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VOT. PX. EVERY MAN IS A VALUABLE MEMBER OF SOCIETY, WHO, BY HIS OBSERVATIONS, RESEARCHES, AND EXPERIMENTS, PROCURES KNOWLEDGE FOR MEN.—SMITUSON. GEC ON IS BCIIN EEO IN 2 PUBLISHED BY THE SMITHSONIAN INSTITUTION. MDCCCLYVII. ADVERTISEMENT. Tus volume forms the ninth of a series, composed of original memoirs on dif- ferent branches of knowledge, published at the expense, and under the direction, of the Smithsonian Institution. The publication of this series forms part of a general plan adopted for carrying into effect the benevolent intentions of JAMES SmirHson, Ksg., of England. This gentleman left his property in trust to the United States of America, to found, at Washington, an institution which should bear his own name, and have for its objects the “increase and diffusion of knowledge among men.” This trust was accepted by the Government of the United States, and an Act of Congress was passed August 10, 1846, constituting the President and the other principal executive officers of the general government, the Chief Justice of the Supreme Court, the Mayor of Washington, and such other persons as they might elect honorary members, an establishment under the name of the “Smrruson1aNn INSTITUTION FOR THE INCREASE AND DIFFUSION OF KNOWLEDGE AMONG MEN.” The members and honorary members of this establishment are to hold stated and special meetings for the supervision of the affairs of the Institution, and for the advice and instruction of a Board of Regents, to whom the financial and other affairs are entrusted. The Board of Regents consists of three members ex officio of the establishment, namely, the Vice-President of the United States, the Chief Justice of the Supreme Court, and the Mayor of Washington, together with twelve other members, three of whom are appointed by the Senate from its own body, three by the House of Representatives from its members, and six persons appointed by a joint resolution of both houses. To this Board is given the power of electing a Secretary and other officers, for conducting the active operations of the Institution. To carry into effect the purposes of the testator, the plan of organization should evidently embrace two objects: one, the increase of knowledge by the addition of new truths to the existing stock; the other, the diffusion of knowledge, thus increased, among men. No restriction is made in favor of any kind of knowledge; and, hence, each branch is entitled to, and should receive, a share of attention. 1V ADVERTISEMENT. The Act of Congress, establishing the Institution, directs, as a part of the plan of organization, the formation of a Library, a Museum, and a Gallery of Art, together with provisions for physical research and popular lectures, while it leaves to the Regents the power of adopting such other parts of an organization as they may deem best suited to promote the objects of the bequest. After much deliberation, the Regents resolved to divide the annual income into two equal parts—one part to be devoted to the increase and diffusion of knowledge by means of original research and publications—the other half of the income to’be applied in accordance with the requirements of the Act of Congress, to the gradual formation of a Library, a Museum, and a Gallery of Art. The following are the details of the parts of the general plan of organization provisionally adopted at the meeting of the Regents, Dec. 8, 1847. DIGI IATIG Sy OJ ANIL WII SSE IP AIRY Oia WEES) IP Iya IN I. To rncrease KNow.LenGe—IE is proposed to stimulate research, by offering rewards for original memoirs on all subjects of investigation. 1. The memoirs thus obtained, to be published in a series of volumes, in a quarto form, and entitled “Smithsonian Contributions to Knowledge.” 2. No memoir, on subjects of physical science, to be accepted for publication, which does not furnish a positive addition to human knowledge, resting on original research; and all unverified speculations to be rejected. 3. Each memoir presented to the Institution, to be submitted for examination to a commission of persons of reputation for learning in the branch to which the memoir pertains; and to be accepted for publication only in case the report of this commission is favorable. 4. The commission to be chosen by the officers of the Institution, and the name of the author, as far as practicable, concealed, unless a favorable decision be made. 5. The volumes of the memoirs to be exchanged for the Transactions of literary and scientific societies, and copies to be given to all the colleges, and principal libraries, in this country. One part of the remaining copies may be offered for sale; and the other carefully preserved, to form complete sets of the work, to supply the demand from new institutions. G6. An abstract, or popular account, of the contents of these memoirs to be given to the public, through the annual report of the Regents to Congress. ADVERTISEMENT. Vv II. To mvcrease Knowirper.—It is also proposed to appropriate a portion of the income, annually, to special objects of research, wnder the direction of suitable (persons. 1. The objects, and the amount appropriated, to be recommended by counsellors of the Institution. 2. Appropriations in different years to different objects; so that, in course of time, each branch of knowledge may receive a share. 3. The results obtained from these appropriations to be published, with the memoirs before mentioned, in the volumes of the Smithsonian Contributions to Knowledge. 4, Examples of objects for which appropriations may be made :— (1.) System of extended meteorological observations for solving the problem of American storms. | (2.) Explorations in descriptive natural history, and geological, mathematical, and topographical surveys, to collect materials for the formation of a Physical Atlas of the United States. _(3.) Solution of experimental problems, such as a new determination of the weight of the earth, of the velocity of electricity, and of light; chemical analyses of soils and plants; collection and publication of articles of science, accumulated in the offices of Government. (4.) Institution of statistical inquiries with reference to physical, moral, and political subjects. (9.) Historical researches, and accurate surveys of places celebrated in American history. (6.) Ethnological researches, particularly with reference to the different races of men in North America; also explorations, and accurate surveys, of the mounds and other remains of the ancient people of our country. I. To pirruss Knowieper.—It is proposed to publish a series of reports, giving an account of the new discoveries in science, and of the changes made from year to year in all branches of knowledge not strictly professional. 1. Some of these reports may be published annually, others at longer intervals, as the income of the Institution or the changes in the branches of knowledge may indicate. 2. The reports are to be prepared by collaborators, eminent in the different _ branches of knowledge. Vi ADVERTISEMENT. 3. Each collaborator to be furnished with the journals and publications, domestic and foreign, necessary to the compilation of his report; to be paid a certain sum for lis labors, and to be named on the title-page of the report. 4, The reports to be published in separate parts, so that persons interested in a particular branch, can procure the parts relating to it, without purchasing the whole. 5. These reports may be presented to Congress, for partial distribution, the remaining copies to be given to literary and scientific institutions, and sold to indi- viduals for a moderate price. The following are some of the subjects which may be embraced in the reports :— TI. PHYSICAL CLASS. . Physics, including astronomy, natural philosophy, chemistry, and meteorology. Nw eRe . Natural history, including botany, zoology, geology, &c. . Agriculture. H 9 . Application of science to arts. II. MORAL AND POLITICAL CLASS. 5, Ethnology, including particular history, comparative philology, antiquities, &e. 6. Statistics and political economy. 7. Mental and moral philosophy. S. A survey of the political events of the world; penal reform, &c. Ill. LITERATURE AND THE FINE ARTS. 9. Modern literature. 10. The fine arts, and their application to the useful arts. 11. Bibliography. 12. Obituary notices of distinguished individuals. If. To prrrusz Know epcr.—Zt is proposed to publish occasionally separate treatises on subjects of general interest. 1. These treatises may occasionally consist of valuable memoirs translated from foreign languages, or of articles prepared under the direction of the Institution, or procured by offering premiums for the best exposition of a given subject. 2. The treatises to be submitted to a commission of competent judges, previous to their publication. ADVERTISEMENT. “fe N DETAILS OF THE SECOND PART OF THE PLAN OF ORGANIZATION. This part contemplates the formation of a Library, a Museum, and a Gallery of Art. 1. To carry out the plan before described, a library will be required, consisting, Ist, of a complete collection of the transactions and proceedings of all the learned societies in the world; 2d, of the more important current periodical publications, and other works necessary in preparing the periodical reports. 2. The Institution should make special collections, particularly of objects to verify its own publications. Also a collection of instruments of research in all branches of experimental science. 5. With reference to the collection of books, other than those mentioned above, catalogues of all the different libraries in the United States should be procured, in order that the valuable books first purchased may be such as are not to be found elsewhere in the United States. 4, Also catalogues of memoirs, and of books in foreign libraries, and other materials, should be collected, for rendering the Institution a centre of bibliogra- phical knowledge, whence the student may be directed to any work which he may require. 5. It is believed that the collections in natural history will increase by donation, as rapidly as the income of the Institution can make provision for their reception ; and, therefore, it will seldom be necessary to purchase any article of this kind. 6. Attempts should be made to procure for the gallery of art, casts of the most celebrated articles of ancient and modern sculpture. 7. The arts may be encouraged by providing a room, free of expense, for the exhibition of the objects of the Art-Union, and other similar societies. 8. A small appropriation should annually be made for models of antiquity, such as those of the remains of ancient temples, Xc. 9. The Secretary and his assistants, during the session of Congress, will be required to illustrate new discoveries in science, and to exhibit new objects of art; distinguished individuals should also be invited to give lectures on subjects of general interest. In accordance with the rules adopted in the programme of organization, each memoir in this volume has been favorably reported on by a Commission appointed ages ADVERTISEMENT. for its examination. It is however impossible, in most cases, to verify the state- ments of an author; and, therefore, neither the Commission nor the Institution can be responsible for more than the general character of a memoir. The following rules have been adopted for the distribution of the quarto volumes of the Smithsonian Contributions :— 1. They are to be presented to all learned societies which publish Transactions, and give copies of these, in exchange, to the Institution. 2. Also, to all foreign libraries of the first class, provided they give in exchange their catalogues or other publications, or an equivalent from their duplicate volumes. 3. To all the colleges in actual operation in this country, provided they furnish, in return, meteorological observations, catalogues of their libraries and of their students, and all other publications issued by them relative to their organization and history. 4. To all States and Territories, provided there be given, in return, copies of all documents published under their authority. 5. To all incorporated public libraries in this country, not included im any of the foregoing classes, now containing more than 7000 volumes; and to smaller libraries, where a whole State or large district would be otherwise unsupplied. OFFICERS OF THE SMITHSONIAN INSTITUTION. THE PRESIDENT OF THE UNITED STATES, Fx-officio PRESIDING OFFICER OF THE INSTITUTION. THE VICE-PRESIDENT OF THE UNITED STATES, Ex-officio SECOND PRESIDING OFFICER. ROGER B. TANEY, CHANCELLOR OF THE INSTITUTION. JOSEPH HENRY, SECRETARY OF THE INSTITUTION. SPENCER F. BAIRD, ASSISTANT SECRETARY. W. W. SEATON, Treasurer. ALEXANDER D. BACHE, JAMES A. PEARCE, | Bxacom COMMITTEE. JOSEPH G. TOTTEN, RICHARD RUSH, WILLIAM H. ENGLISH, | pono CoMMITTEE. JOSEPH HENRY, bo REGENTS. JoHN C. BRECKENRIDGE, . . . . Vice-President of the United States. Roger B. Tangy, . . . . . . Chief Justice of the United States. Wm. B. Macruprr,. . . . . . Mayor of the City of Washington. — James A. Pearce, . . . . . . Member of the Senate of the United States. JAMES, MCOMIASON, 7) oa he sae: ss ce ce a ¢s cc STEPHEN A’ DouGrAss Yat iar cs os a a < cc WituiAM H. Eneuisu, . . . . . Member of the House of Representatives U. 8. FITRAM SWIARNERS 1. uci nia Situs es ‘ . (k= 7) (1s e cos 0) 9 Sin 2 = Ae) Zs (2.) Here for special values, making cos @ successively equal to —e, + 1, —1, and cancelling factors, we obtain for the values of sin z in order:— : R—r Average, sin z = — : : R—r Who, Gy) oS 2 (3.) A (1—e) Shs : R—r Wharinm, Goes 4 (hae @)) Again, taking the length of arc z in the circle whose radius is 1, the breadth of the differential zone upon the planet will be rz; but since, for all the planets, z is less than 1°, its sine may be substituted from either of the former equations, and the same value essentially is represented by Linear breadth of zone = r sin z. (4.) It is also proved in Geometry that the surface of a sphere whose radius is 7, is equal to 47°21; 2 denoting 3.141592; and that the surface of a spherical zone is equal to its altitude multiplied by 277. Now, the altitude of the zone of differ- ential radiation is, in ratio to that of the whole planet, as sin z to 2, or 3 sin z to 1. Hence, representing the whole area of the planet by 1. The proportion of irradiated surface = 4 + 3 sin z. (5.) Whole surface irradiated = (3 + 4 sinz) 47? 7. (6.) Surface of the zone = 27° 7 sin z. (7.) If r be taken in miles, the area will be given in square miles. The following table exhibits some of the primary phases of solar intensity upon the planets ; and was obtained by substituting the proper astronomic elements in formule (3), (4), and (5). Na Average breadth | Greatest breadth | Least breadth Proportion of 4 of zone. of zone. of zone. surface irradiated. Miles. Miles. Miles. Mercury. 4 3 : : 17.89 22.32 14.96 .505991 Venus : c 5 ‘ 0 61.12 61.54 60.70 .503190 Harth L é 6 a 18.29 18.60 17.98 .500231 Mars 3 3 5 i s 6.42 7.07 5.87 .500152 Vesta ; : : a 6 26 .28 24 .500980 Jupiter : é 6 ag 6 34.87 36.62 33.28 .500404 Saturn 6 é 5 : 5 18.17 19.25 17.21 .500222 Uranus : : : ‘ : 4.01 4.20 3.83 .500117 Neptune. : : : : 6.14 6.19 6.08 .500087 In obtaining these tabular results, the earth’s mean distance from the sun was taken at 95,273,870 miles, and its radius at 3,962 miles. It will be perceived that the vast magnitude of the sun brings advantages of INTENSITY OF SUN’S HEAT AND LIGHT. 9 temperature and sunlight similar to those which the preponderance of its mass gives to the steadiness and uniformity of the planetary revolutions. Were the same amount of heat and light, radiated from a smaller body like the Moon, the effects would be restricted to a smaller portion of the Earth’s surface; and the zone of differential radiation would be reversed to one of cold and darkness. But in the present beneficent arrangement, light and heat preponderate, counteracting extremes of heat and cold with a warmer temperature. And this effect is further prolonged by atmospheric refraction and reflection of the rays, which, rendering the transitions more mild and gradual, lessens the reign of night. To estimate this effect of the Refraction of Light, we have only to find two points on the spherical surface of the earth, at such distance that the inclination of the two tangent rays from the Sun falling on them, shall be just equal to the horizontal refraction. The terrestrial radii drawn to these points will evidently be inclined at the same angle as their tangents, which is 34’ nearly, or 40 English miles. Thus it appears that the effect of refraction in widening the irradiated zone of the earth is more than twice as great as that arising from the apparent semi-diameter, or the mere size of the sun. Uniting the two effects, the sun is found to illuminate more than half the Earth’s surface by a belt or zone that is 58 miles in width, encircling the seas and continents of the globe. The advantage of the vast size of the sun is most conspicuous upon the planet Venus, our evening and morning star, where the belt of illumination is sixty-one miles in width, as shown in the preceding table. The next in rank is Jupiter, whose belt of greater illumination is thirty-five miles wide ; while those of Mercury, the Earth, and Saturn, are nearly eighteen miles in breadth. In the last column of the table, it will be observed that the asteroid Vesta, though situated beyond Mars, yet has, in consequence of its smaller size, a greater proportion of illuminated surface than the Earth. From formula (7), it is found that the zone of differential illumination upon the Earth extends over 455,400 square miles; or, including the additional area due to 34 horizontal refraction, it comprehends an aggregate of 1,430,800 square miles of surface. The position of this great zone -is continually changing, and in turn it overspreads every island, sea, and continent. At the vernal equinox, when the Sun is vertical to the Equator, it will readily be perceived that the larger base of this zone is a great circle passing through the Poles and having the Karth’s axis for its diameter. From this position it gradually diverges, till at the summer solstice, one extremity of its diameter will be in the Arctic, and the other in the Antarctic circle. ‘Thence it gradually returns to its former position at the Poles at the autumnal equinox, all the while revolving like a fringed circle around the globe, and accompanied with the lustrous tints and shadows which variegate the dawn and close of day. 10 INTENSITY OF SUN’S HEAT AND LIGHT. SECTION ITI. LAW OF THE SUN’S INTENSITY UPON THE PLANETS IN RELATION TO THEIR ORBITS. Tur preceding Section represents the Sun’s action upon a distant planet at a given distance, or at rest. It is here proposed to examine the effect when the distance is variable; that is, supposing the planet to commence its motion from a state of rest, in an elliptical orbit, to determine the intensity received during its passage through any part, or the whole of its orbit. In the annexed figure, let S denote the Sun situated in one focus; P the Planet’s position at a given time; A, the perihelion or point in the orbit nearest the sun, and B, the aphelion or point farthest from the sun. Let SP or p denote the radius-vector ; ASP or 6, the true anomaly; e, the ratio of eccentricity; and a+nt, the mean ano- maly; », being the mean motion in the unit of time. If A denote the semi-transverse axis, it is well known that A? 2/1—e? will express the whole area of the ellipse, and {3 p dd, the area of the elliptic sector corresponding to 6, where 7 denotes 3.14 1592, or a semi-circumference. Hence by Kepler’s law, that equal areas are described by the radius-vector in equal times, Aav 1—e° f4 p d0::2n:a+ nt. Reducing to an equation and differentiating, 1 do 2 Ta 9 2° (8.) ep Arndt /V1—e Since heat and light vary inversely as the square of the distance p, the second member evidently measures their intensity at any instant. Then, as pointed out in the Calculus, we may regard the second member as the ordinate, and the time ¢ as the abscissa of a curve. Multiplying the equation by dt, there- fore, and integrating between the limits of any two anomalies, @ and 6’, we obtain for the sum of the intensities, (ei as (9.) And’ l—e In interpreting this result, we know that the orbitual motion of a planet is not uniform, being accelerated in perihelion and retarded in aphelion. Hence, in the annual variations of radius-vector, the Earth does not receive equal increments of heat and light in equal times; but the amount received in any given interval, is exactly proportional to the true anomaly or true Longitude described in that interval. INTENSITY OF SUN’S HEAT AND LIGHT. 11 ‘This important law appears to have been first published in the Pyrometry of Lambert. This point being established, let us, in the next place, compare the intensities received by the Planets during entire revolutions in their orbits. In the preceding formula, making —6/ equal to an entire circumference, the sum of the intensities 21 during a complete revolution, is found to be u= Goa We Let this refer to AL nN —— Cx 2 7 AP Gf J WE" n,n’, being inversely proportional to the planets’ periodic times, we have by the third Ci Bats) 3 law of Kepler, n?:”?:: A®: A®, or nA?=n' A”, Whence by substitution and division, we obtain for the relative intensity upon any planet in an entire revolution, OB EE) wu /A'(1—e") In like manner, the ratio of intensity for equal times, depending simply on the inverse square of the distances, will be represented by Ql ; _= 11). i AE ( ) With these last two formulas, the following table has been prepared from the usual astronomic elements :— Now the earth, and accenting the values for any other planet, wu’ = (10). The Sun’s Relative Intensity wpon the Principal Planets. IN EQUAL TIMES. PEAS In A WHOLE REVOLUTION. Mean Distance. Perihelion. Aphelion. Mercury : ; : : 1.643 6.677 10.573 4.592 Venus . . 0 . . 1.176 iLO 1.937 1.885 Karth . : ; 6 0 1.000 1.000 1.084 0.967 Mars 6 ° 0 . : 818 A381 0.524 0.360 Jupiter . ‘ : F 5 439 037 041 084 Saturn . : . : . B24 O11 5 ol) Alo Uranus . 2 . .228 003 .003 -003 Neptune : : : : .182 001 001 001 It should be observed that the foregoing table does not take account of the different dimensions of the planets, but refers to a unit of plane surface upon their -disks, which is exposed perpendicularly to the rays of the perpetual sun. Upon the disk of Mercury, the solar radiation appears to be nearly seven times greater than on the Earth; while upon Neptune, it is only as the one-thousandth part, in equal times. In entire revolutions, however, the intensities received will be seen to approach more nearly to equality. The intensities are thus unequal; and, by a calculation founded on the apparent brightness of the planets as estimated by the eye, Prof. Gibbes has shown, in the Proceedings of the American Association for the Advancement of Science for 1850, that the reflective powers are also greater, according as the several planets are more distant from the Sun. 19} INTENSITY OF SUN’S HEAT AND LIGHT. Another feature worthy of mention, is the resemblance of the earth to the planet Mars; upon which Sir W. Herschel has remarked: “The analogy between Mars and the Earth is, perhaps, by far the greatest in the whole solar system. ‘The diurnal motion is nearly the same, the obliquity of their respective ecliptics not very different; of all the superior planets, the distance of Mars from the Sun is by far the nearest alike to that of the Earth; nor will the length of the Martial year appear very different from what we enjoy, when compared to the surprising duration of the years of Jupiter, Saturn, and Uranus. If we then find that the globe we inhabit has its polar region frozen and covered with mountains of ice and snow, that only partly melt when alternately exposed to the sun, I may well be permitted to surmise that the same causes may have, the same effect on the globe of Mars; that the bright polar spots are owing to the vivid reflection of light from frozen regions; and that the reduction of those spots is to be ascribed to their being exposed to the sun.” Recurring now to equation (9) and the proposition following, it will readily be inferred that during each of the four astronomic seasons of Spring, Summer, Autumn, and Winter, the intensities received from the sun are precisely equal. For in each season, the earth passes over three signs of the zodiac, or a quadrant of longitude. The equality of intensities, however, applies to the entire globe regarded as one ageregate, and is consistent with local alternations, by which it is summer in the northern hemisphere when it is winter in the southern. Deferring the consideration of these local inequalities, however, we may here illustrate the connection of the seasons with the elliptic motion from an ephemeris. In the year 1855, for example, spring in the northern hemisphere, commencing at the vernal equinox March 20th, lasts eighty-nine days; summer, beginning at the summer solstice June 21, con- tinues ninety-three days; autumn, commencing at the equinox, September 23, con- tinues ninety-three days; and winter, beginning at the winter solstice, December 22, lasts ninety days; yet, notwithstanding their unequal lengths, the amounts of heat and light which the whole earth receives are equal in the several periods.’ At the present time the earth is in perihelion, or nearest the sun about the 1st of January, and farthest from the sun on the 4th day of July. A special cause must, therefore, be assigned for the striking fact which Professor Dove has shown by comparison of temperatures observed in opposite regions of the globe, namely: that the mean temperature of the habitable earth’s surface in June considerably exceeds the temperature in December, although the earth in the latter month is nearer to the sun. This result is attributed by that meteorologist to the greater quantity of land in the northern hemisphere exposed to the rays of the sun at the summer solstice in June; while the ocean area has less power for this object, as it absorbs a large portion of the heat into its depths. Had land and water been equally distributed; in other words, were the earth a homogeneous sphere, the alleged inequality of temperature, it is obvious, would never have existed. 