, 2. Berlin. Matthew, W. D. 1907. A Lower Miocene fauna from South Dakota. Bull. Amer. Mus. Nat. Hist., vol. 23, 169-219. Merriam, J. C. 1903. The Pliocene and Quaternary Canidæ. Univ. California, Bull. Dept. Geology, vol. 3, 277-290. Merriam, J. C., and Sinclair, W. J. 1907. Tertiary faunas of the John Day region. Ibid., vol. 5, 171-205. Roth, J., and Wagner, A. 1854. Die fossilen Knochenüberreste von Pikermi in Griechenland. Abhandl. math.-phys. Cl. d. k. Bayerischen Akad. d. Wiss., 7, pt. 2, 389-392, pl. 8, figs. 1, 2. Munich. Berlin. Trouessart, E. L. 1897. Catalogus mammalium, 291. Zittel, K. A. von. 1891-1893. Palæozoologie. Handb. d. Pal., 4, 634, fig. 531. ART. XXXVI.-A New Harmonic Analyzer; by WARREN MASON. Since Fourier first published his "Theory Analytique de la Chaleur," there have been a number of machines called harmonic analyzers invented for the purpose of evaluating his integrals mechanically. Some of these have been in use for over a hundred years, so the only reason for describing another one would be that it is simpler to make or more accurate than other machines. The instrument described in this paper has about the same degree of accuracy as any except the Henrici analyzer, but its main point of interest is that it can be made by anyone without the use of complicated machinery. A periodic curve can be represented by a series of the kind 2 y = A + A, sin a + B, cos a + A, sin 2 a+ B, cos 2 a + . . . where A is a constant equal to the algebraic sum of the area of the two loops forming one wave length, and A1, B1, A2, B2, etc., constants denoting the maximum heights of the respective harmonics. Fourier has shown that the value of any constant A, is given by the integral while the value of the constant B, is given by As in the case of most harmonic analyzers, this machine evaluates the above integrals by tracing an area proportional to the value of the expression. Therefore we may at once write where A is the equivalent area referred to above, and K a constant of proportionality. Substituting the integrals for the above terms, we have x, and y in the following equations refer to the coordinates of the wave form with reference to axes at the origin of, and along the axis of, the wave form, while x', y', which axes. are the coordinates of the derived area, refer to the same. All machines of this type have a definite wave length to analyze, which we will designate by the letter a, then in terms of h and x, is h. Substituting this value of a in equation (2), the expression The machine by which we propose to evaluate the Fourier integrals consists of a framework, an arm, a curve, and a straight edge. The framework is an Lshaped piece of wood or metal, grooved on the bottom to allow a zylonite curve to slip into place when the framework is placed over it. Lugs placed in the framework AM. JOUR. SCI.-FIFTH SERIES, VOL. I, No. 6.-JUNE, 1921. fit into holes on the curve and hold it in place. A series of transparent zylonite pieces, one for each sine or cosine harmonic, on which particular curves have been engraved, are the instrument curves referred to. An arm, made partly of metal, and partly of a zylonite strip on which a straight line has been engraved, is fastened to the framework by means of a pivot O. Fig. 1 illustrates this construction. At the end of this arm a small hole P is bored, in which either a pencil point or the tracing point of a planimeter may be placed. A straight edge fastened to the board on the axis of integration, which is always the Y axis if the curve extends along the X axis, serves as a guide for the machine. The essential operation consists in tracing the wave form to be analyzed with the intersection of the arm and the instrument curve, and at the same time drawing the derived area by means of a pencil point placed in the tracing point of the analyzer. It can be seen from fig. 2, that any ordinate of the wave form is exactly reproduced in the derived area, for when x is constant, the arm is fixed, and draws one ordinate as long as the other. Therefore, since (y-y') = y in equation (5), these factors can be cancelled out leaving the equation |