1 Since the earth is not strictly a sphere, but an oblate spheroid, it evidently presents its least section perpendicular to the rays of the sun at the equinoxes. As the sun’s declination increases, the section also increases and attains its limit at the solstice. The variation, however, appears to be not material, and compensates itself in each season. INTENSITY OF SUN’S HEAT AND LIGHT. 13 SECTION III. LAW OF THE SUN’S INTENSITY AT ANY INSTANT DURING THE DAY. THE rays which emanate from the Sun’s disk into space proceed in diverging lines in the same manner as if they issued directly from the centre. And, on arriving at the Earth, their intensity as before stated will be inversely proportional to the square of the distance. But the more obvious phenomena of solar heat and light are manifested to us under a secondary law. ‘The Sun’s intensity first becomes sensible in the eastern rays of morning; it gradually increases to a maximum during the day; it declines on the approach of the shades of evening, and becomes discontinuous during the night. On the morning following the same course is renewed, and continued suc- cessively through the year. Ordinary sensation and experience lead us to associate the degree of solar heat at any part of the day, with the apparent height which the sun has then attained above the horizon. Indeed, theory determines that at four in the afternoon, or any other instant during the day, the Sun’s intensity is propor- tional to the length of a perpendicular line dropped from the Sun to the plane of the apparent horizon, or varies as the size of the sun’s altitude. The reason of this secondary law will be understood by regarding the beam of solar rays which traverses in a line from the sun to the observer, to be resolved, according to the parallelogram of forces, into a horizontal and a vertical component. The horizontal component running parallel to the earth’s surface is regarded as inoperative, while the vertical component measures the direct heating effect. This relation is more fully shown in the annexed figure, where A denotes the sun’s apparent altitude above the horizon. The sun’s intensity or impulse in an oblique direction will be measured by the inverse square of the distance, or the direct square of the sun’s apparent semi-diameter A. If, therefore, A’ denotes the intensity of the rays in a straight line from the sun, A’sin A, will be the vertical component or heating force of therays. And these terms being in ratio as 1 to sin A, the latter component will - be represented by a perpendicular line from the sun’s centre to the horizon. A Instead of thus decomposing the intensity after the manner of a force in Mechanics, as first pro- posed by Halley, in 1693, the same law may be obtained in an entirely different way from the principle of the inverse square of the distance. ‘The latter mode appears to present it in a more evident light, and was suggested in the original beginnings of the present investigation, which were published in Silliman’s Journal of Science for the year 1850. It proceeds as follows:— 3 A send. 14 INTENSITY OF SUN’S HEAT AND LIGHT. Let ZL = the ‘apparent’ Latitude of the place, D = the sun’s meridian Declination, A = the sun’s apparent semi-diameter, A =the sun’s Altitude, and H = the Hour-angle from noon. Also in reference to future applications, let T = the sun’s true Longitude, and o = the obliquity of the Ecliptic. The horizontal section of a cylindrical beam of rays from the Sun’s disk upon a plain on the Earth’s surface, is well known to be an ellipse; and if 1 denote the sun’s radius, 1 will likewise denote the semi-conjugate axis of this projected ellipse; 1 . while the horizontal projection, me will be the semi-transverse axis. ‘The area Yiatanedoniratecie 1 : of the elliptic projection is, therefore, 1 x sna * ™ ‘But the intensity of the same quantity of heat being inversely as the space over which it is diffused, the reciprocal of this area, or sin A, on rejecting the constant z, will express the sun’s heating effect, supposing the distance to be constant for the same day. But, on comparing one day with another, the intensity further varies inversely as the square of the distance, that is, directly as the square of the apparent diameter or semi-diameter of the disk. Hence, generally, A’ sin A, expresses the sun’s intensity at any given instant during the day. To determine the value of sin A, by spherical trigonometry, the sun’s angular distance from the pole, or co-declination, the arc from the pole to the zenith, or — co-latitude, and the included hour-angle from noon are given to find the third side or co-altitude. Writing, therefore, sines instead of the cosines of their com- plements, sin A = sin L sin D+ cos L cos D cos H. A’ sin A = A’ sin L sin D + A? cos L cos D cos H. (ee) At the time of the equinoxes, D becomes 0, and the expression of the sun’s intensity reduces to A? cos L cos H. That is, the degree of intensity then decreases from the equator to each pole, and is proportional to the cosine of the latitude. At other times of the year, however, a different law of distribution prevails, as indicated by the formula. The intensity at a fixed distance being as the sine of the altitude, it follows that the sun shining for sixteen hours from an altitude of 30°, would exert the same heating effect upon a plain, as when it shines during eight hours from the zenith ; since sin 30° is 0.5, and sin 90° is 1. At least, such were the result independently of radiation. By some writers, the measure of vertical intensity, as the sine of the sun’s alti- tude, has been stated without limitation. Approximately it may apply at the habitable surface of the earth, when the influence of the atmosphere is neglected; yet it is strictly true only at the exterior of the atmospheric envelope which encom- passes the globe, or at the outer limit where matter exerts its initial change upon the incident rays. INTENSITY OF-SUN’S HEAT AND LIGHT. 15 The distinction here explained has not only engaged the attention of the most eminent meteorologists of modern times, but was equally adopted in ancient philo- sophy, as appears in the following passage from Plato’s Phedon, LVIII: “For around the earth are low shores, and diversified landscapes and mountains, to which are attracted water, the cloud, and air. But the earth, outwardly pure, floats in the pure heaven like the stars, in the medium which those who are accustomed to dis- course on such things call ether. Of this ether, the things around are the sediment which always settles and collects upon the low places of the earth. We, therefore, who live in these terraqueous abodes, are concealed, as it were, and yet think we dwell above upon the earth. As one residing at the bottom of the sea might think he lived upon the surface, and, beholding the sun and stars through the water, might suppose the sea to be heaven. The case is similar, that through imperfection we cannot ascend to the highest part of the atmosphere, since, if one were to arrive upon its upper surface, or becoming winged, could reach there, he would on emerg- ing look abroad, and, if nature enabled him to endure the sight, he would then perceive the true heaven and the true light.” In modern times, the researches of Poisson led him to the philosophic conclusion now generally received, that the highest strata of the air are deprived of elasticity by the intense cold; the density of the frozen air being extremely small, Théorie de la Chaleur, p. 460. An atmospheric column resting upon the sea may thus be regarded as an elastic fluid terminated by two liquids, one having an ordinary density and temperature, and the other a temperature and density excessively diminished. . Although the sun’s intensity, which is here the subject of investigation, is the principal source of heat, yet its effects are modified by proximate causes of climate; of which, the following nine are enumerated by Malte Brun:— 1st.—Action of the sun upon the atmosphere. 2d.—The interior temperature of the globe. 3d.—The elevation above the level of the ocean. 4th.—The general inclination of the surface and its local exposure. 5th.—The position of mountains relative to the cardinal points of the compass. 6th_—The neighborhood of great seas and their relative situation. 7th.—The geological nature of the soil. 8th.—The degree of cultivation and of population to which a country has arrived. 9th.—The prevalent winds. The same author observes, in relation to the fourth enumerated cause, that north- east situations are coldest; and southwest, warmest. For the rays of the morning which directly strike the hills exposed to the east, have to counteract the cold accu- mulated there during the night. The heat augments till three in the afternoon, when the rays fall direct upon southwest exposures, and no obstacle now prevents their utmost action. 16 INTENSITY OF SUN’S HEAT AND LIGHT. SECTION IV. DETERMINATION OF THE SUN’S HOURLY AND DIURNAL INTENSITY. In the last Section, the sun’s vertical intensity upon a given point of the earth’s surface at any instant during the day, was proved to be measured by a perpendicular drawn from the centre of the Sun to the plane of the horizon. If perpendiculars be thus let fall at every instant during an hour, the sum of the perpendiculars will evidently represent the sum of the vertical intensities received during the hour, which sum may be termed the Hourly Intensity. The Integral Calculus furnishes a ready means of obtaining this sum. For during any one day, the sun’s distance or apparent semi-diameter, and the meridian Declination, may be regarded as constant, while H alone varies, and the deviations from the implied time of the sun’s rising and setting will compensate each other. Therefore, multiplying the equation of instantaneous intensity (12) by d H, since astronomy shows that H varies uniformly with the time, and integrating between the limits of any two hour angles, H', H’, we obtain an expression for the hourly intensity. In like manner let H denote the semi-diurnal arc, and integrating between the limits 0 and H, we obtain the intensity for a half day, which, on cancelling the constant multiplier 2, may be taken for the whole day, or Diurnal Intensity, as follows :— fa snA dH = A? H sin L sin D+ A* cos L cos D sin H. (13.) The diurnal intensity is, therefore, proportional to the product of the square of the sun’s semi-diameter into the semi-diurnal arc, multiplied by the sine of the latitude into the sine of the sun’s declination, plus the like product of the square of the sun’s semi-diameter into the sine of the semi-diurnal arc multiplied by the cosine of the latitude into the cosine of the declination. This aggregate obviously changes from day to day, according to the sun’s distance and declination. Introducing the astronomic equation, cos H = —tan L tan D, or in another form, sin L sin D : : cos L cos D= = eee the expression reduces to the following: fa sin Ad H = A’ sin L sin D(H—tan FH). It only remains to adopt a unit of intensity, the choice of which is entirely arbi- trary. For the present, and in reference to Brewster’s formula hereafter noticed, we will assume the intensity of a day on the equator at the time of the vernal equinox to be 81.5 units. For this case, where D and ZL are each 0, formula (13) reduces to A’, which is (965”)’; hence 81.5+(965”), or /, will be the multiplier for reducing all other values to the same scale; where the common logarithm of & is 5.94210. Denoting the annual intensity by w, and taking A in seconds of arc, we have in units of intensity, : u=k A’ sin L sin D(H—tan H). (14.) INTENSITY OF SUN’S HEAT AND LIGHT. 7 The following cases under the general formula may here be specified :—— First, at the time of the Hquinowes, D is 0, and consequently H is 6"; substitut- ing these values in (13) and converting into units, u=k J’ cos L. (15.) Hence the sun’s daily intensity for all places on the earth is then proportional to the cosine of the latitude. As the equinoxes in March and September lie intermedi ate between the extremes or maxima of heat and light in summer, and their minima in winter, the presumption naturally arises that the same expression will approximate to the mean annual intensity. The coincidence is accordingly worthy of note, that the best empirical expression now known for the annual temperature in degrees Fahrenheit, given by Sir David Brewster, in the Edinburgh Philosophical Transactions, Vol. IX, is 81.°5 cos L, being also proportional to the cosine of the latitude. It is remarkable that Fahrenheit, in 1720, should have adjusted his scale of temperature to such value, that this formula applies, without the addition of a constant term. Secondly, for all places on the Equator, the latitude Z is 0; and H is 6", or the sun rises and sets at six, the year round, exclusive of refraction. Consequently the Sun’s diurnal intensity varies slowly from one day to another, being proportional to the cosine of the meridian Declination, or, wu =k & cos D. (16.) Thirdly, at the South or the North Pole, the latitude L is 90°; and since tan 90° is infinite, the astronomic relation cos H = — tan L tan D is illusory, except when Dis 0. The physical interpretation of this feature is, that at the North Pole, the sun rises only at the vernal equinox in March, and continues wholly above the horizon, till it sets at the autumnal equinox. ‘Thus to either Pole, the sun rises but once, and sets but once in the whole year, giving nearly six months day, and six months night. Now suppose the six months day to be divided into equal portions of twenty-four hours each; then, in reference to formula (13), H is 12", and the intensity during twenty-four hours of polar day is proportional to the sine of the Declination at the middle of the day ; ox, w= kX’ asin D. This term varies much faster than the cotemporary value on the equator. And comparing the two expressions, it appears that during the summer season, in each twenty-four hours, the Sun’s intensity upon the Equator is to that upon the Pole, in the following proportion :— We sol: wtan D. (17.) Fourthly, at the summer solstice, when the intensity on the Pole is a maximum, D is 23° 28’, and the preceding ratio becomes as 1 to 1.25; or the Polar intensity is one-fourth part greater than on the Equator (Plate IV). The difference evidently arises from the fact that daylight in the one place lasts but twelve hours out of twenty-four, while at the Pole the sun shines on through the whole twenty-four hours. It were interesting to find when this Polar excess begins and ends, which may be ascertained by equating the last two terms of (17). The condition x tan D= 1, thus gives D equal to 17° 40’, which is the sun’s Declination on May 10th, and 13 18 INTENSITY OF SUN’S HEAT AND LIGHT. again on August 3d. Therefore, during this long interval of eighty-five days, com- prehending nearly the whole season of summer, the Sun’s vertical intensity over the North Pole is greater than upon the Equator. 'To this subject we shall again recur in a subsequent Section. Fifthly, having glanced at these particular cases of the formula, let a more com- plete survey be made for the northern hemisphere. And the same will equally apply to the southern hemisphere, allowing for the reversal of the seasons and change of the Sun’s distance. In equation (14), when H exceeds 6", and when the declination D is south, a change of sign would be introduced; but the proper trigonometric signs will be observed simply by using the upper sign in summer, or when the declination is north, and the lower sign during the rest of the year, in the annexed formula of daily Intensity :— u = [5.94210] A? sin L sin D (tan H+ H). (18.) Here brackets include the logarithm of the co-efficient #; is to be taken in seconds of arc; H is the actual length of the semi-diurnal arc to radius 1, and tan His the natural tangent. The subjoined table has been computed in this man- ner, for intervals of fifteen days, and expresses the results in units of intensity. In the last three columns for the Frigid Zone the braces include values for the days when the sun shines through the whole twenty-four hours; the blank spaces indicate periods of constant night. The Sun's Diurnal Intensity at every Ten Degrees of Latitude in the Northern Hemisphere. (Plate I.) A. D. 18538. Lat. 0°. |Lat. 10°.|Lat. 20°. |Lat, 80°. |Lat. 40°. |Lat. 50°. |Lat. 60°. |Lat. 70°. | Lat. 80°. | Lat. 90°. Jan. 1 0 : -| 17.1 | 67.2 | 55.8 | 42.8 | 80.1 | 16.5 OU ieee 960 BANG . 6 -| 78.1 | 68.9 | 58.2 | 45.8 | 32.7 | 19.3 (aD ial Resin. 66 oe eo: 6 : 2a COSC tle a GleOM AOU ade 3836 al 2osOe|alelag 1.4 50 6 Feb. 15 81.0 | 74.7 | 66.6 | 55.6 | 45.1 | 31.9 | 19.0 6.4 ae : Mar. 2 81.6 | 78.0 | 71.3 | 62.9 | 52.7 | 41.1 | 27.9 | 14.5 alls Wie! oie seam ler 82.0 | 80.2 | 76.0 | 69.6 | 61.1 | 50.2 | 87.1 | 25.5 | 11.6 |... April 1 : : .| 80.8 | 81.4 | 79.5 | 75.38 | 68.9 | 60.2 | 49.9 | 38.0 | 25.6 | 20.5 eG : ; .| 79.0 | 81.7 | 82.0 | 79.5 | 75.1 | 68.6 | 61.1 | 51.4 | 44.0 | 44.6 May 1 6 : .| 76.9 | 81.5 | 83.7 | 83.6 | 80.8 | 77.1 | 70.9 | 64.6 | 64.3 | 65.3 BOVE ALG) : é .| 14.7 | 80.8 | 84.7 | 86.7 | 85.7 | 83.3 | 79.7 | 76.8 |} 80.3 | 81.5 Go Bl c : . | 73.0 | 80.1 | 85.1 | 87.8 | 88.9 | 87.8 | 85.7 || 86.8 || 91.0) | 92.4 June 15 0 : =|) 1250 | TONG 85.2) 88.4 901 | 8929 )) 8878) O17 1) 96 87.6 July 1 ¢ : .| 72.0 | 79.5 | 85.0 | 88.5 | 90.4 | 89.5 | 88.4 | 90.8 | 95.1 | 96.6 erg : : .| 73.0 | 79.8 | 84.7 | 87.5 | 87.6 | 86.5 | 84.1 | 84.3 | 88.3 | 89.7 Be Bl 0 6 .| 74.7 | 80.4 | 83.9 | 85.1 | 84.57) 81.6 | 77.8 | 73.4 | 76.2 | 77.4 Aug. 15 6 5 .| 76.7 | 80.8 | 82.7 | 82.4 | 79.8 | 74.7 | 68.2 | 60.9 | 59.2 | 60.1 ca 0) . 6 el ithe |) Ose SOUS I elon eel | Oa8) | 57.38 | 47.7 | 38.8 | 38.9 Sept. 14 . - -| 79.8 | 79.8 | 77.5 | 72.6 | 65.6 | 58.8 | 46.9 | 34.5 | 21.9 | 14.7 BS OX) : : .| 80.5 | 78.4 | 73.8 | 67.0 | 57.8 | 47.0 | 36.2 | 22.5 G0) oo. 6 Oct. 14 : : -| 80.7 | 76.4 | 69.7 | 61.0 | 50.2 | 88.2 | 25.7 | 12.6 1.0 neo. : : -| 79.9 | 78.5 | 65.0 | 54.6 | 42.5 | 30.1 | 17.5 5.2 6 Nov. 13 : 6 1 (858.1080 | 6058.) 4958) 80d 2358 elo 0.9 UB Ps) : : el etloD | (68n8) MINONe 3: || Lous: 1 3ls8 lea et9 GSS eal eneit. Decw3 | 76.9 | 66.9 | 55.4 | 43.0 | 30.3 | 16.3 Ae I no. 20 To indicate the law of the Sun’s Diurnal Intensity to the eye also, I have taken the relative units in the table as ordinates, and their times for abscissas, and traced —t ee = INTENSITY OF SUN’S HEAT AND LIGHT. 19 curves through the series of points thus determined, as shown in the accompanying diagram (Plate I). The Equatorial curve will be observed to have two maxima at the Equinoxes in March and September, and two minima at the Solstices in June and December. Since the earth is nearer the sun in March than in September, the curve shows a greater intensity in the former month, other things being equal. In the latitude of 10°, the Sun will not be vertical at the summer solstice, but only when the Declination is 10° N., which happens twice in the year. The curve corresponds in every particular with the known course of the sun. Above the latitude of 23° 28’, the tropical flexure entirely disappears; and there is only a single maximum at midsummer. For comparison with the curves of Inéensity, I have also traced curves of Tempera- ture observed at Calcutta, in lat. 22° 33’ N.; at New Orleans, in lat. 29° 57; at Philadelphia, in lat. 39° 57; at London, in lat. 51° 31’; and at Stockholm, in lat. 59° 20’. The values for Stockholm represent the averages for every five days during fifty years, as given in the Encyclopedia Metropolitana, article Meteorology. The curve for Philadelphia is adjusted from the daily observations made at the Girard College Observatory from 1840 to 1845, under the direction of Prof. Bache. The rest are interpolated graphically from the mean monthly temperatures. Retardation of the Eefect—In the Temperate Zone the Temperatures will be seen to attain their maximum about one month later than the sun’s intensity would indicate. At Stockholm it is somewhat more than a month; and, during this interval the earth must receive, during the day, more heat than it loses at night ; and, conversely, after the winter solstice, it loses more heat during the night than it receives by day. In illustration of this point, and to approximately verify the _ formula, I here insert a former computation of the sun’s Intensity for the 15th day of each month, on the latitude of Mendon, Mass., and the results are found to agree very nearly with those observed at that place about one month later, as fol- lows: (The observed values are taken from the American Almanac for 1849, and are derived from fifteen years’ observations.) Computed values. Observed values. Difference. Jan. 15. ; : ; 5040 23°.3 2493 Feb. lo . : : +1°.0 Rebw ie : : : 7142 Bey IL SO) dilene, 6 : : : + 4 IWileye, 78 116 E : : 9764 45°.2 45°.8 April “ : : : + .6 ANjouall 60" : ; : 12574 §8°.3 999.0) May, : ; : —3°.3 Mayans: 5 : : 14482 67°.1 64°.5 June “ x ; 3 —2°.6 dwme 8 : ; : 15346 719.1 71°.8 July “ é ; é + 7 Mulhy 9 5 : ‘ 15085 69°.9 68929) Amen c ; : F —!°.0 TAT Se : ; : 13437 62°.3 619.0 Sept. “ : . : — 12.83 Seite < : ; : 10860 50°.3 ASOr Om Octane: ; E , —1°.8 OG “~ ¢ : . : 8080 3879.5 RID | ING ‘ , : +1°.4 INOW "6 : : : 5638 26°.1 BUCK Were, 08 : ‘ i +1°.6 IDG, Hg : : : 4510 20°.9 269.0 Jan. ‘“ : : : soon It may be proper to observe that the formula was divided by sin L, a constant factor; and the numbers in the second column were then successively computed: their sum, divided by twelve, gave 10163 as the mean, to be compared with 47°.1, the observed mean at Mendon. Then as 10163 : 47°.1 :: 5040 : 20°.8, Jan. 15, etc. 20 INTENSITY OF SUN’S HEAT AND LIGHT. Let it also be observed, that the Mendon values are the monthly means, which do not always fall on the 15th day, but nearly at that time. Rate per Hour of the Sun's Intensity—To glance at the subject from another point of view, let us consider the Rate, or the relative number of heating rays per hour. For any day, if we divide the computed Intensity by the length of the day, the quotient will express the average Hourly Intensity, denoted by R& ; thus, E tan H R= 57 = 3 [5.94210] A? sin L sin D(z + 1). (19.) In the accompanying table, the values of the rate R are exhibited at intervals of fifteen days, and for every ten degrees of latitude. From this, Plate II is con- structed ; and for comparison with the Daily Rate of Intensity, the Daily Range of the Thermometer is also delineated for Trinconomalee, on the coast of Ceylon (lat. 9° N.)—taking 5°.72 Fahr. plus 1th of the mean daily ranges, as ordinates; also for Philadelphia (lat. 39° 57’), taking here 7° plus ird of the daily ranges; for Gittingen (lat. 51° 32’), taking rd of the daily ranges; and for Boothia Felix (lat. 70° N.), taking ;',ths of the daily ranges in degrees Fahrenheit as ordinates. These changes are arbitrary, but are analogous to the conversion of thermometric scales, and still preserve the original law of the curves. ‘The peculiar inflexion at the vertex of the curve of Hourly Intensity for latitude 70°, evidently arises from the change to constant day. And apparently the hourly rates of Plate I, coincide more nearly with the temperatures of Plate 1, than do the Diurnal Intensities, or absolute amounts. Average Rate of the Sun's Hourly Intensity, or Relative Number of Vertical Rays per Hour. (Plate Ii.) A. D. 1858. Lat. 0°. |Lat. 10°. Lat. 20°. Lat. 30°. |Lat. 40°.| Lat. 50°. |Lat. 60°.|Lat. 70°. |Lat. 80°. | Lat. 90°. danas. Al 6.43 | 5.89 5.16 4.94 | 3.26 2.08 | 0.88 me ee B= NG 6.51 5.99 5.32) | 4044 1) 3544) 9732 1.12 Bese ae Bio CO BL 6.63 6.20 5.56 4.66 | 3.86 2.75 1.56 0.34 5 ara Feb. 15 6.75 6.388 | 5.85 5.05 4,27 3.22 | 2.11 0.92 Rae Scie Mar. 2 6.80 Geb 9 Gall, WP SEDO) a 4aral 3.78 | 2.70 1.56 0.385 Hise CaN 6.83 | 6.70 6.38 BSI), |), Its) 4.25 Billy 2.21 1.03 30/0 April 1 Gaim Ontloul 6200 6.09 | 5.51 4.73 EC Dial eo 1.64 0.86 Sire seal LG} 6.58 | 6.67 | 6.56 6.21 5.70 5.02 |) 4.24 | 3.29 1.83 1.86 May 1 6.40 6:09) M625" Cr3Bv O68 G) al Osoe AnD OM nanos 2.68 2.72 Brie AKG} 6.23 6.48 6.53 6.40 6.01 5.46 4.71 S100) 3.35 3.40 LET ryt 6.08 | 6.39 6.49 6.36 6.07 5.54 4.78 | 3.62 3.79 | 3.85 June 15 6.00 | 6.388 | 6.45 6.34 6.07 DEON 4.81 3.82 4.00 4.07 July 1 6.01 6.382 | 6.44 | 6.36 6.12 5.58 4.83 3.18 3.96 4.03 Ba Gril 6.08 6.38 | 6.46 | 6.37 6.01 5.51 AO Oso: 3.68 3.14 Sere 6.22 6.46 6.50 GES Qe MONO SH anor ae AEGOu ooo. Solis) alas? Aug. 15 6.39 6.56 | 6.50 | 6.30 | 5.87 5.23 4,38 | 3.48 9.47 2.50 oO 6.54 6.60 6.48 Galea MONO oualeaser 4.05 | 3.10 1.90) | 1262 Sept. 14 6.64 6.60 Ouse s|monee: 5.45 4.70 | 8.68 | 2.61 1.50 | 0.61 OG OK) Gi: |) Osa 6.21 5.68 4.93 4.05 | 8.16 | 2.04 0.89 ets Oct. 14 6.73 | 6.47 6.01 5.36 Alba}, || ebay) 2.56 1.42 0.22 ; C9, 6.66 E29 Dae | bsO0R 2408: 1/3309 2.00 | 0.80 Sons Noy. 13 6.56 6.12 5.48 ALO} We e3() 2.66 1.48 | 0.25 eS 6.46 | 5.95 5.26 | 4.42 3.36 2.28 1.08 Dec. 13 6.40 | 5.86 Selisualas2o) 3.28 2.06 | 0.87 INTENSITY OF SUN’S HHAT AND LIGHT. Dil A close agreement, however, could not reasonably be expected; for the Intensities represent the sun’s effect at the summit of the atmosphere, but the Temperatures, at its base. Indeed, the sun’s intensity upon the exterior of the earth’s atmosphere, like the fall of rain or snow, is a primary and distinct phenomenon. While passing through the atmosphere to the earth, the solar rays are subject to refraction, absorp- tion, polarization and radiation ; also to the effects of evaporation, of winds, clouds, and storms, Thus the heat which finally elevates the mercurial column of the Thermometer, is the resultant of a variety of causes, a single thread in the net- work of solar and terrestrial phenomena. : There is still a general agreement of the delineated curves of intensity with actual phenomena. Should the inquiry be made, in what part of the earth the sun’s intensity continues most uniform for the longest period, an inspection of the flexures of the curves (Plate 1), at once indicates the region intermediate between the Equator and the Tropic of Cancer, on the one side, and of Capricorn on the other: Thus the curve for latitude 10° shows the solar intensity to be nearly stationary during half the year, from March to September. During October and November, it falls rapidly, and after remaining nearly unchanged for a few days in December, it again rises rapidly in January and February. As the sun’s heat is the prime cause of winds, we might infer that this region would be comparatively calm during the half year mentioned, and that in the remaining months there would be greater atmospheric fluctuations. Such were the general indications of Plate I, representing the amounts ; and, on recurring to Plate II, representing the rates of diurnal intensity, the status is pre- cisely similar, except that the region of summer calm is removed further from the equator, and nearer to the tropic. On referring to a recent work on the Physical Geography of the Sea, with respect to this circumstance, I find that “the variables,” or calms of Cancer and of Capricorn, occur in the very latitudes thus indicated by the compound effect of the amount and rate of solar intensity. And further, the annual range of solar intensity, which is least upon the equator, has its counterpart in the belt of equatorial calms, or “ doldrums.” The same effect extends also to the ocean itself, and appears in the tranquillity of the Sargosso Sea. While the curves of intensity for the higher latitudes are significant hieroglyphs of the serenity of summer, and the more violent winds and storms of March and September. The entire deprivation of the sun’s intensity during a part of the year, within the Arctic and Antarctic circles, may also produce a Polar calm, at least during the depth of winter. But the existence of such calm, though probable, can neither be disproved nor verified, as the pole appears not to have been approached nearer than within about five hundred miles. Parry and Barrow believed that a perfect calm exists at the Pole. 4 The connection of the curves of the Sun’s Intensity with the lines of Equatorial and Tropical calms, was suggested by Prof. Henry. 99 INTENSITY OF SUN’S HEAT AND LIGHT. SECTION V. FORMULA AND TABLE OF THE SUN’S ANNUAL INTENSITY UPON ANY LATITUDE OF THE EARTH. By the method explained in the last Section, the diurnal intensity, in a vertical direction, might be computed for each and every day in the year, and the sum total would evidently represent the Annual Intensity. The sum of the daily intensities for a month, or monthly intensities, might be found in the same manner. But, instead of this slow process, we shall first find an analytic expression for the aggregate intensity during any assigned portion of the year, and then for the whole year. The summation is effected by an admirable theorem, first given by Euler; a new investigation of which, with full examples by the writer, may be found in the Astronomical Journal (Cambridge, Mass.), Vol. II, p. 121. Thus, let w denote the wth term of a series, where wu is a function of 2. Attributing to w the successive values 1, 2, 3, 4,.... a, and denoting the sum of the results by = w, it is shown that, du du au = 4 Me Su fudat but qh A UD Pen ee oe AU) Since this important formula has not yet been introduced into any American treatise on the Calculus, I here insert one of the two demonstrations from the Journal referred to, which indeed was suggested by the present research :— Imagine the several terms of the original series to be ordinates of a curve, and erected at a unit’s distance from each other, along an “axis of X;” then, by the well- known formula of the Calculus, ff ud «x will represent the area of this curve. Again, connecting the upper adjacent extremities of the ordinates by straight lines, there will be represented an inscribed semi-polygon made up of parallel trapezoids whose bases are each equal to unity, and their areas equal to 2 (0 + F4)) +3 (Py + Fa) + .... 2 (Fe-» + Fe); adding the contiguous half terms, it becomes > Fy, — 2 Fa, or 2 u — 2 U. Between each trapezoid and the curved line above it, is a small segment ; and if f(a) or w denote the area of the last or ath segment, then = f (x) or > w’ will denote their collective area, The whole curve being made up of the inscribed semi-polygon and these segments, we have fude=su— zu+ su’, or Sus fudx+su—zu With respect to the last term, suppose w’ to be referred to a new curve, as has already been done for w, and so on; then, al Si fude teu — Su’, Sor Ss f Uae tu — Su"... INTENSITY OF SUN’S HEAT AND LIGHT. 93 Subtracting the last of these three equations from the preceding, and that result from the first, and cancelling, Tua fude+iu— ~wde—iw oe ane ul" It is now necessary to determine w’ in aan of u, OF 2 of xv. Recurring to the last segment of the curve above referred to, it is evident that its area above the trapezoid, and denoted by w’, is equal to Developing by Taylor’s theorem; since uw = F,), du Cu au Be-y = Ha — de + T2da— 128de* du au f Fe-y dz = [Fy C2 aro ais 1938da > eee Substituting the two right-hand values in the former equation, the first terms will cancel each other, leaving an ; Gu : ea 221i ee 22 a? ee 80 dat a an That is, each derived function is equal to — ;4,th of the second differential coefficient of the preceding, + 5';th of the third, &c. U S028 lpg aod Ml, yf un au 1 au 7 du Fu 2 we EB gs 120 Pa du lu Pu al da + fu'dx—... -=th gp 28 dae Feds Substituting these last two values in the ee above, du Pu Sua fuda+ tut y 50s I UW eee O} as was to be demonstrated. Let it now be applied to different examples of series, whose wth term is a function of a. I. To find the sum of the arithmetical progression, d+2d+3d4+...+ad=2u. ere) (Li eds ae Whence Su=tard+ttad+id+C. If Lig ia hen iy, ide @ Subtracting, 5 wu = + a(@d +d); which result coincides with the common arithmetical rule. Il. To find the sum of the geometrical progression, Ope GF do OPES 5 fob to OF Q4 INTENSITY OF SUN’S HEAT AND LIGHT. ar ; log 1" Here u=ar"'; fe dx= du : 2) Fre ar’ logr; Ae ar log? r; &c. The sum of the coefficients of a7” being constant, let it be denoted by B; then will SoS bar &C, Ifv=0, ar=Bar+C. IGE @ = Il, 0O= Ba+C. ar?+)__ ay Whence > u = nr reese on which also agrees with the well known rule. III. To find the sum of the trigonometric series, sina + sin2a+sindsa+t....+ sinwva. 1 Here u=sinwva; fu da =—~ cosxa. du Gu : a = AC0SHA; 73 = — A COS xa; dx 2 Chae ‘ proceeding, therefore, as in II., we have yu=2sinxa+ Beoosxat C. Ifa (0; 0= 6B + C: Su=tsinza+ B(cosxa—l1). If «= 1,sina=2 sina + B(cosa—1), SUN a cos ta And 13S 3 ee SS cosa—1 sin 4a ies cos t a(cos “a— 1) Su= 2 sinxa— 2 sin a Reducing to a common denominator, we have by Trigonometry, costa—cos(x+2)a sin(a+1)iasinzaxa 2sin za TT Sin 2 a Su= The formula of summation has its failing cases; but these may be pointed out as plainly as those of Taylor’s Theorem. Without entering here into a full dis- cussion, it must apply in all cases where the summation is in its nature possible, and the differential co-efficients do not become infinite. It applies rigorously where the terms are all positive, and the differential co-efficient becomes zero, as in Example I.; also where the collective co-efficient can be represented by a second constant, denoted by B, and so can be eliminated, as in Example II. and III. Had not advantage been taken of this feature in the last Example, the sum were repre- sented by the following series, which still converges rapidly when a does not much exceed unity: 1 Su, or > sinxa= — 7 cos wa + tsinaxat z,acoswa—7ize@cosxat....+C. Having now demonstrated the formula of summation, let it be applied to (18) where the diurnal intensity is measured by u= A? (sin L sin DL + cos L cos D sin H). INTENSITY OF SUN’S HEAT AND LIGHT. 25 It may be remarked that the arc H can be developed in terms of its cosine; A? may be expressed in powers of cos 6; and thus wu may be represented entirely in terms of the true longitude 7; and ultimately in terms of the mean longitude or anomaly; as, u= A+ Bsin(b+ ax) + Csin(c + 2ax)+4+ Dsin(d + 3aa)+...; where a or n denotes the Sun’s daily motion in longitude, or arc 59/8”; which is .0172. This arc being so much less than unity, shows that the regular process of summation without a second constant, will converge with extreme rapidity, stopping at the first differential co-efficient, and leaves us at liberty to determine the sum du. ‘ f ude+rrut A in such manner as may be most convenient. “ax Therefore, let « or ¢ denote the number of days elapsed after the beginning of the year or epoch; ” being the mean daily motion in longitude ; @ + n¢# ora’ + na, the mean anomaly; T, the true longitude, and P the longitude of the perihelion, so that the true anomaly 6 = 7— P,andd@=dT. Also, if w denote the obliquity of the ecliptic, then by Astronomy, sin D = sino sin T. Since cos H =— tan L tan D, we have sin? H = 1— tan’ L tan? D, or again cos’ L cos* D sin? H = cos’ L cos’ D — sin? L sin’? D. Substituting in the last mem- ber, 1 — sin? D for cos’ D, also 1 for cos? L + sin? L; then dividing by cos’ L, and taking the square root, : in? D sina\*.. Dein = [14 = f1— nT. 21, cos D sin nose E, (= +) sin (21.) With respect to A’, let us here write its values from equation (8), and another value given by the ordinary polar equation of the ellipse ; assuming A to be 1; and c, a new constant such that, since d @ is equal to d T, ik Oe cdT _—c(1 + ecos6y p ndavi—e& (1—ey © Substituting now the third members of the last two equations in place of the first members which occur in the preceding expression for u, and multiplying by dz, caT 5 2 eee: ; sin L sing sin T.H + cos L si (o) sin? T . (23.) The next step is to integrate this equation, where in the first term, sin w sin T has been substituted for its equal, sin D. The integral of the last term is readily : : : es SOC) identified as the arc of an ellipse whose eccentricity is RSIS therefore let (22.) ee f d Z| 1— (=5) sin’ T = E, an elliptic function of the second SPINES. Again, integrating the variable factors of the first term by parts, f sn T.HdT= — H cosT + f cos Td H. To obtain d H in a function of T, let us differentiate sin D = sin sin T, and cos H = —tan L tan D, giving cos Dd D = sin w cos Td T, : tan Ld D tan L sinw cos Td T ere and sin Hd H = TD Whence d H = RMT CASED COSuIDO! on substituting 4 26 INTENSITY OF SUN’S HEAT AND LIGHT. for sin H cos D its equal from (21), and for cos’ D its equal 1—sin’ @ sin? T’; then multiplying by cos 7, we have, tan L sina cos’ Td T (1 — sin’ o sin’ T) Ji sin aa sin? T Here in a changed form, siz cos’ T = sin o — sin w sin’ T, which is equal to 1 2 —— [(1—sin’® o sin’ 1) + sin? @—1], therefore writing — cos’ a in place of sin’ o—1, TO) and then separating the expression into two parts, we obtain after cancelling the common factor, tan L dT cos od T feosTdH=J | 5 > ae = 2 =}. (24, sin @ 2 Ji-( ws) sivT (1—sin*osin’T) q 1 (2S) sin’ T e aT Now let = === = F, an elliptic function of the first species ; and cee (o @ ) Ge TB J cos L Cs bs aN f : : = II, an elliptic function of the third species, (1—sin’ o sin* 7) Sin © es — (mney sin? T (aT according to Legendre and other geometers. Adopting these designations, we have now defined the terms of f udax, Passing over 3 w, as already known, the next term of the general formula of summation (20), is <4 : “. which is determined as follows: Taking the logarithmic differential of (13) a in its simplified form, u= A’ sin L sino sin T (H — tan H). du 2dA 1 d Cee ee eee T+(1 nae ot es tan H° Again, taking the logarithmic differential of the first and last members of (22), e —2esinddT i Galeeercosid GE first and third members of (22), 7— = a = “_ And the value of d H has Z ax cad T already been found; whence by making the indicated substitutions and changes, a Ue OED v1l—é —2esin6 tan? H tan L sin w cos T lay c Tsecosp 2 oo is (H—tan ie Dae The last term may be further simplified by multiplying and dividing by sin T, then substituting sin D for sin o sin T, and — cos H for tan L tan D, and so cancelling tan H, as shown in the result which follows. Referring to (20), and collecting the terms of summation represented by 5 w, we obtain the annexed general expression of the Sun’s intensity for any assigned part of the year; thus, recollecting that d 0 = d T, we find —— Also equating the eS INTENSITY OF SUN’S HEAT AND LIGHT. Dai c. cos L fu dx= ae 5 | B—tan Lsino cos. H+ ta’? L. F—tan*L cos’. mt} n + 2u =2 A’ (sin ‘L sin D.H + cos L cos D sin H) du uL?nd/ 1—e/— 2e sin 0 tan H cot T Lidge a 1a c Gaecos Gan dE Se tan Hl oe) Besta Ol — eer t Having thus obtained © u, we may regard it as an implicit function, varying continuously with the longitude T, which returns to the same value at the end of a tropical year. Taking, then, the sum of the above terms as an integral between the limits, 7’ = 360°, and 7’= 0; the purely trigonometric terms and constant haying the same values at the beginning and end of the year, will vanish, leaving only the three elliptic functions, multiplied as follows:— coos L z F Sie ——= | EE" + ta’ LL. F" — ta’ L cos’. Tl” ' 5 (2G) (25.) Ae . smo Here the eccentricity or common modulus is METER The Sun’s Annual Intensity upon any latitude of the Earth is thus proportional to the sum of two Elliptic circumferences of the first and the second order, diminished by an Elliptic circumference of the third order. On the Equator, L and tan L are 0, cos L is 1, and the expression reduces to Cc E" {4 = Fee (27.) This proves that the Sun’s annual Intensity on the n —eé Liquator is represented by the circumference of an ellipse, whose ratio of eccentricity is equal to the sine of the obliquity of the ecliptic. In the Frigid Zones, where the regular interchange of day and night in every twenty-four hours, is interrupted, the formula will require modification, though the general enunciation of the elliptic functions remains the same. The year in the Polar regions is naturally divided into four intervals, the first of which is the dura- tion of constant night at mid-winter. The second interval at mid-summer is constant day; the nd and fourth are intermediate spring and autumnal intervals, when the sun rises and sets in every twenty-four hours. For a criterion of the beginning and end of the winter interval, we evidently have H = 0; and for the limits of the summer interval H = 12". During the winter interval, there is of course no solar intensity. The intensity of the spring and autumn intervals will be found by integrating (25) between the including limits, which results, added to that of the summer interval, give the annual intensity. First, then, to examine the summer interval; H is 12 hours or x, sin H is 0, and consequently by (23), cd T csin L sinw cos T.2n fudenJf ——— sin L sina sin T . 2 = — — ——— nJ/1—e n/ 1—e cisely equal to the second term of (25), at the end of the spring, and at the beginning of the autumnal interval; so that on integrating between these limits, it 1 will entirely disappear; and the same will apply to 2 w + {4 e dx , which is pre- For at the begin- 28 INTENSITY OF SUN’S HEAT AND LIGHT. ning of the spring, and end of the autumn interval, when H is 0, 2 w becomes 0; : du . : and wu being a zero factor, 515 in (25) reduces to 0, ‘Then exclusive of the three dx elliptic functions, the intensity of the spring interval will be 2 w+ 75 zt —0; a that of the autumnal interval, 0 — 2 wu’ — +, Se and for the summer interval, by GP a du bw + 7); —_— 2 u — ;1, —_; the sum of which is evidently 0. dic ee The expression of annual intensity thus reduces to the three elliptic functions in (26) integrated between the limits of the spring and autumnal intervals. Their collective differential in (23) and the analysis subjoined to it, will give, by making Bye sino sin T Gig IG Ae tee cd Gee a4 PV Beer As sin LtanL Sup db iam Deis © n/1— cosZ (1 — cos’ L sin* Z) cos Z sin Ltan L cos L cos Z + sin? L re cos L cos Z +— may take the form —————,,——__, or Here co = Gs) 7) Note e cos L cos Z ose 1 — cos? L sin? Z sin” 0 il cos L eae OF 3| ——= —1+4+(1— sin? int Z) |, cos L cos Z cos L cos Z Lsin® @ st Again, differentiating the above value of sin Z, mo) cosL cosZ PCOS) L coo Ld Z d T= - . aL= =- whence sino cosT’ sino (2 $ Ey TaGaE ? 1— sin? Z (=) cdZ COS’ @ eae ae ne = = + sin’ @ 1—( ———) sin? Z — NSino / —e? “ 1 ee EY’ sin? Z eZ (ay \ \ sing sive DL cos? @ Res ey sel = TS (1—cos’ L sin’ Z id Ree Gey sin? Z BY7iA0) €. COS" @ udxz=— 2 g nsma / 1—e? ‘As before remarked, these three integrals are to be taken between the limits of the spring and autumnal intervals. At the beginning of the former and end of the ) Fs tao. E—sin LE, latter, H is 0; whence cos H or 1 = — tan L tan D; and D = 90° — L taken with an opposite sign for south Declination. In this case, ‘ sino sin T sin D sin Z = = — = —l,or Z = 270°. cos L cos L At the end of the spring, and at the beginning of the autumnal interval I is 12°; cos H or —1 = — tan L tan D; whence D is 90° — L, sin Z = 1, or Z = 90°. Now the elliptic functions integrated between the limits, Z = 270°, Z = 90° give semi-circumferences for the spring interval, and the same for the autumnal interval, the sum of which will be entire circumferences. We have, therefore, for the Annual Intensity in the Frigid Zones, INTENSITY OF SUN’S HEAT AND LIGHT. 99 4¢ 0080 2 eo = n sino / 1—e? | F4 tan’o. E' — sin? L. TI’ i. (28.) COS de sin@’ being the reciprocal of the modulus in (26); but the intensity is still denoted by three entire elliptic circumferences. At the Poles, where L is 90°, and cos L is 0, the expression of annual intensity 2censinw RECUCESM Ole ——— nJ/ 1—e? Here the eccentricity or common.modulus of the three elliptic integrals is (29.) The three species of elliptic functions are known to represent four equal and simi- lar quadrants, as in the ellipse. Extensive tables have been published by Legendre, of the numeric values of H and F; and in his Traité des Fonctions Elliptiques, Vol. I. p. 141, the value of the quadrant II’ is given in terms of Hand F. Thus, if « denote an axillary arc, such that c’ sin’ « = n, a negative quantity, less than 1; then, do tan x “T= é FS Seca ! Bees ! ” SG +nsin’o) V1—c' sin® 0’ Tete /1—ec sina COE alae ea): Comparing with (24), sin? x = oH Es TY = FF’ + ae (F" Ew — E' Fo); substituting this value into (26), we find for the ie Intensity in the Torrid and Temperate Zones, Swe = a (sin L cos @ . Figo 1) + c08 L) + 5 (0) OF. sin_L (sin? tan L— cosa. E _1))] We have heretofore denoted whole circumferences by the double accent, thus EK” = 4 #’. In (30) H’, and F” denote quadrants; F'2_1) and E >_ 7, elliptic Tbe SiN osL modulus ; Z denoting the latitude of the place, and » the obliquity of the ecliptic. The interpolation of Legendre’s tables for second differences, is described in Vol. II. p. 202 of the Fonctions Elliptiques. From the Polar Circle to the Pole, oISED SIN® functions whose amplitude in Legendre’s system is 90° — is the common will denote the common modulus, « becomes @, and ¥ 1—c’ sin?x = sin L; hence by (28), the Annual Intensity in the Frigid Zone 1s, Sa fe Seppe (sin L cosa. F(x) + Sino) + \ G1) - ‘Fr cos w cos L (cot w cos L—tan L. Ew))| With respect to the unit of measure for annual intensity, the mean tropical year contains 365.24 days; let this represent the annual number of vertical rays imping- ing on the equator; that is, let the sun’s intensity during a mean Equatorial day be taken as the thermal Unit, and let the values for all the latitudes be converted in that proportion. Also denoting the annual intensity on the equator by 12, the mean equatorial Month may be used as another thermal unit. And taking the annual intensity on the equator as 81.5 Units, with reference to Brewster’s formula, the intensity on other latitudes may be expressed in that proportion. 30 INTENSITY OF SUN’S HEAT AND LIGHT. With the aid of Legendre’s elliptical tables, and formulas (27), (80), (31), (29), the computation of annual intensities is entirely practicable. The results con- verted into units, with differences for every five degrees of latitude, have been carefully verified and tabulated as follows :— The Suns Annual Intensity. A herms her: hermal Diff. 9 Thermal | Thermal | Thermal Diff. exten, Ga ie Dae days. Textil. units. months. days. days. 0° 81.50 12.00 365.24 1.27 50° 55.73 8.21 249.74 20.92 5 81.22 11.96 363.97 3.78 55 51.06 7.52 228.82 21.06 10 80.388 11.83 | 360.19 6.28 60 46.36 6.83 207.76 ORME 15 18.97 11.63 | 353.91 8.70 65 41.92 6.17 187.85 14.81 20 77.03 11.84 | 345.21 11.01 70 88.61 5.69 173.04 9.82 25 74.57 10.98 | 334.20 13.20 75 36.42 5.36 163.22 6.59 30 71.63 10.55 321.00 15.30 80 34.95 5.15 156.63 3.80 3 68.21 10.04 | 305.70 17.15 85 34.10 5.02 152.83 1.24 40 64.39 9.48 | 288.55 18.76 90 33.83 4.98 151.59 0.00 45 60.20 8.86 | 269.79 20.05 From this table it will be seen that, at the Tropic of Capricorn, or of Cancer, the Sun’s annual Intensity is but eleven thermal months, being twelve on the Equator. In the latitude of New Orleans, the annual intensity in a vertical direction is ten and a half thermal months, and in the latitude of Philadelphia, nine and a half. At London the annual intensity is reduced to eight thermal months; and at the Polar Circle, to six months, being just one-half the value on the Equator. Thus the intensity irregularly decreases, till it terminates at the South or North Pole, where the annual intensity is but five thermal months. Again, it will be interesting to note the analogy which the differences for every five degrees of latitude, in the last column of the table, bear to the corresponding differences of height in the atmosphere which limit the region of perpetual snow. It has been observed that the different heights of perpetual frost “decrease very slowly as we recede from the equator, until we reach the limits of the torrid zone, when they decrease much more rapidly. The average difference for every five degrees of latitude in the temperate zone is 1,318 feet, while from the equator to 30°, the average is only 664 feet, and from 60° to 80°, it is only 891 feet—import- ant meteorological phenomena depend on this fact.” (Olmsted’s Natural Philosophy.) The differences of computed annual intensity in the table vary in a manner precisely similar. While in the Temperate Zone, the decrease for every five degrees of lati- tude is from 13 to 21 thermal days, yet it averages only about 6 thermal days within the Tropics and beyond the Polar circles. The line of congelation evidently rises in summer, and falls in winter, between certain limits. With reference to the connection between these annual Intensities and the observed annual Temperatures, the analogy of the Centigrade scale shows that units of intensity may be converted into degrees Fahrenheit, by a multiplier and constants; thus, d = (w—i) y+. Since the values of the multiplier y, and constants 7, a are not precisely known, a graphical construction will be employed ; and it is plain that INTENSITY OF SUN’S HEAT AND LIGHT. 31 if computed intensities and observed temperatures both follow the same law of change, their delineated curves will be symmetrical. eneretore! taking the latitudes for ordinates, and the Annual Intensities in ine table for abscissas, we obtain the curve of Annual Intensity (Plate III.); and, in the same manner, the curve of Annual Temperature. It will be seen, no doubt with interest, that the curve of annual intensity is almost symmetrical with that of European temperatures, observed mostly on the western side of that continent. But the curve of American temperature based on the U.S. Army Observations for places on the eastern portion of the continent, diverges from the curve of intensity, and indicates a special cause depressing these temperatures below the normal standard due to their latitudes. At Key West, on the southern border of Florida, the divergence commences, and on proceeding northwardly, continually increases in magnitude; that is, so far as reliable observations have been made along the expanding breadth of the North American continent. It were natural to suppose that the annual temperature would be defined by the annual number of heating rays from the sun. Indeed on and near the tropical regions, the curves of annual temperature and solar intensity are symmetrical. But in the polar regions, the irregularity of the intervals of day and night, and of the seasons, and various proximate causes, introduce a discrepancy, which the principle of annual average does not obviate. The laws of solar intensity, however, have been determined; the laws of terrestrial temperature will require a special and apparently more difficult analysis. It has been inferred that there are two poles of maximum cold about the latitude of 80° north, and in longitudes 95° E. and 100° W. ‘The fewness of the observa- tions, however, in that remote Hyperborean region, leave this question still open to investigation. The more recent “isothermal lines of mean annual temperature” published by Prof. Dove of Berlin, in 1852, indicate but one pole of cold, and that is very near the geographical Pole. SECTION VI. AVERAGE ANNUAL INTENSITY OF THE SUN UPON A PART OR THE WHOLE OF THE EARTH’S SURFACE. Havine determined the value of >w representing the Sun’s vertical intensity upon a single unit or point of the Karth’s surface, let us next ascertain the average annual intensity upon a larger area, a zone, or the entire surface of the globe. After which, we shall glance at some of the climatic alternations which are most clearly made known and interpreted by the mechanism of the heavens. Regarding the earth as a sphere whose radius is unity, cos L will be the radius, and 2 7 cos L the circumference of the parallel of latitude Z. It is evident that 32 INTENSITY OF SUN’S HEAT AND LIGHT. the intensity upon a single point multiplied by the circumference 2 x cos L, will express the sum of the intensities received upon the whole parallel of latitude ; consequently > w.22cos L.d L integrated between the limits of LZ and L/ will denote the sum of the intensities upon the zone or surface between the latitudes L and L’. By Geometry, the surface of this zone is proved to be equal to (sin L — sin L') 2x. Therefore the sum of the annual intensities divided by the surface, will evidently give uw, the average annual intensity of the Sun upon a unit of surface in that zone, as follows :— det Me Su.coseLdL sin L — sin Li To find the value of this integral, } « must first be.developed in terms of cos L. It is shown in (23), and in the analysis following that equation, that the annual intensity, exclusive of terms cancelled by the integration, is (32.) na cos Td T » A—sin*o sin’ ees SO ap sin’ J 2L sin? o cos L 4c >u=————. 3 | cos L. Hy | nJ/ 1— yee -(33.) From the well known formula for the rectification of the ellipse, we have in the first place, ; OPO OU @ sin’ @ sin® @ cos L. E’ = + (cosL—4 ai User” ais ee 175 a (34.) Next, to find the value of the last integral, let the radical of the denominator be first developed, and its terms multiplied into the other factors separately; then, preparatory to integration, let each numerator be divided by its denominator, as follows:— OOS. T — sin? T sin’ @ RO) mT oe ‘osin” pli +3 cos” a rE A to): (1—sin?@ sin? oie) fi sin 2 sin? T “ (2) (0) (¢) ; i ale oe 1 — sin? T eee sin? « ~~ 1l—sivrasiv TT sin2a 1 — sin? sin? T ACH aye 2 @O-= 1 sin? w sin® T cos? T 1 (— cos’ T + (a). ~~ Qc0s L 1 —sin?o si?’ T 2 cos L 3 sin' @ sin* T cos? T 3 (c) = q x 2 (= 8 cos’ L 1—sivasin® T 8 cost L sin” sin” T cos’ T — cos’ T + (a)). (d)= a (— sin* o sin* T cos’ T — sin? o sin? T cos? T — cos? T + (a)). (e)= os (—sin’ @ sin’ Tcos’T— sin‘ a sin* T'cos* T— sin’ @ sin? Tcos°T — cos*T + (a)). Multiplying now each term by d T, and integrating between the limits of T = > and 7’ = 0, we obtain the following results:— er INTENSITY OF SUN’S HEAT AND LIGHT. 33 e D) f @) a w= — scot 2 mee Ce Here substituting 4 — 3 cos? T 2 sino 9 L— sin’ o sin’ T for its equal sin? T, the last term will take the known form of ay ——_, where 9 p+ qcoso represents 2 7’; and by the Calculus its value between the proper limits, reduces to ae Henee f (a)d T= % (= —_—? 7 > == or Vv p—¢F COS@ Sin? @ since [Fone rare, were f oarad (1+ Sie), 1. suv GO) Since sin” T'cos’ T may take the form cos? T— cos* T’; the formula of the Integral : a ut 8 [Oa , MS SO 3 Calculus readily gives fo dT 9 ( ae ) as 8 2 sinto / 8cost L : : ie 1— cosa 5 In like manner ((d)d T= = (— =. sint@— % sin?>@—1 : Ke ) 9) EG Rae eee sin? o ) 16 cos’ L 1— cos w 35 And ((e)dT=2 — 73, sin’ o— 7 sinto — 3 si? a = he 2 ze ae ) 9) ( Bercy © Ree ere sia 1128 cos L The general formula (33) may be written— 4¢ sin? = sin’ @ Soc } cos LE’ adT+ bdT+. : n/1—e ZS J w’ > u nv 1— when L is 0, and cos LZ is 1. Tn this manner, and denoting the logarithms of the co-efficients by brackets, we find for the present century, > u = [2.543225] cos L + [1.197235] sec L + [1.211695] sec? L + (36.) [3.819015] sec’ L + [4.616548] sec’ L + [5.509114] se? LD +....J) > Or in numbers, 15.748 0.1628 0.00659 0.000414 os 3 006 sso tk >u = 349.3 2cos L + TE Ee cos L ae cos’ L a ( ) 5 3o4 INTENSITY OF SUN’S HEAT AND LIGHT. These formulas of Annual Intensity are applicable to the Torrid and Temperate Zones, and would have given those portions of the table in the last section with nearly the same facility as elliptic functions, but for the slow convergence of the series in the higher latitudes; the elliptic expressions are also preferred for the future case of secular values. Denoting the co-efficients of (36) by a,b, c,.... and with reference to formula (32), multiplying by cos L d L, and integrating, Su.csLdL=acseL .@dL+b.dL+ GeGill Waco lG 5, cos’ LL cos' LL cos’ L Su.cosLdL=atL+2sinLecosL)+bL+4ctanL+ Jee (ie) +e( Se EN al ( sin L a dL eee 5cos’ L 5” cos' L Tcos' L I~ cos’ L The last two integrals are given in the respective preceding terms. To determine the correction C, make Z equal to 0; in this case, the surface being 0, the left hand member and all the other terms vanish, except C, which is, consequently, 0. The next process is to find a similar formula for the Frigid Zone. Accordingly from (28), and the analysis preceding that equation, we have, (38.) z COsar cos Loose Zd Z | “ Sin w . (89. 2U= es Ey + ————— ? 9 (lL—cos’ L sintZ),|1— eos sin? Z | sin” @ This equation has precisely the form of (83); but there, corresponds to 90°—L here; and Z there, corresponds to 90°—o here; 7’ there, corresponds to Z here, and has the same limits of integration. Hence, by making the proper substitutions in (35) we may pass at once to the series for the annual intensity in the Frigid Zone} as here subjoined. Qcn | : : 1—snL 1—sinL—tooeL 1—sin L— cos L—3 cosh Sy ee si Lise ot : — = a aT ey A 2 sina 8 sin’ w 16 sin’ o 4, OG ley OO L— 3 cos* L — +, cos® DL), ble ae aiereis 40, 128 sin’ o 699) Multiplying this equation by cos L dL, or D sin L, and integrating, 2cen ' sno siv L sin L— + sin? L Pe C8 Od 5) ann sin L—3 sin? L — Jee. 3sinL) N—-5 aan § sin 3 L+ LO sinL) \ (AL) ats 8 sin’ @ zs 16 sin’ o yao” Here N denotes the numerator of the preceding fraction. Now, integrating between the limits Z = 90°, and L = 90° — o = 66° 32, also introducing the con- stant multiplier described after (35), we shall find for the Frigid Zone, fSu.cosLdL= [2.580718] } 9 4 iene gO) cae which is EY) equal to 13.733. Again, by formula (38), taking Z between the limits 0 and 23° 28’, we find the like sum between the equator and tropic, for the Torrid Zone, to be 141.86. INTENSITY OF SUN’S HEAT AND LIGHT. 35 And taking Z between the limits 23° 28’ and 66° 32’, the like sum for the Tem- perate Zone is 143.46 Substituting these values in equation (32), dividing by the denominator, and then converting into the same thermal measures, which were employed in the last Section, we obtain these final results:— The Sun's Average Annual Intensity. Thermal days. |Thermal months.| Thermal units. Upon the Polar Zones . é : é : : 166.04 5.45 37.05 « «Temperate Zones. : : : : 276.38 9.08 61.67 i ehornicyZonem : : 0 : : 356.24 11.70 79.49 « “ whole Harth . é : : : ‘ 299.05 9.83 66.73 Thus it appears that the Sun’s annual intensity upon the whole earth’s surface from pole to pole, averages 299 thermal days, being about five-sixths of the value on the equator. Though the figures in the last column are strictly units of intensity, yet as shown by the curves, they also approximately represent annual temperatures, except near the Poles. Following these indications, the mean annual temperature of the whole earth’s surface must be somewhat below 66° Fahrenheit. In comparison with this result, the mean annual temperature found by Prof. Dove, from a vast number of observations, may be introduced, which is approximately 58°.1 Fahrenheit. The like value found from the formula of Brewster, is fs 81°.5 cos? Ld L, which is 0 64°. 0 Fahrenheit. SECTION VII. ON SECULAR CHANGES OF THE SUN’S INTENSITY. In relation to secular variations of intensity, we shall adopt the hypothesis that the physical constitution of the sun has remained constant. ‘The secular changes here considered, therefore, are those which depend solely on position and inclina- tion, according to the laws of physical astronomy. The recurrence of Spots on the Sun’s disc, has lately been discovered to observe a regular periodicity. But their influence upon temperature appears to be insuffi- cient for taking account of them.’ A writer in the Encyclopedia Britannica, article Astronomy, states that “in 1823 the summer was cold and wet, the thermometer at Paris rose only to 23°.7 of Reaumur, and the sun exhibited no spots; whereas, in 4M. R. Wolf, in the Comptes Rendus, XXXV, p. 704, communicates his discovery that the minima of solar spots occur in regular periods of 11.111 years, or nine cycles in a century—and that the years in which the spots are most numerous are generally drier and more productive than the others—the latter being more humid and showery. Counsellor Schwabe, after twenty-six years of observation, does not think that the spots exert any influence on the annual temperature. 36 INTENSITY OF SUN’S HEAT AND LIGHT. the summer of 1807, the heat was excessive, and the spots of vast magnitude. Warm summers, and winters of excessive rigor have happened in the presence or absence of the spots.” Proceeding now to investigation, our first inquiry will relate to changes of the sun’s annual intensity upon the earth’s surface regarded as one aggregate. In Section II, formula (10), let the accented letters refer to the earth at an antecedent or future epoch; then, since Astronomy proves that the semi-transverse axis A is invariable, e” » we have for the proportion of intensity at the secular epoch d a (42.) In the Connaissance des Tems, for 1843, Leverrier has exhibited the secular values of most of the elements of the planetary orbits during 100,000 years before and after Jan. 1, 1800. The eccentricity of the earth’s orbit at the present time being .0168, the value 100,000 years ago, and the greatest in that interval was .0473. Substituting these in the preceding expression, we find that the sun’s annual intensity at the former epoch was greater than at present by one-thousandth part. Now this fraction of 365.24 days, counting the days at twelve hours each in respect to solar illumination, amounts to between four and five hours of sunshine in a year ; and by so small a quantity only has the sun’s annual intensity, during 100,000 years past, ever exceeded the yearly value at the present time. Nor can it depart from its present annual value by more than the equivalent of five hours of average sun- shine in a year, for 100,000 years to come. The superior and ultimate limit given by Leverrier, to which the eccentricity of the earth’s orbit may have approached at some very remote but unknown period or periods, is 777. At such epoch, the annual intensity is computed, as before, to have exceeded the intensity of the present by thirteen hours of sunshine in a year. On the other hand, the inferior limit of eccentricity being near to zero, indicates only fowr minutes of average sunshine in a year, less than the present annual amount. Between these two extreme limits, all annual variations of the solar intensity, whether past or future, must be included, even from the primitive antediluvian era, when the sun was placed in his present relation to the earth. By the third law of Kepler, on which equation (10) is based, these results are rigorous for siderial years; and by reason of the slight but nearly constant excess, the same may be concluded of tropical or civil years. or the annual variation of the tropical year is only — 0d.000 000 066 86. The preceding conclusions, it is proper again to observe, refer to the whole earth’s surface collectively. Let us,in the next place, inquire concerning changes of annual intensity upon the diferent Latitudes of the earth. According to formulas (30) and (31), this variation will be a function of the eccentricity e, and the obliquity o. For the present, let it be proposed to compute the annual intensity for an epoch 10,000 * Professor Henry was the first to show, by projecting on a screen in a dark room the image of the sun from a telescope with the eye glass drawn out, that the temperature of the spots was slightly less than that of the other parts of the solar disc. The temperature was indicated by a delicate thermo- electrical apparatus. Professor Sechi, of Italy, afterwards obtained the same result.—See S¢lliman’s Journal, Vol. XLIX, p. 405. INTENSITY OF SUN’S HEAT AND LIGHT. 37 years prior to A. D. 1800. The eccentricity of the orbit, e’, was then .0187, accord- ing to Leverrier; and for the obliquity of the ecliptic, the most correct formula is probably that of Struve and Peters, quoted in the American Nautical Almanac. It is true, their formula may not strictly apply for so distant a period; but, since the value 24° 43’ falls within the maximum assigned by Laplace, it must be a com- patible value, though its epoch may be somewhat nearer or more remote than 10,000 years. Therefore, epeinne this value of w, 24° 43’ in equations (80), (31) and multiplying by ajoeaeee ————., in order to substitute the proper eccentricity, and com- paring the ee ae with the table for 1850, given in Section V, as a standard, we find the annual intensity on the equator, at the former period, to have been 1.65 thermal days less than in 1850; the differences for every ten degrees of latitude are as follows:— Change of the Sun’s Annual Intensity 8,200 Years B. C., from its Vaiue in A.D. 1850, taken as the Standard. (Plate III.) Latitude Difference in thermal days. || Latitude. |Difference in thermal days. |) Latitude. [pitterence in thermal days. 0° —1.65 || 30° 08 | 60° 42.11 10° —1.58 | 40° —.29 | 70° “5.52 20° mS | 50° +68 | g0° +7.18 } | 90° +17.64 | These results are exhibited graphically also on Plate III; from which it appears that the annual intensity within the Torrid Zone ten thousand years ago, averaged one thermal day and a half less than now; while from 35° of latitude to 50°, com- prehending the whole area of the United States, it was virtually the same as at the present day. But above 50° of latitude, the annual intensity was then greater in an increasing rate towards the Pole, at which point it was between seven and eight thermal days greater than at the present time ; in other words, the Poles both North and South, 10,000 years ago received twenty rays of solar heat in a year, where they now receive but nineteen. Owing to change in the obliquity of the ecliptic, the Sun may be compared to a swinging lamp; at the former period, it apparently moved farther to the north and to the south, Baus more rapidly over the inter- mediate space. The maximum variation of the obliquity of the ecliptic according to Laplace, without assigning its epoch, is 1° 22’ 34”, above or below the obliquity 23° 28’ in the year 1801.1 Now the difference recognized in our calculation almost reaches this limit, being 1°15’. As the secular perturbations are now understood, therefore, it follows that, since the Earth and Sun were placed in their present relation to each other, the annual intensity upon the Temperate zones has never varied (Plate IIT); between the Tropics, it has never departed from its present annual amount by more than about 54,th part, and is now very slightly increasing. The most perceptible 1 Mécanique Céleste, Vol. II, p. 856, note, Bowditch’s translation. 38 INTENSITY OF SUN’S HEAT AND LIGHT. difference is in the Polar regions, where the secular change of annual intensity is more than four times greater than on the Equator; in its annual amount, the Polar cold is now very slowly increasing from century to century, which effect must continue so long as the obliquity of the ecliptic is diminishing. And thus, so far as relates to a decreased annual intensity, the celebrated ““ North-west passage” through the Arctic sea will be even more difficult in years to come than in the present age. Having now considered the secular changes of annual intensity upon the earth and its different latitudes, let us next examine the secular changes of intensity in relation to the Northern and Southern hemispheres. 'The earth is now nearest the sun in winter of the northern hemisphere on January Ist, and farthest from the sun in summer, on July 4th. This collocation of times and distances has the advan- tage of rendering the extreme of summer cooler, and of winter, north of the equator, warmer than it would be at a mean Aigienes from the sun. But south of the equator, on the contrary, 1t exaggerates the extremes by rendering the summer hotter and the winter colder. Benne estimating this difference, we may observe that the perigee advances in longitude 11’.8 annually ; by which the instant when the earth is nearest the sun, will date about five minutes in time later every year. ‘The time of perihelion which now falls in January, will at length occur in February, and ultimately return to the southern hemisphere the advantage which we now possess. Indeed, it is remarkable that the perizee must have coincided with the autumnal equinox about 4,000 B. C., which is near the time that chronology assigns for the first residence of man upon the earth. For ascertaining the difference of intensity, we know that the sun’s declination goes through a nearly regular cycle of values ina year. The formula cos H =—tan LI, tan D then shows that the length of the day in the southern hemisphere is the same as in the northern hemisphere about six months earlier, Recurring to formula (18), it appears that the difference of intensities will then depend chiefly on the values of A’, Now, for the northern winter on January me A’ isi ae to . The ratio gets te for winter in the southern hemisphere, July a— (1+ e 2 of daily intensity of the northern, is to the southern then as one to ra ; or as +¢ 1tol—4e nays that G 1 to 1—,',._ And the like ratio for the summer intensities isas1ltol +. But 1, is the extreme deviation for a few days only; the mean between this andl 0, or 545, ‘would seem more correctly to apply to the whole seasons of summer and winter. Taking then {1th of the greatest and least values of daily intensity, Section IV, for the nee zone, it appears that winter in the southern hemisphere is now about 1° colder, and summer 3° hotter than in the northern hemi- sphere. ‘The intensities during spring and autumn may be regarded as equal in both hemispheres. And the summer season of the south temperate zone being hotter, is also shorter by about eight days, owing to the rapid motion of the earth about ne perihelion. In confirmation of these last deductions, the younger Herschel refers to the glow and ardor of the sun’s rays under a perfectly clear sky at noon, and observes, INTENSITY OF SUN’S HEAT AND LIGHT. 89 “one-fifteenth is too considerable a fraction of the whole intensity of sunshine, not to aggravate, in a serious degree, the sufferings of those who are exposed to it with- out shelter. The accounts of these sufferings in the interior of Australia, would seem far to exceed what have ever been experienced by travellers in the northern ‘deserts of Africa. The author has observed the temperature of the surface soil in . South Africa, as high as 159° Fahrenheit. The ground in Australia, according to Capt. Sturt, was almost a molten surface, and if a match accidentally fell upon it, it immediately ignited.” (Herschel’s Astronomy.) The phenomenon is of sufficient interest to warrant a glance at the secular values. The eccentricity, 100,000 years ago, has already been stated at .0473; and the formula of the proportional general difference of the winter intensities, in the northern and southern hemispheres 1 — 2 e, becomes 1 — .0946; and the maximum difference 1 — 4 e becomes 1 —.1892. Thus the difference of winter intensities between the northern and southern hemispheres, and likewise of summer intensities, was then about three times greater than at the present time. But this wide fluc- tuation of summer and winter intensities, in relation to the two hemispheres, scarcely affected the aggregate annual intensities, as before shown. From occasional Historic notices of climate, it has been assumed that the winter season in Europe was formerly colder than at the present time. The rivers Rhine and Rhone were frozen so deep as to sustain loaded wagons; the Tiber was frozen over, and snow at one time lay forty days in the city of Rome; but the history of the weather presents winters of equal severity in modern times.! In the United States, likewise, since the period of our colonial history, the indications of an amelioration of climate are not conclusive. The great snow of February, 1717, rose above the lower doors of dwellings, and in the winters which closed the years 1641, 1697, 1740, and 1779, the rivers were frozen, and Boston and Chesapeake bays were at times covered with ice as far as the eye could reach; but the like occurs at similar intervals in our day. Mild winters, too, have intervened, and the other seasons are also very variable. The general indications, however, give rise to the question, whether there is a cause of change of climate in the course of the sun ? About two thousand years ago, in the time of Hipparchus, 128 B.C., the obli- quity of the ecliptic, or the sun’s greatest declination, was 23° 43’. It has now decreased to 23° 273’; therefore, at the former epoch, the sun came farther north and rose to a higher altitude in summer; and went farther south and rose only to a lower altitude in midwinter. ‘There is then an astronomic cause of change, of which we propose to determine more precisely the effect. For this purpose, the formula of daily intensity (18) may be written, w = [1.90746] € ata - Ce P)) sin L sin D (tan H+ Ff). — e 1 Thus, in the famous winter of 1709, thousands of families perished in their houses; the Arabic Sea was frozen over, and even the Mediterranean. The winter of 1740 was scarcely inferior, and snow lay ten feet deep in Spain and Portugal. In 1776 the Danube bore ice five feet deep below Vienna. 40 INTENSITY OF SUN’S HEAT AND LIGHT. Here, for A, there is substituted its equal .9; also gene- Il te —_ Gee 960” rally sin D = sino sin T, and cos H = —tan L tan D. For secular values, if ¢ denote the number of years after, and — ¢ before, the year 1800, e = 0.0167836 — .0000004163 ¢; P= 279°31/10” 4+ 1.0315 ¢; Mean obliquity o = 23° 27'54"’ — 0.4645 t — 0”.0000014 #. At the solstices of summer and winter TJ is 90° or 270°, and D is a; also let the latitude LZ be 40°, which is nearly the latitude of Philadelphia, also of southern Italy and Greece. Computing now for B.C. 128, and for A. D. 1850, the daily intensities at the summer solstice are 90.45 and 90.05 thermal units, and at the winter solstice 28.67 and 29.04 respectively. The differences .40 and .37 must correspond almost precisely to degrees of the thermometer; and halving them for the whole seasons as before described, we are conducted to the following conclusion. In the time of Hipparchus, or about a century before Julius Cesar, Virgil, Horace and Ovid flourished, wnder the latitude of Italy and Greece the summer was two-tenths of a degree Fahrenheit hotter, and the winter as much colder, than at the present day. The similar changes of solar intensity upon the United States in two hundred years, can only be made known by theory, and are evidently very slight. ‘There has been, therefore, no sensible amelioration of climate in Europe or America from astronomical causes. The effect, however, of cutting down dense forests, of the drainage and cultivation of open grounds and woodlands admit of conflicting interpretation, and appear but secondary to the atmospheric fluctuations which are governed by the changes in the relative position of the earth and sun. Before leaving the subject, the inquiry may arise respecting Geological changes, whether the secular inequalities have ever been of such value under the present order, as to admit of tropical plants growing in the temperate or frigid zones. In reply, as the annual intensity could never have varied in any considerable degree, the change must consist entirely in tempering the extremes of summer and winter to a perpetual spring. And this could not happen on both sides of the equator at once; for the same arrangement which made the daily intensities in the northern hemisphere equable, would subject those of the southern to violent alternations; and the wide breadth of the torrid zone would prevent the effects being conducted from one hemisphere to the other. Let us then look back to that primeval epoch when the earth was in aphelion at midsummer, and the eccentricity at its maximum value—assigned by Leverrier near to .0777. Without entering into elaborate computation, it is easy to see that the extreme values of diurnal intensity, in Section IV, would be altered as by the US G Pas Cf would diminish the midsummer intensity by about 9°, and increase the midwinter intensity by 3° or 4° ; the temperature of spring and autumn being nearly unchanged. But this does not appear to be of itself adequate to the geological effects in question. It is not our purpose, here, to enter into the inquiry, whether the atmosphere was once more dense than now, whether the earth’s axis had once a different incli- nation to the orbit, or the sun a greater emissive power of heat and light. Neither multiplier ( Nis that is 1 —0.11 in summer, and 1 + 0.11-in winter. This “5 INTENSITY OF SUN’S HEAT AND LIGHT. 4] shall we attempt to speculate upon the primitive heat of the earth nor of planetary space, nor of the supposed connection of terrestrial heat and magnetism ; nor inquire how far the existence of coal fields in this latitude, of fossils, and other geological remains have depended upon existing causes. The preceding discussion seems to prove simply that, under the present system of physical astronomy, the sun’s intensity could never have been materially different from what is manifested upon the earth at the present day. The causes of notable geological changes must be other than the relative position of the sun and earth, under their present laws of motion. If we extend our view, however, to the general movement of the Sun and Planets.in space we find here a possible cause for the remarkable changes of temperature traced in the geological periods. For as Poisson conjectured, Théorie de la Chaleur, p. 438, the phenomena may depend upon an inequality of temperature in the regions of space, through which the earth has passed. According to a calculation quoted by Prof, Nichol, the velocity of this great movement is six times greater than that of the earth in its orbit, or about 400,000 miles per hour. In this motion, continued for countless ages, the earth may have traversed the vicinity of some one.of the fixed stars, which are suns, whose radiance would tend to efface the vicissitudes of summer and winter, if not of day and night, with a more warm and equable climate. This may have produced those luxuriant forests, of which the present coal fields are the remains; and thus the existence of coal mines in Disco, and other Arctic islands, may be accounted for. If no similar traces exist in the Antarctic zone, the presumption will be strengthened, that the North Pole was presented more directly to the rays of such illuminating sun or star. Indeed, by this position, all possibility of conflict with Neptune, and the other planets which lie nearly in the plane of the ecliptic, was avoided. The description of such period, with strange constellations and another sun gleaming in the firmament, their mysterious effects upon the growth of animals and vegetation, their untold vicissitudes of light, shadow and eclipse, belong to the romance of astronomy and geology. As in the ancient tradition described by Virgil in the sixth Kclogue :— * Jamque novum terre stupeant lucescere solem : Altitis atque cadant submotis nubibus imbres : Incipiant silvee quam primum surgere, quumque Rara per ignotos errent animalia montes. It is evident that, in receding from the sphere of intensity of such star, as a comet from the sun, the earth’s annual temperature would very slowly decrease in process of time, according to the temperature of the space traversed. And, at a remote distance from the stars, the temperature of space ought to remain stationary ; as the mean annual temperature of the earth has remained for at least two thousand years past, and without doubt will so continue for ages to come. 42 INTENSITY OF SUN’S HEAT AND LIGHT. SECTION VIII. ON LOCAL AND CLIMATIC CHANGES OF THE SUN’S INTENSITY. As the principal topics under this head have been anticipated in the former por- tions of the work, they need not here be repeated. The inequality of winter, and especially of summer intensities in the northern and southern hemispheres, has already been discussed in the last Section, and ascribed to the changing position of the sun’s perigee. Let us now pass to another local inequality, which consists in the difference of daily intensities at two places situated on the same parallel of latitude, but separated by a considerable interval of longitude. This difference arises solely from hourly change of the Sun’s Declination, while moving from the meridian of one place westward to the meridian of the other; the Sun in the interval attaining a higher or lower meridian altitude. For example, the latitude of Greenwich, near London, is 51° 28/39”. Following this parallel:west to a point directly north of San Francisco, in California, the differ- ence of longitude is 122° 28’ 2’. At the time of the autumnal equinox, the daily change of the sun’s declination is 23’ 23’. Consequently, in passing from the meridian of Greenwich to that of San Francisco, the declination is diminished by os x 23/23", or by 157.3. When the Sun’s Declination is 0, at apparent noon at Greenwich, on Sept. 21st, it will be 7’ 57.3 S. at noon in the longitude of San Francisco on the same day ; the semi-diameter being 15’ 59” or 959” for Greenwich, and 959’.1 for San Francisco. With these elements, let the sun’s daily intensity be computed for both places by formulas (18), (18). The result is 50.13 thermal units for Greenwich, and 49.91 for the place north of San Francisco, on the same latitude. The difference is .22 corresponding to nearly + 2° Fahrenheit; and by so much the intensity upon the zenith of Greenwich is greater, on the same day. At the vernal equinox, March 20, the sun’s daily change of declination would be in the opposite direction, and the difference would become — +° F. The inequality of this species thus compensates itself in theory, leaving the yearly intensity the same for all places having the same latitude. For further reference on this point, the daily changes of declination, near the first of each month, are subjoined as follows :— January, 95’ May, | 18: September, 22’ February, 18’ June, 8’ October, 23' March, 23’ July, 5! November, 18’ April, 23! August, 17 December, 9’ In this connection, it may be observed that Nervander, Buys Ballot, and Dove have developed a slight inequality of temperature dependent upon the Sun’s rota- tion around his axis, and having the same period of about 27 days; but this result is not confirmed by Lamont, Poggendorff’s Annalen for 1852. INTENSITY OF SUN’S HEAT AND LIGHT. AU With respect to maxima and minima, Plate I exhibits a resemblance to two summers and to two winters on the Equator—the sun being vertical at the two equinoxes. On receding from the equator, but still in the torrid zone, the sun will be vertical at equal intervals, before and after the summer solstice, which intervals diminish as the sun approaches the Tropic ; the sun being vertical to each locality, when his declination is equal to the latitude of the place; as indicated in the annexed diagram. On arriving at the Tropic in the yearly motion, the sun can be vertical but once in the year, namely at the summer solstice. At all places more distant from the equator the sun can never be vertical, but will approach nearest this position at the solstice in summer (s), and be farthest from it at the solstice of winter (w). Thus in the torrid zone, the sun’s daily intensity has two maxima and two minima annually; in the temperate zones, one maximum and one minimum; and in the frigid zones, one maximum. Owing to change of the sun’s distance, the intensity is not precisely the same at the autumnal equinox as at the vernal; the difference, however, being smail, may here be neglected. And for more full illustration, we exhibit a different projection of the Table in Section LV, showing (Plate IV) the Sun’s Diurnal Intensity along the meridian at intervals of thirty days, from June to December, and approximately for the other months. The alternate curves will of course show the sun’s changes of intensity in intervals of sixty days. It will be seen that the sun’s least yearly range of intensity is not on the Equator, but about 3° of latitude from it north and south. Here the daily heat is most constant, and perpetual summer reigns through the year. In like manner, the diverging curves show an increasing yearly range, which is greatest in the Polar regions. Also the changes from one day to another are most rapid in spring and autumn. The greatest intensity occurs at the summer solstice, June 21, and the least, at the winter solstice, December 21; so that the yearly range from minimum to maximum is a little wider than the drawn curves indicate. Near the Polar-Circle, a singular inflection commences in summer, and the temperature rises rapidly to the Pole. These laws of Intensity are subject to the retardation in time, mentioned in Sec- tion IV, when applied to temperatures; and thus will correspond, generally, with observations. For example, the thermometric column will, during the month of May, rise faster at Quebec than in Florida, and still more rapidly at the Arctic Circle. It was proved, in Section IV, that the Sun’s intensity upon the Pole during eighty-five days in summer, is greater than upon the Equator. Indeed, at the summer solstice it rises to 98.6 thermal units, corresponding nearly to 98° Fahren- heit, which singularly coincides with the temperature of the human body, or blood heat. Though this circumstance may invest the Hyperborean region with new inte- rest, still we cannot assume a brief tropical summer with teeming forms of vegetable and animal life in the centre of the frozen zone. For the measured intensity refers - 44 INTENSITY OF SUN’S HEAT AND LIGHT. to the outer limit of the atmosphere, upon which the sun shines continually, but from a low altitude which cannot exceed 23° 28’. Much of the heat must, there- fore, be absorbed by the air, as happens near the hours of sunrise and sunset in our climate. Also “the vast beds of snow and fields of ice, which cover the land, and the sea in those dreary regions, absorb in the act of thawing or passing to the liquid form, all the surplus heat collected during the continuance of a nightless summer. But the rigor of winter, when darkness resumes her tedious reign, 1s likewise mitigated by the warmth evolved as congelation spreads over the watery surface.” (Hncyc. Brit., article Climate.) The sun’s intensity may yet have a somewhat greater effect upon the pole, where it pierces a thinner stratum of the atmosphere than over another portion of the earth’s surface. For, in consequence of the centrifugal force of the earth’s diurnal motion, the particles of air in all other parts of the earth, being thrown outwards, tend to an increased thickness, in spheroidal strata. We might thence infer that a less proportion of the sun’s rays would be absorbed, and a greater portion trans- mitted through the atmosphere, to the surface of the earth. However this may be in the immediate vicinity of the Pole, yet in the high latitudes hitherto visited by navigators, and which are not nearer than about five or six hundred miles from the North Pole, according to Dr. Kane and others,‘ a dense and lasting fog prevails after the middle of June, through the rest of the summer season, and effectually prevents the rise of temperature which the sun’s intensity would otherwise produce. The question of an open, unfrozen sea in the vicinity of the North Pole, has not yet been definitely settled. In this connection we shall only glance at some of the evidences on both sides, without discussing further a subject still unreclaimed from the domain of uncertainty. “Of this I conceive we may be assured,” says Scoresby, Vol. I, p. 46, “that the opinion of an open sea around the Pole is altogether chimerical. We must allow, indeed, that when the atmosphere is free from clouds, the influence of the sun, notwithstanding its obliquity, is, on the surface of the earth or sea, about the time of the summer solstice, greater at the Pole by nearly one-fourth part, than at the equator.” Hence it is urged that this extraordinary power of the sun destroys all the ice generated in the winter season, and renders the temperature of the Pole warmer and more congenial to the feelings than it is in some places lying near the equator. Now, it must be allowed, from the same principle, that the influence in the parallel of 78°, where it is computed in the same way to be only about one forty-fifth part 1 “The general obscurity of the atmosphere arising from clouds or fogs is such, that the sun is fre- quently invisible during several successive days. At such times, when the sun is near the northern tropic, there is scarcely any sensible quantity of light from noon to midnight.” (Scoresby’s Arctic Regions, Vol. I, p. 378.) “The hoar-frost settles profusely in fantastic clusters on every prominence. The whole surface of the sea steams like a lime-kiln, an appearance called the frost smoke, caused, as in other instances of the production of vapors, by the waters being still relatively warmer than the incumbent air. At length the dispersion of the mist, and the consequent clearness of the atmosphere announce that the upper stratum of the sea itself has become cooled to the same standard; a sheet of ice quickly spreads, and often gains the thickness of an inch in a single night.” 2 See Section IV (17). The value was first determined by Halley, Phil. Trans., 1693. INTENSITY OF SUN’S HEAT AND LIGHT. 45 less than what it is at the Pole, must also be considerably greater than at the equa- tor. But, from twelve years’ observations on the temperature of the icy regions, I have determined the mean annual temperature in latitude 78° to be 16° or 17° F. [that is, about fifteen degrees below freezing point]; how then can the temperature of the Pole be expected to be so very different 2” After some further argument, the author remarks in a note: “Should there be land near the Pole, portions of open water, or perhaps even considerable seas might be produced by the action of the current sweeping away the ice from one side almost as fast as it could be formed. But the existence of land only, I imagine, can encourage an expectation of any of the sea northward of Spitzbergen being annually free from ice.” On the other hand, the following indications in favor of an open sea, are derived from a recent article upon Arctic Researches, announcing that “the existence of the long suspected unfrozen Polar Sea has been all-but proved.” First, it was found that the average annual temperature about the 80th parallel, was higher by several degrees, than that recorded farther south. At the island of Spitzbergen, for example, under the 80th parallel, the deer propagate, and on the northern coast the sea is quite open for a considerable time every year. But at Nova Zembla, five degrees further south, the sea is locked in perpetual ice, and the deer are rarely, if ever seen on its coast. This has led physical geographers to suppose that the milder temperature of Spitzbergen must be attributable to the well-known influence of proximity to a large body of water; while the contiguity of Nova Zembla to the continent was thought to account for the severity of its climate. Secondly, Captain Parry reached Spitzbergen in May, 1827; from thence he went northward two hundred and ninety-two miles in thirty-five days, during which it rained almost all the time. The ice being much broken, and the current setting toward the south, he could not make way against it, and was compelled to return, which the current greatly facilitated. Besides the current here noticed by Parry, others had been determined before, and more have been ascertained since; so that powerful currents of the Arctic Ocean southward, may be considered as established. Thirdly, in 1852, Captain Inglefield, while making his summer search for Sir John Franklin, in the northeast of Baffin’s Bay, beheld with surprise “two wide openings to the eastward into a clear and unencumbered sea, with a distinct and unbroken horizon, which, beautifully defined by the rays of the sun, showed no signs of land, save one island.” Further on he remarks, “ the changed appearance of the land to the northward of Cape Alexander was very remarkable. South of this cape, nothing but snow-capped hills and cliffs met the eye; but to the north- ward an agreeable change seemed to have been worked by an invisible agency— here the rocks were of their natural black or reddish-brown color; and the snow which had clad with heavy flakes the more southern shore had only partially dappled them in this higher region, while the western shore was gilt with a belt of ice twelve miles broad, and clad with perpetual snows.” To these may be added the discovery of the southern boundary of an open Polar sea, in the expedition from which Dr. Kane has just returned, October, 1550. “There are facts,” observes this distinguished explorer, “to show the necessity and certainty of a vast inland sea at the North. There must be some vast receptacle 46 INTENSITY OF SUN’S HEAT AND LIGHT. for the drainage of the Polar regions and the great Siberian Rivers. To prove that water must actually exist, we have only to observe the icebergs. ‘These floating masses cannot be formed without terra firma, and it is a remarkable fact that, out of 360°, in only 30° are icebergs to be found, showing that land cannot exist in any considerable portion of the country. Again, Baffin’s Bay was long thought to be a close bay, but it is now known to be connected with the Arctic Sea. Within the bay, and covering an area of ninety thousand square miles, there is an open sea from June to October. We find here a vacant space with water at 40° temperature— eight degrees higher than freezing point.”* SECTION IX. ON THE DIURNAL AND ANNUAL DURATION OF SUNLIGHT AND TWILIGHT. Havine thus far considered the intensity of solar radiation upon any part of the earth, we shall lastly pass to examine its duration. In several publications it has been stated that “the sun is, in the course of the year, the same length of time above the horizon at all places.” On applying an ‘ accurate analysis, however, it appears, as will presently be shown, that the annual duration of sunlight is subject to a very considerable inequality. This annual ine- quality increases with the distance from the equator, and is proportional to the sine of the longitude of the sun’s perigee. The longitude of the perigee on Jan. 1, 1850, was 280° 21’ 25”, and increasing at the rate of 61”.47 annually; the sine of the longitude of the perigee is therefore decreasing in value every year, and with it, the inequality of sunlight. At the present time it amounts, in the latitude of 60°, to 36 hours—being additive in the northern, and subtractive in the southern hemisphere. ‘That is, in the latitude of 60° north, the total duration of sunlight in a year is 36 hours more, and in the latitude of 60° south, 36 hours less than on the equator. At either Pole the ine- quality amounts to 92 hours, or more than seven and a half average days of twelve hours each. ‘ The epoch when the inequality was at its last maximum, is found by dividing the present excess of the longitude of the perigee above three right angles, by the yearly change. ‘The excess, in 1850, was 10° 21’ 25”, which divided by 61”.47 gives a quotient of 606.5 years; which refers back to the period of the middle ages, A. D. 1248. At a still earlier epoch, this inequality must have entirely vanished. At that * A reference to Plate IV will confirm what was before known from observations that the extremes of summer and winter temperature range through wider and wider limits from the equator towards each Pole. The application of this general law favors an, open Polar sea in summer, as actually seen by explorers, and more recently by Dr. Kane’s party in the month of August. But it equally indicates that the sea is frozen over in winter, when there appears no assignable cause, but a calm atmosphere, to mitigate the most intense cold. INTENSITY OF SUN’S HEAT AND LIGHT. 47 epoch, the line of the apsides evidently coincided with the line of the equinoxes, which is computed to have been about 4,000 years before the birth of Christ, at which time chronologists have fixed the first residence of man upon the earth. The luminous year was then of the same length, at all latitudes, from pole to pole. Though the annual Duration of sunlight thus varies from age to age, and in the northern hemisphere differs from the southern; yet such is the law of the planet’s elliptic motion, that the sun’s annual Intensity at any latitude north, is precisely the same as at an equal latitude south of the equator. This immediately follows from formula (33), where the annual Intensity is developed in a series of powers of cos L, which is always positive, whether the latitude Z be south or north. Proceeding now to direct investigation, the half day with its augments, may be represented under the general form, H + increase by Refraction + Twilight. The first term H is found from the astronomic equation, tan L sin w sin T Beh ores ; ; ; Vie eT and this may also take the form! of elses sin ( tan L sin sin T ) V¥ 1—sin’ @ sin’ T. Let wu = 2 H, or twice the semi-diurnal arc; then the sum of all the daily values of wu through the year, may be found by the method of summation described Soy n(1 + ecos(L—P))’ 3 29 2 (1 — e)* sin™ (tan L tan D) d T 1 = SSS SS BE ETL 3 5 JS eae eae mak n i > (1 + ecos(T—P)yP oe cos H = —tan LtanD =— (43.) in Section V. By (22) we have dx = whence, The general formula of summation, Section V, has the terms 2 u + +, ae @ which in the present case vanish between the limits 7’ = 0, and 7’ = 27; as will appear from developing u or 2 H by (43), in terms of sin T. For the annual value is ‘therefore, >uw= ( uwdzx. Developing the denominator of 44), and substituting for IE fo) fo) D in the numerator, seems f sin (nEsho 8 7) aT } 1—2ecos(T—P) n 0 J/1—sin?o sin? TD +3 cos’ (I—P)—.... ar ae (45.) It is evident that sin — here would develope in odd powers of sin T, which mul- tiplied by d T, and integrated between the limits of 0 and 27, will vanish, as appears from the formulas of the Integral Calculus; when multiplied by d 7’. cos T;, or d sin T, and integrated between the same limits, they also will vanish, being _ powers of sin T. Also developing cos (I’— P) into cos T'cos P + sin T sin P, and neglecting terms, which would so vanish by integration, 1 On this and the following pages, s’m—!y denotes the arc whose sine is x; where x represents any given quantity. ; 48 INTENSITY OF SUN’S HEAT AND LIGHT, ay? ee Su=n2x eet (u—F)a T } —2esin Psin T—4 & (sin? P sin’ T + 3 sin P cos’ P sin T cos*T)—.... 5 (46.) ‘ a Here HI = has been substituted for its equal from (43); multiplying the —? into the following term, and integrating between the limits 0 and 27, the result vanishes. Also the terms multiplied by 4¢’ being small; it will be sufficient for them to develope from (43), to the first power, HT a = tan Lsinw sin T—.... by which their integral is immediately found to be — 4’ tan L sino x (sin? P.in + 3sinP cos’ P . 7); or—sensinasinPtanL. Besides this, it only remains to integrate the first term depending on H sin T'd T; but this corresponds to the first term of the formula of annual intensity (23); and if S denote thermal days in the Table of Section V, then f 9 Hsin TdT =([3.61540] Ssec L—E) 4 cot L cosec o; whence finally, converting into hours, 16 e(1—e)! sinP = 1S sas Se eR aG ((3.61540] S sec L — E’) cot L + §emsintotanL+....¢. (47.) On the equator, Z is 0, and the last part vanishes, leaving for the annual dura- tion of sunlight, vw 12", where w denotes the number of days 365.24. Therefore « 12" represents the mean value of the annual duration of sunlight, and the following terms express the Annual Inequality. When the. latitude is south, both cot L and tan L change sign; so that the inequality then becomes negative. For A. D. 1850, sin P is negative; substituting the value of this and the other elements for that epoch, yu=x12" + [2.16700] x {[3.61540] S sec L— F} cot L+[3.88700]tanL +.... (48.)' Here brackets include the logarithms of the co-efficients. By this formula the inequality may be readily computed for any latitude between the Equator and the Polar Circle. In the frigid zone, the summer period of constant day will make another formula necessary. As explained in Section V, the year in that zone may be divided into four periods or intervals. At the beginning of the spring interval, H is 0, and = — (90° — L); at the end of the spring and beginning of the summer interval, H is 12", and D = 90° — L; at the end of the summer and beginning of the autumn interval, also, D = 90° — L; and at the end of the autumn interval D = — (90° — L). oe) enables Sin w us to define the lengths of the intervals. Thus the summer interval is measured by the sun’s longitude passed over from 7’ = sin i =o T=2a—sin (22), SIN & SIN With these data, the equation sin D = sin w sin T, or T = sin ( INTENSITY OF SUN’S HEAT AND LIGHT. 49 : : cos L or the length of the arc is 7 — 2 sin —* (2 sino daily motion in longitude, and multiplied by 24, will give the number of hours of ). This divided by mn, the mean : : 6 oon Woes . cos L sunshine during the summer period, which is =| nm —2 sin? (2—)). n sina For the spring and autumn intervals, when day and night alternate, the values must be found by the general formula of summation. Here u = 2H = + 2sin—" (tan L tan D). (49.) 2 tan L sino cos Td T a oe (50) (1 — sin’ @ sin’ T) a 1— au = sin? T 1 _n(l + ecos P cos T+ esin P sin Lye dx adT(i—e): du Whence it will be seen that all the terms of 2 wu + +5 a vanish between the x limits of T = sin—1 — =, Sun * (eae: and T= sin ~ (qo) sin~ MG =i SIN @ SiN SiN SIN® 4. en. sin P sinw tan L cos T sin T ® sin T si . Here make ‘3 (1— sin’ @ sin” ay 1— (25) si T oe except the following, cos” HIE) ab = sin Z,and the expression becomes 4 en sin P sin 1b le sin’ Ztan Z sino iid: . And 3(1— cos’ L sin® Z ) this when taken between the proper limits of Z = + 90°, — 90°, evidently vanishes. Tt only remains to find if u d x between the same limits for the spring and the autumn interval. These limits show that the sun’s longitude passed over in the cos L two intervals is 4 sin ~? (=) which divided by » gives the number of days. sino This multiplied by the first term of w which is a or 12", and added to the like result for the summer period, gives 12 x as ora 12%. Andif sinT=— ie sin Z, OY n SiN @ sin D = cos L sin Z; then for the whole year, in hours, 2m ee sin L sin Z dT Sus oly in -.(51.) 2618 n Sys PN Se) (ae cos(T= Py It is here assumed that the integral will be taken successively between the limits of Z = 5 : 5 — 5 5 de m that is through a whole circumference. LL : Butd T= cos L OWL ayy Tempel Ee are oD . As the whole function sinw cos T’ sin se eee & sine? Z ‘aw! of Z by which d Z is multiplied, would evidently develop in odd powers of sin Z, it follows as in the former operation, that terms which would vanish by integration T 50 INTENSITY OF SUN’S HEAT AND LIGHT. may be neglected in advance, leaving for the last factor, eee as in (46), —2esin P sin T— 4 € (sin® P sin? T + 3 sin P cos’ P sin T cos? T’) — Substituting here for sin T its equal °° , Z; the first term of the product is smo 9 a gin 2. sip ( sin L sin Z >) cos L sinZcosZdZ Sito [el eo ee lie sin? Ge sin? @ JV 1— cos? L sin? Integrating this by parts, we have Qesin P. sin*(_#! sin L sin Z = 1008 L fas : = /1— cos Lsin?Z sin? @ ne? mZ.aZ. 1— cos’ L sin? Z Multiplying both numerator and denominator of the last term by the radical, it takes (sin L — sin L cos’ L sin* Z) the form of ramiescitiae 9 sin’ @ sin L dZ Z (1—cos* L sin’ - We Cos Ee sin’ @ sito Ji— 2 1— cos! L LE int Z “sino : sin L ae by + (sin L — — SU wv designate elliptic functions. When integrated between the above named limits, or an entire circumference, the former term of the integral vanishes, leaving only _ 8esin P sin L (E" — cos’ @. TY’). Wise Developing only to the first power, the next term to be integrated is _ 4 sin’? P cos’ L : . j -_— sin L sin* Z d Z, which between 0 and 2 z, gives sin’ @ 4 : ; cos’ L —dseéxn sin? P sin L. —__. sin’ @ — sin L cot? .1; where the letters F and I As the remaining terms are still smaller they may be omitted; whence Some 16e(1 ae é) sin P | si ay __ sin cos? @ W .2618 n sino SING SiN @ 43 gsi Fst 1008 Es ; (52.) sin? The multiplier for converting } w in Section V into thermal days S, is DiGi sean ¢ 365.24 | sin’ Lcos’@ IV 1.5065 S__cos’o : ; whence by (28 i vy its € 1.5065’ ar: sino 365.24 — sina eS ae substituting this, we have for the year 1850, ; Su=a12'+[2.16700] = sme, =. [B. 61540] > — —E+(1— Oe Ei ‘SIN 4 noes sin Lcos* Boe. (53.) Here the modulus or eccentricity of the elliptic quadrant is UND ; and the brackets Sin @ denote logarithms of the co-efficients. Such is the formula for the Frigid Zone. INTENSITY OF SUN’S HEAT AND LIGHT. 51 By means of equations (48), (53), I have computed the annual duration of sun- light & (2 H), according to the rising and setting of the sun’s centre, without regard to refraction. It is the half of 365.24 days, or 182.62 days increased by the quan- tities in the following table, for the northern hemisphere, and diminished by the same for the southern hemisphere :— | Annual Inequality of Sunlight. Latitude. Inequality. Latitude. Inequality. - 0° Oh. 00 m. 50° 24h. 08 m 10 3,25 60 360661 20 7 07 70 66 52 30 eS 80 86 = 02 40 16 840 90 92 Ol Having thus discussed the duration of Sunlight, let us next consider its increase by Refraction, and by Twilight. ‘The mean horizontal refraction, according to Mr. Lubbock’s result, is 2075”, or 34'35”; the barometer standing at 30 inches, and the thermometer at 50°F. But as this is somewhat greater than what has been usually employed, we shall adopt 34’ as the mean value for determining the increase of daylight by direct refraction. With respect to the duration of Twilight, A. Bravais, who has made extensive observations upon the phenomenon, observes, in the Annuaire Météorologique de la France for 1850, p. 34: “The length of twilight is an element useful to be known: by prolonging the day, it permits the continuance of labor. Unfortunately, philoso- phers are not agreed upon its duration. It depends on the angular quantity by which the sun is depressed below the horizon; but it is also modified by several other circumstances, of which the principal is the degree of serenity of the air. Immediately after the setting of the sun, the curve which forms the separation between the atmospheric zone directly illuminated by the sun, and that which is only illuminated secondarily, or by reflection, receives the name of the crepuscular curve, or Twilight Bow. Some time after sunset, this bow, in traversing the heavens from east to west, passes the zenith; this epoch forms the end of Civil Twilight, and is the moment when planets and stars of the first magnitude begin to be visible. The eastern half of the heavens being then removed beyond solar illumination, night commences to all persons in apartments whose windows open to the east. Still later the Twilight bow itself disappears in the western horizon; it is then the end of Astronomic Twilight ; it is closed night. We may estimate that civil twilight ends, when the sun has declined 6° below the horizon; and that a decline of 16° is necessary to terminate the astronomic twilight. ‘“‘T depart here from the general opinion, which fixes at 18° the solar depression at the end of twilight, and at 9° that which characterizes the end of civil twilight. 1 The phenomenon is equally conspicuous in the west, before the rising of the sun, and in certain states of the atmosphere is scarcely less beautiful than the rainbow, for the symmetry and vivid tinting of its colors. 52 INTENSITY OF SUN’S HEAT AND LIGHT. The numbers which I have adopted are derived from numerous observations.” “The shortest civil twilight takes place on the 29th of September, and on the 15th of March; the longest on the 21st of June. The shortest astronomic twilight occurs on the 7th of October, and on the 6th of March; the longest on the 21st of June, in this latitude. Above the 50th degree of latitude, twilight lasts through the whole night at the summer solstice.” The analytic solution of the problem to find the time of shortest twilight was first given by John Bernoulli; the result, found in various works, is expressed by the two equations, sin £ — 5 2 Th 2 \ coslat Here ¢ denotes the duration of shortest twilight, and m is the sun’s depression 16° or 18° below the horizon. To pursue the discussion of the physical details of twilight, would occupy too much space, and we shall here only glance at the method of Lambert for de- termining the height of the atmosphere from twilight. The demonstration is based upon the examples solved in Geh- ler’s Physikalisches Worterbuch. Lambert found that when the true depression of the sun below the horizon was 8° 3, (b), the height of the twilight arch was 8° 30, (a); and when the true depression of the sun was 10° 42’, the altitude of the bow was 6° 20’. In the figure let C denote the centre and A B the surface of the earth; D HE, the outer limit of the atmosphere; B, the place of the observer; and E, the position of the bow. Let r denote the refraction due to the altitude (a), then the angle H BH = a— ‘=a’, When the sun’s centre is apparently in the horizon of A, it is really about 34 below it. Denoting this horizontal refraction by 7’, and deducting it from 6, leaves the angle H BS=b—r’ =U’; where BS is parallel to the tangent A D. But the ray of light after passing A is further refracted by 7’ or 3¥ to E. The angle H BS or U, according to a proposition of geometry, is measured by the arc A B; whence the angle AC B= 0’; then drawing the chord A B, and ~ denoting the earth’s radius by R, the isosceles triangle A C B gives A B=2Rsinzv’. In triangle A B EH, the angle A is evidently 2 6—7’; and deducting the other three angles of the quadrilateral from four right angles, leaves the angle E = 180° —a—b'+7; then, sin Lor sin (a + U—1r’): sinh — 1) :: AB: BH= sin Dec. = — tan § m sin lat. a 2 R sin $b’. sin(2 era) (54.) sin(a’ + b’—1' In the triangle CB E, two sides and the included angle 90° + a’ are now given to find the third side CE; from which deducting R, leaves the required height of the atmosphere. INTENSITY OF SUN’S HEAT AND LIGHT. 53 - With this mode of calculation, the first observations of Lambert, before stated, determine the height to be 17 miles; and the second observations, 25 miles. And a still later observation would have given a still greater height, owing, perhaps, to the mingling of direct and reflected rays. The subject awaits further improve- ment; though some extensions have been made by M. Bravais, in the Annuaire Météorologique de la France for 1850. If we regard only the appearance of the Twilight bow, the limits of the sun’s depression assigned by M. Bravais are doubtless nearly correct, namely 16° for astronomical, and 6° for civil twilight. But, regarding only the actual intensity of light falling upon the eye, it appears that the effects of the bow are further increased by indefinite reflection among the particles of air, and this may increase the average limits to 9° for civil, and 18° for astronomical twilight. Without determining which view ought to be adopted, a mean has here been taken, and the following tables have been calculated on the assumption that the sun is 73° below the horizon at the end of civil twitight ; and 17°, at the end of astronomic twilight. The increase of the day by Refraction and by the twilights, may all be compre- hended in one general formula. Let m denote the sun’s depression below the horizon at the end of either period; then the distance from the Pole to the zenith, 90° — L, the distance from the Pole to the sun, 90° — D, the distance from the zenith to the sun 90° + m, or three sides of a spherical triangle are given to find the hour angle H+ YT, as in the following equation :— — sin L sin D— sin m sin m OAC ae re cos L cos D a ee cos L cos D Here + denotes the increase by refraction or by Twilight, according as m is taken ain oe ae Te, Oe IW, - When twilight lasts through the whole night, it is evident that at the commence- ment and at the end of such period, r= 12"— H. Substituting this value in (55), Ste S00 ID Sat , or cos(L + D)=sin m; that is, D=90°— L—m. (56.) cos L cos D The corresponding yearly limit for constant sunlight has already been found to be indicated by D=90°— LL. The lowest latitude where this is possible is evi- dently Z = 90° —a, or at the Polar Circle. In like manner, the lowest latitude where twilight through the whole night occurs, is L = 90° —o —m = 49° 32’ north or south of the equator. During the long night in the Polar regions, twilight will be, for a time, im- possible ; that is, so long as the sun continues more than 17° below the horizon. The limits of this period will be defined by making H +7 equal to 0, in (55); whence L — D = 90° + m, or D= — 90° —m + L. (57.) The corresponding yearly limit of sunlight is indicated by D= —90°+ LZ. But the application of these limits is reserved till after an expression for the annual duration of twilight has been found by the method of summation described in Sec- tion V. For this purpose, equation (55) may be put under the form of ede =) Sen 58 Tae H+ cos (cos H TE a) (58.) (55.) —l= 5A INTENSITY OF SUN’S HEAT AND LIGHT. Developing in powers of sin m by Maclaurin’s Theorem, sin m tsin’?msin LsinD 1 ...5 (cos L +(3sin® L—1)sin*D) ~ / cos L—sine aap (cos? L— sin’ D)} eee (cos’ L—sin® D) 59 Oy ayn ( 3sin Lsin D 5 sin® L sin? D ) es go) (cos’* L—sin*? D)z — cos’ LL. — sin® D)} With respect to the yearly limits already assigned, (55), (56), (57), we know that in the lower latitudes, twilight recurs regularly, while the sun’s longitude T varies from zero to an entire circumference; but in the Polar zone, this continuity is interrupted, Still, in integrating for the yearly duration of twilight between the CHOI : é : : : proper limits, 4 w + 31, —— being expressed in terms of sinD or sinT will vanish, even The in the Polar zone, leaving only fr udx. And with respect to da, since cos Td Tis d sin T, which multiplied into the development of 7, would integrate in powers of sin T which vanish, we may reject all such factors in advance, leaving, dig | om ae d T[1—2esin P sin T + 3 e?(cos’* P—cos2Psin?T)+....]. (60.) Were ae multiplied into (59), making w= 27, and substituting for sim D its equal sin w sin T, then integrating between the proper limits, and dividing by in order to convert arc into hours of time, we should obtain the annual duration of twilight expressed in elliptic functions. It will be more convenient, however, to resort to circular functions. To obtain the duration of Twilight in another form, let IV denote the mera of Night, from the end of the evening twilight to midnight, or from midnight to the morning twilight, computed by the sun’s midnight declination. ‘The duration of N will correspond to any assumed depression or elevation of the crepusculum circle, or to any compatible value of m. Then N = 12°—(H +7); sin L sin D + sin m cos Lcos D dN _—sin L—sinmsinD _ — sin L — sinm sin D ETO = “3 me ——<—————— d sin D cos L cos’ D sin N © cbs? 2D V cos? L—sin?m— sin? D —2sin Lsin msin.D cos N = —cos(H +7) = Developing cos’ D into the numerator under the form of (1 — sin’? D)~'; also resolving the radical into two factors, one of which is / cos? L — sin® m, and de- veloping the other into the numerator to the fifth power of sin D; then pul ane the factors, and employing Maclaurin’s Theorem, or integrating; also making cos? L — sin? m = s; Nice (2 aS sin L sin Dew 3 sin m cos” m sin®D sin L cos L, Pansy Si 6 sz 3 si’ L sin? My ae pl sin m Gee (cos 2m-+ 2+ ( cos2L 4+ 2+ 3 sin? L(1 + sin?m) i 5 sin* = sin 2) sin’ D 5 oe s sin L, 3 sin? m (1 n : Risin. 78 i = Vicor Oe (1 + sin? L) + 4 a 5 sin® DL sin® m (sin® m + D4 10s! \ 5 2 Bieeineely int . ae a i sin* I sin*m ) .. sin m 3 sin? 90 a oe Oh sin’ D— 5 | ¢0s Dhan tte apnea L (1 + sin? m) + 4 ne va $ ——— INTENSITY OF SUN’S HEAT AND LIGHT. Be 5 sin’ L (sin? m (sin? L 4+ 3) + 2) aL 30 sin’ TL sin? m(% + £ sin? m) i S 3? 315 ae sin* m \ ae Dee sin m os L by — N,,— N,,.... we have, N= ye N, sin D— N, sin? D — N, sin? D— N, sint D—.... Multiplying this by the former series for d #, and integrating the products, after (62.) Here let us put cos N’ = ; and denoting the co-efficients of sin D, sin? D.... 5 . 4 6 C oe ys TU substituting sin o sin T for sin D, and dividing by 3 24" (1 — 02)? 2 7t S2N= N’[T(1 + 38¢’ cos’ P) + 2 e sin PcosT—38 ecos2P fi4....] + sino N,[(1 +43 cos’ P) cos T+ ZesinP (+ Be’ cos2P f+ esl 2 3 — Se N, [i+ 3 cos P) { —2esinP ( —3 ecos2P f —. Nene _ six [(1 +3 & cos? "P) { —2esinP ( —3 e” cos 2P f—.. soll (G3) — mani a Oe 160s? "P) { —2esinP ( —3 e cos 2P (—. he ail re OM [143 cos" P){—2esinP ( —3e cos2P ( —.. ia] as a [143 cosP)(' —2e sin P ('— det cos 2 Pf — gat isi JC. The integral signs here designate the following quantities :— __ sin fe T i= fie TaT= net op ie a ee ae : oh sm4T sn2T , 3T f=sem GU Gg] 9 = a5 7 dt. on (64.) ie 5cos3 T 5 cos T ‘TdT — 698 5) coe J pae de ~ 80 a8 8 ___ sin 6 Ly asm4F lisn2T oT ar 2 64 RCL Gis ais In the year 1850, @ = 23° 272’; P= 280° 222’; e= .01676; tages oye 3143¢e’cos-P 1,000027; 2 ¢ sin P= —.032972; 3 e? cos 2 P= —.000788; 7! U—#)? _ 443.80. n.7 For the lower and middle latitudes, where 2 .N and 2 (H + 7) alternate in every twenty-four hours through the year, we may integrate through an entire circum- ference. In this case, equation (63) is materially simplified; and denoting by brackets the common logarithms of the co-efficients, > 2N=[3.44564] N’ — [1.26253] N, — [2.04360] N,— [1.55940] N, : — [0.03944] N, — [3.37930] N, — [3.68312] N.—.. - (ee 56 INTENSITY OF SUNS HEAD AND LIGHT: At the Pole, the duration of twilight is easily found by noting'in the ephemeris the time at which the sun’s declination south, is equal to the depression of the crepusculum circle below the horizon; this instant and the equinox being its limits of duration. As before indicated, the limit of refractional light is when the sun is 34 below the horizon, or m = 34’; civil twilight, when m = 72°; and common or astronomical twilight when m= 17°. Thus we shall find, Annual Duration. Sunlight. | Refractional Civil | Astronomic Darkness. | zy (2H). Light. Twilight. Twilight. 3 (2). North Pole. | 186d. 11h. 2d. 22h. 38d. 15h. 94d. 16h. 84d. 3h. Lat. 40°. 183d. 8h. Id. 14h. Q1d. 6h. 49d. Qh. 132d. 20h. Equator. 182d. 15h. ld. 5h. 15d. 21h. 36d. Lh. 146d. 14h. From this table, it appears that the annual length of darkness diminishes from the equator to the pole; while the duration of twilight increases from about one month on the equator to three months at the Pole. In this latitude, about thirty- eight hours of daylight, at the sun’s rising and setting, are annually due to atmo- spheric refraction. The second, fifth, and sixth columns correspond to the formula > (2H) +5 (27) +> (2N) = 365° 6". In further illustration of this subject, the duration from noon to midnight, or from midnight to noon, of Sunlight, Astronomic Twilight, and Darkness are exhibited to the eye in the accompanying Plate V, for every day in the year, on different latitudes. On the equator, it will be seen that Twilight has its least value, and is almost uniform through the year. In the latitude of 40°, the limiting curves of twilight bend upward in an arch-like form. The upper curve at the same time recedes from the lower, and encroaches upon the duration of darkness, till, as shown for latitude 60°, twilight lasts through the whole night in summer. If the first and last extremities of the curves at January and December be united to complete the circuit of a year, darkness there, will be represented by an elliptic segment ; the longest nights and shortest days being at mid-winter. In approaching the highest latitudes, the lines which form the limits continually change their inclina- tion, till at the Pole, they become perpendicular to their position at the Equator. The present Section contains formule and tables for determining both the diurnal and the yearly limits of twilight, with tabular examples for A. D. 1853, computed for 34’, 7° 30’, and 17°, depressions of the crepusculum circle below the horizon; the reasons for which have before been stated. Although these phenomena are varied by mists and clouds, and by the atmospheric temperature and density, still the assumption of mean depressions, has been necessary in order to obtain a general view of their laws of continuance. The duration of moonlight which is unattended by sensible heat, has not been discussed. From this source, the reign of night is still further diminished, till in this latitude, the remaining duration of total darkness after twilight and moonlight, can scarcely exceed three months in the year. The interval towards the close of astronomic or common twilight, corresponds to what is commonly termed, in the country, “early candle-light,” when the glimmering INTENSITY OF SUN’S HEAT AND LIGHT. 57 landscape fades on the sight, and the stars begin to be visible. The end of civil twilight marks the time at which some city corporations in Europe are said to have made regulations for lighting the street lamps. In conclusion, without entering into further details, the connection of solar heat and light has enabled us to exhibit, by the same formule and curves, the intensities of both in common. Indeed so close is the analogy that even the monthly height of the mercurial column, which shows the temperature, indicates generally the average intensity of sunlight in that locality. Half Days, or Semi-Diurnal Ares, in the Northern Hemisphere. 1853. Lat. 0°. | Lat. 10°. | Lat. 20°. | Lat. 80°. | Lat. 40°. | Lat. 50°. | Lat. 60% | Lat. 70°. | Lat. 80°. | Lat. 90°. . Io TN, h. m. h. m. Ino: 306 |} ls te h. m. h. m heme: h. m h. m. Jan. 1 6 00 5 43 5 24 5 03 | 4 37 3 58 2 51 0 00 0 00 0 00 CG 18 6 00 5 44 5 28 5 09 4 45 4 11 3 13 0 00 0 00 0 00 CO Bil 6 00 5 48 5 35 5 18 5: 00 4 33 3 49 2 04 0 00 0 00 Feb. 15 6 00 5 51 5 41 5 30 5 17 4 58 4 29 8 29 0 00 0 00 Mar. 2 6 00 5 55 5 50 5 44 5 3 5 26 5 10 4 40 3 00 0 00 eG 6 00 5 59 5 58 5 57 5 56 5 54 5 51 5 46 5 382 0 00 April 1 6 00 6 04 6 07 6 11 6 16 6 22 6 32 6 51 7 49 | 12 00 GE 6 00 6 07 6 15 6 24 6 385 6 50 7 12 7 59 | 12 00 | 12 00 May 1 6 00 6 11 6 22 6 3 6053 yet WS 7 52 9 12 | 12 00 | 12 00 Bar alt) 6 00 6 14 6 29 6 46 7 08 7 38 8 28 | 10 50 | 12 00 | 12 00 CS Bik 6 00 6 16 6 34 6 54 Wg UY 7 55 8 58 | 12 00 | 12 00 | 12 00 June 15 6 00 6 18 6 3 6 58 7 25 8 04 9 14 | 12 00 | 12 00 | 12 00 July 1 6 00 6 17 6 36 6 57 23 8 02 9 09 | 12 00 | 12 00 | 12 00 “16 6 00 6 16 6 33 6 52 lealyy e ol 8 51 | 12 00 | 12 00 | 12 00 eo Bil 6 00 6 18 6 28 6 44 7 04 7 32 8 19 | 10 20 | 12 00 | 12 00 Aug. 15 6 00 6 10 6 21 6 33 6 48 7 09 7 42 8 53 | 12 00 | 12 00 Se 0) 6 00 6 06 6 13 6 21 6 31 | 6 44 7 04 43 | 10 14 | 12 00 Sept. 14 6 00 6 02 6 05 6 08 6 11 6 16 6 23 6 37 7 18 | 12 00 Og OS) 6 00 5 59 5 57 5 54 5 52 5 48 5 43 5 33 5 03 0 00 Oct. 14 6 00 5 54 5 48 5 41 5 32 5 20 5 02 4 27 2 20 0 00 ee) 6 00 5 51 5 40 5 28 5 13 4 53 4 22 38 14 0 00 0 00 Noy. 13 6 00 5 47 5 33 By ig 4 57 4 29 3 43 1 46 0 00 0 00 oo ks 6 00 5 44 5 27 5 08 4 43 4 09 3 09 0 00 0 00 0 00 Dec. 13 6 00 5 43 5 24 5 03 | 4 387 3 OT 2 49 0 00 0 00 0 00 | Increase of the Half Day at Sunrise, or Sunset, by Refraction. | | | 1855. Lat. 0°. Tat. 10°. | Lat. 20°. | Lat. 30°. | Lat. 40°. | Lat. 50°. | Lat. 66°. | Lat. 70°. | Lat. 80°. | Lat. 90°. | | a ss m. m. in. m. m. m. m. m. m. m. January 2.5 2.5 2.6 2.8 3.3 4.4 6.7 0.00 0.00 0.00 February 2.4 2.4 2.5 2.7 3.1 3.8 5.1 9.0 0.00 0.00 March 2.3 2.3 2.5 2.7 3.0 3.8 4.6 7.0 14.0 0.00 April 2.3 2.4 2.5 2.8 3.2 3.8 5.0 8.0 0.00 0.00 May 2.4 2.5 2.6 3.2 3.5 4.5 6.1 22.0 0.00 0.00 June 2.5 2.6 2.8 3.1 3.7 4.9 7.6 0.00 0.00 0.00 July 2.5 2.5 2.7 3.0 3.5 4.7 6.7 0.00 0.00 0.00 August 2.4 2.5 2.5 2.8 3.2 4.0 5.2 9.7 0.00 0.00 September | 2.3 2.4 2.5 2.7 3.1 3.7 4.6 7.0 14.7 0.00 October 2.3 2.4 2.5 2.7 3.1 3.7 4.9 7.5 24.3 0.00 November 2.4 2.5 2.6 2.8 3.2 3.9 5.9 16.3 0.00 0.00 December 2.5 2.5 2.7 2.9 3.5 4.6 7.5 0.00 0.00 0.00 58 INTENSITY OF SUN’S HEAT AND LIGHT. Duration of Civil Twilight, Morning or Evening. 1853. Lat. 0°. | Lat. 10°. | Lat. 20°. | Lat. 30°. | Lat. 40°. | Lat. 50°. | Lat. 60°. | Lat. 70°. | Lat. 80°.) Lat. 90°. m. m. m. m. m. m. h. m. h. m. h. m. h. m. January 32 33 34 37 43 57 1 16 3 21?| 000 | 0 00 February 31 31 32 35 40 49 1 15 1 40 4 01?; 0 00 March 30 30 32 35 39 50 1 03 129 | 3 04 | 12 00? April 30 31 33 36 41 50 ANOS i209 0 00 0 00 May 32 33 34 42 45 58 1 37 1 10'; 0 00 0 00 June 33 34 B 40 48 64 2 46'|) 0 00 0 00 0 00 July 32 33 35 8 46 61 2 03 |. 0 00 | 0 00 0 00 | August 31 32 33 36 42 52 115 8 Ose O Wo 0 00 September 30 31 32 3 40 47 1 02 1 35 4 42! 0 00 October 30 31 32 385 40 4y 1 Ol Th Bik 3 26 | 12 00? November Bil |) BY 34 37 42 51 1 10 2 16 0 00 | 0 00 December 33 3 35 38 44 60 122 | 2 427} 0 00 0 00 Duration of Astronomical Twilight, Morning or Evening. 1853. Lat. 0°. | Lat. 10°. Lat. 20°. | Lat. 80°. | Lat. 40°. | Lat. 50°. | Lat. 60°. | Lat. 70°. | Lat. 80°. | Lat. 90°. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m h. m January TGS | ES TE ae) SE Es SS) OL BS 2 BO BEE) 2b BaP | @ OO February TO) aM) pa ales IE ak 83 1 43°} 220 | 3 382 | 7 492) 12 002 March WS OSS LOR a oe A at oa ALS) a UXO) Was Zee a OL We By cu Te Gh A | Er OO? April L097) oo) 2a 86 2 OU 13) 06) |) 40125) 10) 00) 2000 May Th WO} th eb ae) I aS Oh aly 3 33'| 1 107} 0 60 | 0 00 June 114 / 117 1 23 | 135 | 159 | 38 56!) 2 46'| 000 | 0 00 | 0 00 July WT) oe Sie ak eal 1 32 | 154 | 259 | 3 .09'| 0 00 ; 0 00 | 0 00 August TU) ay a ARNIS) oy) ab Pay oI 2K). ey LL 4 18'| 3 07'| 0 00 | 0 00 September) 108) 1.09) 113) 1 18 | 1 31 1 51 230 | 5 23'| 4 42") 0 00" October TOS) sy DEO: fe Te So PT) ak BS) dba 218 | 3 25 | 7 48 | 12 002 November (U2 key oy 22 SS ol S22 20d a oe 2378 10700 Mecemberd|] V4 TAO eS a Oat WZ OO onan vonOdzdmtsimosoal000 + Twilight through the whole night. 2 Twilight without day. Nore.—Astronomical Twilight includes the duration of Civil Twilight. PUBLISHED BY THE SMITHSONIAN INSTITUTION, WASHINGTON, D.C., November, 1856. ia AR | ve i ay bye a to) NSiTs AA 7? Nah DIURNAL oe iy Sinclair's hth, Philad® T INTERN SITY, VAL Ay BS pbis sf ty no A Hot 7 THE SUNS DIR Phil* th, s hi clair T. Sm 2 TESTI = 4 R HOUR OF THE PE = 4 a i RA’ VA RAG A + DAIL ai Ayub iti IG SUopye TS Sinclair's Jith, Philad* Ssi7Ty, ca q THE SUNS ANNUAL INTED pth, Phil® Sinclair's = T ae fe Bele DITRNAL INTENSITY ALONG THE MiRIDIAN, 9 SUNS IV. Polar Reoions. x 2 3 RH a & yn ine] a E AT INTERVALS OF THIRTY DAYS. Torrid Zone. fay DIRATION OF SUNLIGHT, TWILIGHT AND DARKNESS, Vv. = March. April May June — July Aus : EQUATOR. Darkness. LAT. 40° PHILADELPHIA . Sunhoht. Twilight. Darkness. LAT. 60° STOCKHOLM. oO ht. Twalidht. Sunlio NORTH POLE. St acca ali Constant Day. Twiloht. Darkness. T. Sinclair’s lith Phil Oe 2, Wes ie SMITHSONIAN CONTRIBUTIONS TO KNOWLEDGE. ILLUSTRATIONS OF SER EA bE... Gil 0-L. OG. BY EDWARD HITCHCOCK, LL. D., PROFESSOR OF GEOLOGY AND NATURAL THEOLOGY IN AMHERST COLLEGE. [ACCEPTED FOR PUBLICATION, JANUARY, 1856. ] y ot ‘ * eee | | as JosurH Henry, — | : Secretary Son ‘a i T. K. AND P. G. COLLINS, PRINTERS, : ; PHILADELPHIA. ACB a Oh = C:O NTE) N Iss. JP AL IIe IC, ON SURFACE GEOLOGY, ESPECIALLY THAT OF THE CONNECTICUT VALLEY IN NEW ENGLAND. INTRODUCTORY REMARKS TERRACES AND BEACHES Different kinds of terraces 1. River terraces 2. Lake terraces 3. Maritime terraces Sea beaches General lithological character of retranee and peaches Origin of the materials . Arrangement of the materials Details of the facts Former basins in the Gunneaiitart mailey Basins of the tributaries Mode of representing the terraces andl Deaenes 1. SECTIONS OF TERRACES AND BEACHES ON CONNECTICUT RIVER 1. In basin No. 1, from Middletown to Holyoke, commencing at the noth end Geoinere 19). 2. In the basin from Mount Holyoke to Mettarmamape (Toby), (Gecions foe 12) The Deerfield basin (sections 13—16) : c : The Westfield basin (sections 17—21) . In the basin extending from Mettawampe to the mouth of Miller s river (section 22) 4. In the basin extending ftom the modi of Miller’ s river 40 Bretileborcel (sections 28—26) 5. In the narrow basin from Eereleporenen to peters Falls (coat 2731) . In the basins extending from Bellows Falls to Wells river eae 32, 33) Terraces chosen as the sites of towns Terraces and beaches out of the Connecticut valle? but in New England or New York (sections 34—40) Terraces on rivers and lakes at the west in our country Delta and Moraine terraces i) on) 2. SURFACE GEOLOGY IN EUROPE Wales England il = : a SDMpPDnaanamrant MA — = He oo © — ~ bp eee le lor ya bo bo = a bo bo Or bo 26 26 30 82 34 34 35 1Vv TABLE OF CONTENTS. PAGE Treland ‘5 : : 5 : : Sra rats 3 35 Scotland 5 : 2 E 5 : 6 4 < 36 Valley of the Rhine . : : - : ° : . 38 Switzerland. : 7 0 i cate . 5 i 39 France 5 = é a ; ; 6 0 9 43 Seandinavia . 5 5a 3 3 J ; z . 43 8. TERRACED ISLAND IN THE HAST INDIAN ARCHIPELAGO . . 6 3 43 OTHER FORMS OF SURFACE GEOLOGY 3 : 0 0 e E 9 44 1. Sea-bottoms . : 5 j i 6 5 6 3 6 44 2. Submarine ridges. é 0 : é fi hate : : 44 3. Osars ; f : : 5 é 0 3 : 45 4. Deltas and dunes : 3 ‘ ° : 0 ‘ ; 45 5. Changes in the beds of rivers 2 : : 5 5 3 : 46 1. On Connecticut river . is p : 5 : : 3 46 2. In Orange, New Hampshire : 0 0 0 0 0 4T 3. In Cavendish, Vermont . : 3 : 5 0 0 4 48 4. On Deerfield river . A 5 : 5 ; ‘ . 48 5. On Agawam river ; : Q 0 : : 3 ; 49 RESULTS OR CONCLUSIONS FROM THE FACTS 5 : 5 5 ; z 3 49 ORIGIN OF THE DRIFT. ‘ ; fs 6 . 6 ; 6 : 72 1. Glaciers 5 : 4 ‘ i 5 : ! : 3 72 2. Icebergs 6 4 : : : é . . é : 72 3. Mountain slides 5 i 5 F $ 6 , : A 73 4, Waves of translation : : 5 4 4 Fi ‘ : 73 5. Ice floods. : 5 : : ‘ : : : ; 13 TABLE OF HEIGHTS OF RIVER TERRACES AND ANCIENT BEACHES . 6 3 i ; 76 Je AGIs Oe Sit Ite ON THE EROSIONS OF THE EARTH’S SURFACE, ESPECIALLY BY RIVERS. GENERAL REMARKS iS vittg : : . : : : 3 é 81 AGENTS OF EROSION é é d : 6 4 : : é 7 82 1. Atmospheric air ; , : : ; 5 ¢ . 82 2. Water : ; ; E : : ‘ . o . 83 CONJOINED RESULTS OF THESE AGENCIES ‘ ; é ; : 9 85 1. In the character of the present shores of men ocean . 85 2. In the extensive denudations of the strata by oceanic peaney, vilien the eariaee ai continents sunk beneath, and emerged from, the waters : : : 86 3. Erosions by drift : : F ; : 6 6 : : 88 4. Erosions by rivers. é 0 89 Marks by which river action can be listinemned rom arit agency : ; 89 Marks by which to distinguish between fluviatile and oceanic agencies : : 90 Modes and extent of erosion by rivers : : . : : . 91 Caution in the application of the preceding rules . . : é : 93 TABLE OF CONTENTS. Vv PAGE Devan OF FACTS 6 : 94 1. In the hypozoie or place cry neantine race) ach as arises) mica ndisie, falcon Ta &e. 94 a. In Buckland, on Deerfield river, a little west of Shelburne Falls : 94 6. Ancient river bed at the summit level of the Northern Railroad in New Hap: shire. ° : : c : : 6 : 96 ec. The Duttonsville jgnlf : : ; . 6 : : . 1038 d. The Proctorsville gulf - : , . : : . 104 2. In metamorphic and silurian Pols and newer aeandeiones ¢ 6 : 5 LOY 38. In limestone chiefly . : 0 ; 6 6 0 é SeuslalyG 4. In unstratified rocks chiefly . 5 : 6 : : : 5) Uy) Conclusions : 5 6 : 3 6 : : : Be) a} = SPINA IE ICE TRACES OF ANCIENT GLACIERS IN MASSACHUSETTS AND VERMONT = 129 INDEX . : 5 3 5 3 A : 5 eres 5 o Aldle) EXPLANATION OF THE PLATES . é 5 0 5 5 F 3 5 153 ILLUSTRATIONS OF SURFACE GEOLOGY. IP ua\ Ji Jt dt ON > Ukr A Clk Gr 0 LOG Ne ESPECIALLY THAT OF THE CONNECTICUT VALLEY IN NEW ENGLAND. CORRECTIONS. A change in the arrangement of the Plates, after a part of this Memoir was printed, makes a few corrections of reference necessary. Wherever on pages 6, 7, and 8 Plate XI is referred to, it should read Plate XII. Page 7, line 19 from bottom, for Fig. 3, read Fig. 2. Page 1, line 16 from bottom, for Plate IX, Fig. 2, read Plate X, Fig. 1. ON SURFACE GEOLOGY, ESPECIALLY THAT OF THE CONNECTICUT VALLEY IN NEW ENGLAND. IntropuctorY REMARKS. Ir has not unfrequently happened that those geological phenomena which lie nearest and most open to observation, have been the last to engage attention. The crystalline rocks were much earlier studied than the fossiliferous; and of the latter, the older and most deeply seated were well understood before Cuvier and Brogniart turned the attention of geologists to the tertiary deposits. It was not till a much later date, that the drift deposit, although so widely spread over the surface in northern regions, received any careful examination. And the subject of terraces and ancient beaches, is only at this late period beginning to call forth eareful and thorough investigations; although these forms of gravel, sand, and loam, present themselves along nearly all our rivers, around our lakes, and towards the shores of the ocean. I do not mean that these terraces, &c., have been entirely unnoticed by geologi- eal writers of the last quarter of a century. In the writings of Dr. Macculloch, more than thirty years ago, may be found some most beautiful delineations of these phenomena, and accurate descriptions of the very remarkable and peculiar terraces, called the Parallel Roads of Glen Roy, or Lochaber, which have engaged the attention of more subsequent writers than almost all other forms of the terrace. In the year 1833, the writer of this paper, in his Report to the Government of Massachusetts on its Geology, devoted some pages to a description of the river ter- races; and gave a theory of their formation, different from that usually received. But no accurate details of facts accompanied these views. - Some elementary treatises on geology have, within a few years past, presented the subject of terraces and ancient beaches. This is especially the case in the writings of Sir Charles Lyell. That gentleman, also, has given to the public, through learned societies and journals, several detailed descriptions of these phe- nomena in particular localities. The work, however, which seems to me to mark an era in this department of science, both in its presentation of facts and ability in reasoning, is Charles Dar- win’s Geological Observations on South America. It must have required extraordi- nary industry to collect the facts, and great familiarity with geological dynamics to 1 Y) SURFACE GHOLOGY. arrive at the conclusions, ‘This work was published in 1846, and directs geologists to the only true method of arriving at the truth on this subject, viz: by a careful investigation of the facts. The work, however, which first awakened a more especial interest in my mind, probably because it came under my notice earlier than that of Mr. Darwin, was Robert Chambers’ Ancient Sea Margins, published in 1847. Though dissenting from some of Mr. Chambers’ theoretical views, I saw at once that he had given us an example of the true mode of getting at the truth on this subject. The nume- rous cases of the elevation of terraces and beaches in Scotland above the ocean, which this work contains, showed us that the same facts were needed in other countries. I felt desirous of throwing in my mite towards the work, so far as the valley of Connecticut River is concerned, though a bad state of health was a still stronger motive for engaging init. But so many new views did my labors open upon me, that I have been stimulated to devote not a little time and labor to the subject of surface geology during the last seven or eight years. And I have been led to extend my observations beyond my expectations, not only in this country, but in Europe. I find the field to be a very large one; and that I have only begun to explore it. I have seen enough, however, greatly to modify, and as it seems to me to clarify, my views of the superficial deposits of the globe; and I venture to state my facts and conclusions before the scientific public. I use the term Surface Geology, to embrace the results of all those geological agencies that have been in operation on the earth’s surface since the tertiary period. Ail the changes that have taken place since that time, I regard as belong- ing to a single and uninterrupted formation, viz: the alluvial. The forces which were acting at its commencement are still in operation: but they have varied greatly in intensity at different times. Hence they have left various and peculiar products, of which the following are most worthy of note. Drift unmodified. Drift modified, which exhibits itself in the following forms :-— Beaches, ancient and modern. Submarine Ridges. Sea Bottoms. Osars. Dunes. Terraces. Deltas. Moraines. To which should be added the Erosions of the surface, from which the materials have been derived. If we were to attempt to arrange these products in a chronological order, we might designate four periods, beginning with the oldest. The Drift Period. The period of Beaches, Osars, and Submarine Ridges. The Terrace Period. The Historie Period. ee INTRODUCTORY REMARKS. 3 All the agencies, however, that have produced the above phenomena, are still in operation in some part of the globe; therefore, the above periods are intended to designate only the times when the different agencies were most intense, and pro- duced their maximum effect. In a strict sense, they are contemporaneous. ‘The Historic Period, however, merely designates the time since man and contemporary races have been upon the globe; and though it marks out an important zoological epoch, science has not yet been able to discover any correspondent geological change; though the presumption is, that one must have occurred, either local or general. Itis my purpose to go into a detailed description, in this paper, of only a part of the phenomena of surface geology, as enumerated above. I started with the intention of studying only the terraces and ancient sea-beaches in the vicinity of Connecticut River. I found these subjects, however, so closely related to other points, that to investigate a part would cast light upon the whole. The subject of erosions has specially attracted my attention, and, since these are not confined to the alluvial period, I shall treat of them in a separate paper. Unexpectedly, also, the marks of what I suppose to have been ancient glaciers, descending from the Hoosac and Green Mountains, fell under my notice; and I have devoted another short paper to an elucidation of the facts. In the present paper, I shall confine myself chiefly to beaches and terraces, with their associated phenomena, submarine ridges and old sea-bottoms. The subject of drift must, of course, receive some attention; since the other forms of detritus are mainly modified drift. But I assume that the general facts as to the phenomena of drift are understood by the reader. At the first, I did not expect to extend my observations beyond the valley of Connecticut River. But, during the six years that have elapsed, I have travelled extensively, both in this country and in Europe, with an eye always open to sur- face geology, and usually with some kinds of instruments for measuring heights. The facts thus obtained, sometimes indeed but few and unimportant, I shall em- brace in this paper. It is well known that, usually, geological maps exhibit but little of surface geology; save where the drift or alluvium is so thick that the subjacent rocks cannot be ascertained. Were the surface geology well exhibited in such a region as New England, these subjacent rocks would occupy but a small space. I have appended to this paper, a few imperfect maps of this character. One represents, as far as I have been able to trace it out, the surface geology of the Connecticut valley; and others, certain spots, chiefly in that valley, much more limited. It has been an object of strong desire with me, to construct a similar map of the whole of Massachusetts; and the Legislature of the State have given me assistance to col- lect the facts. If life and ability to labor be continued to me long enough, I shall hope to accomplish this object. The present paper is a preliminary to such a work. Several terms, mostly new, and necessary to a right understanding of surface geology, will need definition. Drifi is a mixture of abraded materials—such as boulders, gravel, sand, and mud—mixed confusedly together for the most part, but sometimes laminated, and occupying the lowest part of the unconsolidated strata, and lying immediately 4 SURFACE GHOLOGY. upon tertiary deposits, where they are present, or upon older rocks, where they are not. Modified Drift—When drift has been acted upon by waves, or currents of water, the boulders are reduced in size, they are smoothed and rounded, their strie are generally obliterated, and all the materials are redeposited in regular layers, being sorted into finer and coarser deposits, according to the velocity of the currents. These I call modified drift, which constitutes nearly the whole of what usually goes by the name of alluvium, and assumes various forms, according to circumstances. In this paper, the term alluvium includes not only modified but unmodified drift, for reasons which will appear in the sequel. Sea-Bottoms.—The bottom of the ocean, along the coast, is in many places covered by deposits of sand and gravel, left there seemingly by tidal action, and presenting often numerous ridges and depressions. Often, too, bars are formed across the mouths of harbors, producing lagoons. Hooks, also, are produced, where the cur- rents sweep around headlands. While these deposits are beneath the waters, they go by the name of shoals. If these shoals, bays, and harbors be raised out of the ocean, although they will be exposed to the modifying influence of rivers and rains, their essential characteristics will be long preserved; and my impression is, that these old sea-bottoms may still be traced in many parts of our country, to the height of 1,000 to 2,000 feet above the present ocean. Submarine Ridges.—By this term, I intend to designate certain ridges of sand and fine gravel that must have been formed beneath the waters, and yet are dif ferent from those ridges called shoals, and, perhaps, from any other submarine deposit described by Lieutenant C. H. Davis, in his admirable paper, in the Memoirs of the Academy of Arts and Sciences, “On the Geological Action of the Tidal and other Currents of the Ocean.” The great peculiarity of these submarine ridges is, that they slope in two directions—towards the lake or the ocean, on whose borders they lie, and towards the country; a fact which indicates subaqueous formation. The natural ridges around Lakes Ontario and Erie, are a fine example of the phe- -nomenon I am describing. (See Charles Whittlesey’s excellent paper, Am. Journ. Sci.,N.s., X, 31.) Perhaps, also, I may be able to point out one or two examples on the sea-coast. Osars.—These are similar ridges, formed beneath the waters, by currents piling up materials behind some obstruction. Their form is very much like that of a canoe turned over. I have not been able certainly to identify any ridges of sand or boulders in our country with the osars which I saw in Europe. But M. Desor, whose opportunities for observation upon this phenomenon have been very exten- sive, speaks of osars as occurring along the shores of Lake Superior. I have marked four on Map No. 1, (Plate III,) in N. H., viz: in Union, at the White Mountain Notch (at Fabyans), and a little south of Conway; but they are of doubtful character. I use the terms dune and delta in their common acceptation. The same is true of moraine, excepting that I think I have found some ancient moraines that have been subsequently modified by the action of water, whereby the coarser detritus has been more or less covered by water-worn and sorted materials. TERRACES. 5 Terraces and beaches form, perhaps, the most important feature of surface geology ; and, as I have directed my attention chiefly to these, I shall go into more details as to their nature and characteristics. It is hardly necessary to say that, though the term terrace applies to any level-— topped surface, with a steep escarpment, whether it be solid rock or loose materials, it is only the latter kind which are treated of in this paper; for I shall describe only those terraces which have been formed since the drift period—not even those which may be unconsolidated in the tertiary strata. Terraces are of three kinds :— 1. River Terraces. These are the most perfect of all, and are found along the shores of almost all rivers; but especially those passing through hilly countries, and forming narrow basins with a succession of gorges. River terraces may be subdivided into four varieties, differing in position, and probably, also, in their mode of formation. 1. The Lateral Terrace.—This is the ordinary terrace, which we meet along the banks of a river, often many miles in length, and sometimes even miles in width. 2. The Delta Terrace.—This occurs at the mouths of tributary streams, and was most obviously a delta of the tributary; but, as the waters sunk, the delta was left dry, and the tributary cut a passage through it, so as to form a terrace of equal height on opposite banks. 3. The Gorge Terrace.—This occurs either above or below the gorges of a stream, and is intermediate between the lateral and delta terraces, graduating into both. 4, The Glacis Terrace.—This is not level topped, but slopes gradually both ways from its axis—on the side next the stream much more rapidly than on the other. Outwardly it resembles the glacis of a fortification, and hence the name. It is usually found in alluvial meadows, and might, perhaps, be regarded as merely the uneven surface of a lateral terrace, as it is seldom more than a few feet high. But in some of the high valleys of the Alps, I found broad terraces sloping very rapidly towards the stream to its very brink, as well as in the direction of the currents, and Mr. Darwin describes the same kind of terrace in the high valleys of the Andes. Such terraces, then, I should regard as the true type of the glacis terrace, rather than those undulations of surface which we see in alluvial meadows. 2. Lake Terraces. These scarcely differ from the lateral terraces of rivers. Indeed, many small lakes, and even some of the larger ones, appear to have been merely expansions of rivers, such as are now seen in great numbers in the basin of the Upper Mississippi, west and southwest of Lake Superior. (See Nicollet’s Map.) These were formerly retained by barriers at a higher level when the terraces were formed, and, as those barriers have been worn away, the terraces have been left on their borders. 6 SURFACE GEOLOGY. 3. Maritime Terraces. Perhaps I ought not to speak of terraces as existing on the margin of the sea, but to regard all accumulations of sand and gravel there as beaches. Some of these accumulations, however, are so nearly level-topped as not to differ from genuine terraces, and this is the main distinction which I would make between terraces and beaches. It is not, however, a distinction of much practical import- ance. At the mouths of rivers, the two varieties are often seen running into each other. Moraine Terrace.—I apply this term to a peculiar form, not unfrequently assumed by the more elevated terraces, exhibiting great irregularity of surface; elevations of gravel and sand, with correspondent depressions of most singular and scarcely describable forms. I prefix the name moraine terrace to such accumulations, under the impression that stranded ice, as well as water, was concerned in their production. Sea Beaches. The most perfect of these are seen along the sea-coast in the course of forma- tion. They consist of sand and gravel, which are acted upon, rounded, and commi- nuted by the waves, and thrown up into the form of low ridges, with more or less appearance of stratification or lamination. As we rise above the terraces along our rivers, and often on the sides of our mountains, we find accumulations of a similar kind, evidently once deposited by water, and having the form of modern beaches, except that they have been often much mutilated, by the action of water and atmospheric agencies, since their deposition. These have hitherto been con- founded with drift, but they nearly always lie above it, and show more evidently the effects of some comminuting, rounding, and sorting agency—of water, indeed, since this is the only agent that could produce such effects. They evidently belong to a period subsequent to the drift, and I cannot doubt that they once constituted the beaches of a retiring ocean. The proof of this will be given further on. I have spoken of these beaches as lying above the terraces. I mean that they are at a higher level often, but geologically they are lower. When terraces occur as well as beaches, the latter always are seen at a higher level than the former; usually forming fringes along the sides of mountains. Yet in other places rivers may exist at a much higher level, which have terraces also; and usually above them we find beaches, still retaining the same relative position to the terraces. General Lithological Character of the Terraces and Beaches. As a general fact, I give the following description, applicable to the terraces and ancient beaches :— 1. The most perfect terrace is an alluvial meadow, annually more or less over- flowed, and increased by a deposit of mud or sand. Rarely are the materials as coarse as pebbles, except on a small scale. Yet usually they are sorted, laminated, and stratified. (See A on Fig. 1, Plate XI, which is an ideal section across a valley.) ae — TERRACES. 4 _ 2. Ascending to a second terrace, we almost invariably find it composed of coarser materials; or, perhaps more frequently, of sand at the top and clay at the bottom ; though sometimes the sand is all removed. (See B on Fig. 1, Plate XI.) 3. Rising to a third terrace, we usually find a mixture of sand and gravel; the latter not very coarse, the whole imperfectly stratified, and also sorted; that is, the fragments in each layer have nearly the same size; as if the waters that removed and deposited the materials, had a different transporting power for each stratum. (See C, Fig. 1, Plate X.) 4, A fourth terrace is sometimes found still higher, differing from the last only in being of coarser, but still of decidedly water-worn materials. (D, Fig. 1, Plate XI.) There is another important distinction. Hitherto the tops of the terraces have been for the most part level, unless worn away by agents subsequent to their formation. But now we find their surface not unfrequently piled up into rounded or curved masses with corresponding depressions, resembling what is called a chopped sea, or the eminences and anfractuosities on the surface of the human brain. The depressions are not valleys, which might have been made by currents of water, but irregular cavities, often a hundred feet deep, or more, usually not more than twenty or thirty, and perhaps more frequently not over ten or fifteen. Yet the materials forming the boundaries of these depressions are always water-worn and sorted, either sand or gravel. These irregular cavities and elevations do not always appear in connection with the fourth terrace, but sometimes with the fifth and sixth. Yet I believe there is never a level-topped terrace above them (that is, older) in the same series; and they are always below the beaches. They are a singular feature in the terrace landscape, and are among the most difficult of all the phenomena of these formations to account for satisfactorily. I shall of course recur to them again in a subsequent part of this paper. (See D, Fig. 1, Plate XI.) Plate IX, Fig. 3, is a sketch taken in the west part of Pelham, in which we see the more-perfect lower terraces, succeeded by others having the peculiarity of outline above described. Such sketches, however, give but a faint idea of these moraine terraces, as I now call them. They are shown also imperfectly on Plate IX, Fig. 2, taken in Russell, on Westfield river, with the Pentagraph Delineator, by Mr. Chapin, its inventor. 5. Above the irregular terrace just described, we find other accumulations of decidedly water-worn materials, generally coarser, the fragments of rolled and smoothed rock being sometimes a foot or two in diameter; yet still more or less sorted, so as to bring together those of a determinate size, or rather those not exceeding a certain size. Coarse sand, however, constitutes the greater part of the deposit, and sometimes the whole of it. Its outline is rounded, rarely with a level top for any considerable distance. Yet in its longest direction it maintains essen- tially the same level, and often may be seen for many miles,at the same height, and more or less worn away, as a fringe along the sides of the hills that bound a valley; appearing, in fact, as if these deposits once formed the beaches of estuaries that occupied those valleys; and such I suppose they were. (See Fig. 1, H, Plate XI.) As we rise above the most recent ancient beach, we find others at different levels, of materials less water-worn, more irregular in their form, and less con- 8 SURFACE GEOLOGY. tinuous in the direction of the valley. They seem to have constituted shores when the waters were higher, when less land was above the surface, and conse- quently the waves had less power to wear away and comminute the rocks. 6. Passing beyond and above the terraces and beaches, thus lying at the bottom, and along the sides of the valleys, we reach the genuine drift deposit (F, Fig. 1, Plate XI,) consisting of materials that are coarser, more angular, and less arranged in strata and lamine. These are strewn promiscuously over the hills, except those quite steep and high. They are also seen occasionally in the valleys, wherever the terraces and beaches have been worn away or never existed. Yet it must be con- fessed that it is often not possible to draw a distinction between the oldest beaches and the drift. They pass insensibly the one into the other. The large blocks of the drift are indeed frequently angular, but they are mixed with finer materials that have been ground down and rounded, either by aqueous or glacial agency; and the oldest beaches seem to be of essentially the same materials, somewhat more modified. It is important, also, to mention that what appears to be genuine drift, is some- times found mixed with, and sometimes superimposed upon, the beach and terrace materials. This is especially true of large erratic blocks. And it shows us that the drift agency, whatever it was, occurred in some places, after the modifying agency that formed the older beaches and terraces had been for a time in operation. Or, more probably, it was the same agency in modified forms that produced all the phenomena. Below the drift we find the consolidated strata. (G, Fig. 1, Plate XI.) _ The views that have now been presented I have attempted to exhibit to the eye on Fig. 1, which is an ideal section across a valley, showing the manner in which the terraces, beaches, and drift are usually found; the newer deposits being chiefly formed by the denudation and modification of the drift which lies beneath the others. But as to the number of terraces, their relative height, &c., we find in nature a great variety, and this section is intended only to give the general impres- sion that has been made on my mind by all the cases which I have examined. Origin of the Materials. 1. I have already said that the beaches and terraces appear to be mainly modi- fied drift. The agency by which the former have been produced, commenced the process of separation and comminution, carrying it at first only far enough to form the higher and coarser beaches. ‘The work still went on with another portion, till it was reduced into finer materials for the higher terraces—and still finer for the lower terraces, until, when it came to the lowest of all—our present alluvial mea- dows—the fragments had been brought into almost impalpable powder, so as to form fine loam. 2. Such a work could not go forward with fragments already detached from the ledges, as was drift, without subjecting the solid rocks to erosion, wherever exposed. Accordingly a part of the materials of the terraces and beaches must have been derived from this source. How deep in any place these erosions have ARRANGEMENT OF THE MATERIALS. 9 been made, may be learned by ascertaining how near the bed of the stream we find drift stris and furrows. From some facts of this sort, I am satisfied that though fluviatile erosion has been considerable in some places, even as much as 200 or 300 feet, in general no great amount of the detritus of terraces has been thus produced, except in loose materials. Arrangement of the Materials. 1. Stratification and Lamination.—All these deposits are more or less stratified, and most of the finer varieties are also laminated. The lamination is not unfrequently oblique to the stratification. The former is frequently inclined some 20° to the horizon, the latter usually quite horizontal, though the strata or laminz of clay are sometimes plicated. The Loess of the Germans, or Limon of the French, along the valley of the Rhine, is usually represented as neither stratified nor laminated. That it is a fresh-water deposit, all admit; and that the terraces along the Rhine are mainly composed of it, I was pspenll by Professor Noggerath, of Bonn, as I ascended that river in his company, in 1850. That it is also more or less stratified, I cannot doubt. Indeed, so it is represented by Sir Charles Lyell. But from its composi- tion (fine calcareous clay), we might presume that lamination would be mostly absent. The other deposit, apparently without stratification or lamination, is what in Scot- land is called bowlder clay; that is, clay containing pebbles and frequently quite large bowlders. Some which goes by this name in Scotland may be unmodified drift: but where it was pointed out to me, by Dr. Fleming, in Edinburgh, it appeared to be drift modified by aqueous action and deposited in the turbulent waters of the ocean. In this country the clay sometimes so much predominates that it is used for making bricks. I cannot doubt that imperfect stratification may be found in it. And here I ought to remark, that when a deposit has been exposed to the weather, even for a short time, all traces of stratification and lamination disap- pear: ie when fresh excavations are made in it, both these structures are distinct. By examining many such cuts, made by canals and railroads, T have frequently found the structure beautifully developed where no trace of its parallel arrange- ment could be seen at the surface. Even beds of pebbles, apparently thrown pro- miscuously together, are often found to be arranged in a stratiform manner. 2. Sorting —Wherever a section is made into a terrace, composed of clay, sand, and pebbles, we see that these varieties of material are usually arranged in distinct layers, the coarser together and the finer together. The impression is irresistible on the mind, that the water, which made the deposit at one time, had only velocity sufficient to move the finest sediment: at another, sand, finer or coarser; at an- other, small pebbles; at another, large pebbles; and sometimes to urge along masses of considerable size. In such cases the stream chose out and carried for- ward the largest pebbles or blocks, which its particular velocity would raise, leav- 9 a 10 SURFACE GEOLOGY. ing other fragments for a time when its power should be increased. In this way have the materials been sorted out more nicely than any mechanical skill could do. Details of the Facts. I now proceed to give an account of the facts which I have collected respecting terraces and beaches, within the last six or seven years. I began their examina- tion in 1849, and have since pursued it as diligently as my time and means would allow. And having, during that period, traversed several of the countries of Kurope, I improved the opportunity to notice these phenomena, though it was out of my power to make very numerous measurements. I have also travelled some- what extensively in our own country, to complete the comparisons. But it is along Connecticut river and its tributaries that I have made the most careful and consecutive observation. After reading Mr. Chambers’ Ancient Sea Margins, I felt desirous of determining the true heights of the terraces in this valley, by mensura- tion. For a time I used the common levelling instruments, and thus obtained numerous sections. This method I found, however, to be so laborious, in a coun- try like ours, where so few heights away from our railroads and canals have been ascertained, that some other method would be important, where the beach or ter- race to be measured was distant from any such ascertained heights. I obtained an Aneroid Barometer; but my early trials with it were so unsatisfactory that I gave it up in despair. But when I reached Liverpool, and was desirous of visiting the mountains of Wales, I purchased another, and found the results so satisfactory in the measurement of Snowdon and Cader Idris, that I carried it with me in all my wanderings. In going to Ireland, however, the hair-spring that regulates the index, was broken by the rough usage of my luggage. It was mended in Edin- burgh, but broken again before I reached Frankfort on the Main. Again I had it mended, and made use of it in Switzerland and Savoy. On my return to this country, I wished to ascertain whether the accidents to which it had been subject had affected its range. I soon discovered that they had. But instead of attempt- ing to use the adjusting screws, I obtained from the Smithsonian Institution the loan of one of Green’s Syphon Barometers, and commenced a series of observations in connection with the Aneroid. ‘Those were at length reduced, and thus making the Syphon Barometer the standard, I ascertained the error of the Aneroid, and found that for every tenth of an inch it gave only 78.47 feet of altitude. Thus was I able to correct all my observations made in Europe, after the injury of the instrument, and the results I shall give below. Having used the Aneroid Barometer so extensively, it might be desirable that I should go into details respecting the results, as compared with other measurements, in order to decide how much dependence can be placed upon the instrument. But these details would occupy too much space. If in my power, I hope to present them in some other form: for my own conviction is, that though this instrument cannot be depended on for nice observations, such as the mathematician needs, yet it is a most valuable help to the geologist. I think it can be depended on almost as confidently as the Syphon Barometer, except perhaps for very great altitudes. FORMER BASINS IN THE CONNECTICUT VALLEY. 11 In nearly forty observations, upon heights varying from 260 to 5000 feet, the dif ference between the two instruments rarely exceeded twenty feet, and in only one or two cases of great altitude, approached 100. Such an approximation to the truth, surely the geologist must regard as of great value, especially as the observa- tions can be made with so little inconvenience and delay. One of the most serious drawbacks upon this instrument, as appears to me, is the difficulty of adjusting it, or of ascertaining its range. In either case several observations must be made upon heights of several hundred feet. This is great labor for every turn of a screw. My experience leads me to conclude that to resort to the air-pump in such cases is not reliable. Former Basins in the Connecticut Valley. Originally, when the river stood at a higher level, this valley consisted of a suc- cession of basins, or expansions in the stream, separated, or perhaps connected by ridges, through which gorges were cut, and deepened by the river alone, or with the aid of the ocean. At present, so deeply has the bed been worn down, that these narrow lakes or ponds have disappeared. But they have left evidence of their former existence by the terraces on their borders. The following ancient basins are well marked. 1. From the mouth of the river to Middletown, a distance of twenty-five miles, it is bounded by steep and rocky hills, with a narrow meadow occasionally. Where the river enters this mountainous region, just below Middletown, the gorge is the narrowest: but in its whole extent it has every appearance of having been formed by the joint action of the river and the ocean. At Middletown the first, the longest, and the widest of these basins commences, and extends to Mount Holyoke, in Hadley, a distance of fifty-three miles. On the west side, however, the high land opens to the southwest of Hartford, so that on the line of the Hartford and New Haven Railroad, the summit is only a few feet above Connecticut river. It is certain, therefore, that when the river chose its present bed through the rocky region below Middletown, that bed must have been excavated nearly to its present depth; otherwise the water would have chosen the valley of the railroad in its way to the ocean. The passage through the mountains must have been lower than through Meriden, &c., to New Haven. At Enfield, in this basin, the river has cut through a sandstone range of con- siderable height. The highest terraces, however, rise above the rocks in most places; yet, during the deposition of the lower terraces, the long basin above described must here have been divided into two of nearly equal size. 2. The second basin extends from Holyoke to Mettawampe (Toby,) in Sunder- land, and Sugar-loaf, in Deerfield. From Holyoke, this basin must have extended southerly along the west side of Mt. Tom, and the other almost continuous trap ranges that extend to New Haven. Through this valley runs the canal railroad from New Haven to Northampton. But nowhere is this valley more than one hundred and thirty-four feet above the Connecticut at Northampton, and this is not so high as some of the terraces. The second basin, also, extends northerly from Sunderland, on the west side of 12 SURFACE GEOLOGY. Sugar-loaf and Deerfield Mountain, through Deerfield, Greenfield, and Bernardston. Here it joins the fourth basin of the Connecticut in the west part of Northfield ; so that the second and fourth were one basin when the higher terraces were de- posited. On its west side, this second basin must have been not less than one hundred and ten miles long. 3. The third basin extends from Mettawampe to the mouth of Miller’s river, in the northeast part of Northfield. It is narrow, and not more than eight or ten miles long. 4, The next basin reaches from the mouth of Miller’s river to Brattleborough. Some of its higher terraces extend across the barrier into No. 3, and also, as already stated, into No. 2, in Bernardston. Though seventeen miles long, it is narrow. 5. From Brattleborough to Westminster, seventeen miles, the bed of the river may be considered as a deep gorge through the mountains, similar to that south of Middletown. Through Westminster to Bellows Falls, embracing Walpole also, is a short, but very distinct basin, five miles long, with numerous terraces. Terraces also exist in most parts of the gorge, but they are narrow. 6. The next basin extends from Bellows Falls to North Charlestown, fourteen miles, where the mountains close in upon the river, as at Bellows Falls. Yet some of the highest terraces, at both extremities, pass over into the adjoining basins. 7. I regard the next basin as extending from Charlestown to Ascutney Mountain in the south part of Windsor, ten miles, although some of the terraces extend northerly into the next basin. Yet I cannot doubt, but that this mountain once formed a gorge. 8. The basins become less distinct as we ascend the valley, and I have not studied them as carefully in its upper part. I should say that we might regard an eighth basin as reaching as far as Fairlee, although the hills several times crowd closely upon the river south of that place. 9. From Fairlee, through Haverhill to Bath, the valley is wider, and the ter- races numerous and distinct. This basin may extend beyond Bath, which is the northern limit of my examinations. This spot is two hundred and ten miles from the ocean in a direct line along the rivers. On the map of the valley (Plate III,) accompanying this paper, I have marked the above basins more distinctly probably than facts will justify. But in the absence of all accurate delineations of our topography on the published maps of New Eng- land, I thought it would not be improper to represent elevations that do actually exist, in order to make myself better understood, even though they be more promi- nent than in nature. I would here take occasion to remark, that the most serious obstacle to my pro- eress in these investigations has been the want of accurate maps of the districts explored. Frequently have I spent the day (and the same experience is fresh in my mind as to older rocks) and have got a clear conception of the terraces, beaches, and hills in a considerable district. But on opening my map to delineate the same, I have often found, to my discomfiture, that no such region exists on the map as existed in my mind, and which I found in nature; and hence the greatest inac- MODE OF REPRESENTING TERRACES AND BEACHES. 13 curacy must be the result, and often total discouragement. Tor I should thus be charged with errors of observation by future geologists, when the fault lay solely in the maps. Massachusetts is the only State in New England that has con- structed an accurate map of its surface. And in that State the topography was omitted till near the close of the survey, and then hastily observed; so that it only presents us with insulated hills and ranges, as if they rose out of a level surface; whereas, no idea is presented of the longer and broader features of the country ; the comparatively low region, for instance, of twenty miles from the coast; the valley of Worcester, of the Merrimack, of the Connecticut, and the deep valleys of Berkshire. Imperfect maps are one of the great disadvantages under which American geologists labor, of which the European geologist knows but little. And it must be a long time before the matter is much mended. Basins on the Tributaries. The tributaries of the Connecticut exhibit successive basins of the same general character as those above described. But there are two of unusual importance, which I have examined. One is on the Agawam river, in Westfield, and the other on Deerfield river, in Deerfield. In the latter basin especially, we have an epit- ome of most of the facts concerning river terraces and changes in the beds of rivers. That spot I have, therefore, studied with care, and shall present a separate map of its features, and also of the Westfield basin. » Of some other peculiarly interesting places in respect to their terraces, I shall, also, present maps, on a larger scale than the general one. One will be given of the terraces at Bellows Falls, another of those in Brattleborough, and a third of those on Fort river, in Amherst and Pelham. Mode of Representing the Terraces and Beaches. On the general map of Connecticut river, from its mouth to Wells river in Vermont, a distance of two hundred and ten miles, I have attempted to exhibit the principal terraces by colors. There are many smaller ones, however, omitted; nor have I attempted to give the true width of the terraces with any degree of accu- racy. Only where the basins are the widest, there I have represented a greater breadth of terraces. ‘To give the terraces with entire accuracy, over so wide a region, would require a great amount of labor in observation, and then it would all be useless, because of the great imperfection of our present maps. All I have attempted, therefore, is an approximation to the truth. In the vicinity of my residence (Amherst) I have delineated the terraces with more accuracy, I hope. But in some parts of the river, especially its southern aud northern limits, I have not been able to examine with the care which would have been desirable. I trust, however, that my maps will answer for all the purposes I have in view. This I believe is a first attempt of this kind, and I have been led to feel how desirable a work it would be to present a map, on a similar plan, of all the terraces, beaches, drift and other forms of surface geology in the northern parts of our country. In the vicinity of Amherst I have attempted to show what I conceive would be a desirable 14 * SURFACE GEOLOGY. map for the whole country. But the work would be Herculean, even for New England. Yet if I were a younger man, I should have the ambition to attempt it. The colors on all the maps are the same for the same terraces, reckoning upward from the river. The lowest meadow I call the first terrace, and then count them upward; thence it follows, that the same color does not always represent terraces of the same height, since they vary in this respect on different streams; and, in general, the size and height of the terrace correspond to the size and height of the river. As to the beaches, I represent them all by one color, as I have not explored them with sufficient accuracy to enable me to make any correct distinction between the higher and the lower, nor do I know of any important object to be accom- plished by such a distinction. 1. Sections or TERRACES AND BEACHES. The larger part of the terraces which I have measured, I have also shown by sections across them, down to the level of the rivers on which they are situated. This will give a clearer idea of their relative size than description can do. Tables of their Heights. To save prolix details, I have thrown together into a table at the end of.this paper the heights of all the terraces and beaches which I have measured; their heights above the river on which they are situated; and usually, also, above the ocean. The manner in which the heights were obtained is also indicated. When measured by levelling, no mark is attached; when by the Aneroid Barometer, the letters A B; and when by the Syphon Barometer, the letters S B are added. The number of heights given is 219. Details of Sections. By means of maps, and sections, and tabulated heights, I hope to make facts on this subject understood without much detail. Yet the sections will require some explanations. I shall describe them by reference to the basins in which they occur. 1. In Basin No. 1, from Middletown to Holyoke, commencing at the North End. 1. In South Hadley. (See Section No. 1, Plate I.) The section commences at Mt. Tom, in Northampton, and runs east across Connecticut river. On the east side it strikes a high gorge terrace, which has been partially worn away by the river. The line of the section is only a few rods south of the gorge between Holyoke and Tom. East of the high terrace is a small stream, that seems to have been instru- mental in forming the lower terrace, which runs along the south side of the Hol- yoke range to Belchertown, sloping towards the Connecticut. This section might have been more instructive if extended to that place; but I have not obtained the requisite data, and those which I have used are merely barometrical. 2. No. 2 extends from Connecticut river at Willimansett, in the north part of DETAILS OF SHCTIONS. 15 Chicopee, at the foot of South Hadley Falls, to the high, sandy plain which extends easterly and southerly through South Hadley, Granby, Springfield, &. This plain is a little short of two hundred feet above the river, and two hundred and seventy- four above the ocean. It is essentially composed of sand, and I think that it sinks as we go south. Hast of this plain we strike beds of gravel, with irregular eleva. tions and depressions. Above these are accumulations of coarse materials, once beaches probably, but I have not measured their height. J am sure they may be found at different altitudes, even to the top of the hills lying east of this part of the Connecticut Valley and the ocean, as high as one thousand feet. 3. In Springfield, a little north of the centre of the city, and running from the river southeasterly, so as to cross the principal terraces in that place. The third terrace is the isolated remnant of one, probably of the same height as the first one we meet in ascending from the main street eastward, on which so many delightful residences have been chosen by the citizens. The intervening space, as shown on the section, was probably worn out by Connecticut river, which might formerly have run there, when at a higher level, or at least, a part of it. The terrace marked as one hundred and thirty-six feet above the river, is that on which the United States Armory is situated. I did not actually level to the top of these two right hand terraces; but have no doubt that their height is nearly as given in the section. 4. In the extreme northern part of Long Meadow, on the road to Springfield, commencing at the river, and running southeasterly to the level of the plain on which most of Long Meadow, and the higher part of Springfield, are situated. This upper terrace extends, with some irregularity of surface, eastward about nine miles to the railroad station in Wilbraham on the Western Railroad. Northward it reaches the foot of Holyoke in South Hadley, though broken by several streams. To the south, it reaches a ridge of sandstone, commencing at Enfield Falls in Con- necticut, and extending easterly to the hypogene rocks of Monson and Stafford ; though there may be places where the terraces overlie the sandstone, so as to con- nect with the upper terrace south of Enfield, that extends as far as Glastenbury. (See Terrace No. 2, Plate IIL.) 5. In East Windsor, commencing at the Connecticut river, and extending east- erly to the broad plain, on which stands the Theological Seminary, past which the section runs. 6. In East Hartford, from Connecticut river, at the south part of the village, to the sandy plain a little eastward. This plain I have supposed to be the same as the upper terrace of all the previous sections. If so, it slopes southerly as follows, in a distance of forty or fifty miles, viz: at South Hadley (Mt. Holyoke) it is 292 feet above the ocean; at Willimansett, 268 feet; at Springfield and Longmeadow, 200 feet; at East Windsor, 96 feet; and at Hast Hartford, 61 feet. But this point demands more careful examination than I have given it. 7. In Glastenbury, south part of the town. Then the valley becomes narrower, and, indeed, Rocky Hill, a trap bluff, appears on the west side of the river; and we may regard these as gorge terraces, such as form on the up-stream side of a barrier. Hence, as I find is usual, they are higher than those in the central parts 16 SURFACE GEOLOGY. of a basin. Yet the upper terrace of this section extends almost uninterruptedly to Middle Haddam, or Chatham. It is composed of sand, with coarse gravel, or even bowlders a foot or two in diameter. It is more irregular at the top than the lower terraces, and is, in fact, a moraine terrace. 8. In Wethersfield, a little north of the village, from Connecticut river west- ward, the highest terrace is probably the same as Main Street, in that village. It is sandy; the lower one loam. 9. This section begins near the mouth of Farmington river, on the bank of the Connecticut, and runs southwesterly to the level of the village, which stands on the highest terrace observable in that vicinity. This is sandy, the lower one loam. 2. Sections in the Basin from Mount Holyoke to Mettawampe. ( Toby.) To the surface geology in this basin I have devoted more time and attention than in any other, because I reside in it, and have lived in it most of my days. 10. The valley of the Connecticut, in the region of Northampton and Amherst, is not less than fifteen miles wide, from the old beaches on one side to those on the other.. From the north part of Northampton, through Hatfield, Hadley, and Amherst, to the middle of Pelham, I have carried a level more than eleven miles, and the section, No. 10, presents the results. It shows, first, terraces on several existing small streams, besides the Connecticut; secondly, terraces and beaches on what I regard as two ancient beds of the Connecticut, one along the west side of Amherst, and the other along its eastern side. The ridge between is mainly com- posed of rearranged and water-worn materials; but the surface is too irregular for terraces, and I fancy that they might have formed beaches, though terraces occur on their sides; thirdly, as we approach Pelham, we come upon the upper part of a small stream, called Fort river, which descends from the hills of Pelham, almost in the direction of the section. On both sides of this stream I found numerous terraces, some of them delta terraces, and others, lateral terraces; although not all of them are very perfect, yet lying at a convenient distance from my residence, I have given them a good deal of attention, and regard them as very instructive. I have thought that they deserved a separate map, which I have given (Plate VI, Fig. 2,) as they could not be represented on the general map. The general section I have carried along the south side of the stream, as high as the terraces exist, and then it is continued across the south branch of the stream (a mere brook), so as to cross what I regard as three beaches; one of them more than 1,000 feet above Connecti- cut river. The highest of the terraces, No. 9, which is 383 feet above Connecti- cut river, occupies a gorge having Mount Hygeia' on the north, and a correspond- ing elevation, less bold, on the south. Above this spot is a depression, or basin, above which, on the north side of the stream, occur several distinct terraces, lying against Mount Hygeia; while at a still higher level, on the north, are large banks 1 T apply this name to a bluff 706 feet above Connecticut river, rising directly above a fine mineral spring, of the chalybeate character, in a most romantic dell. DETAILS OF SECTIONS. 17 of coarse sand, which I regard as an ancient beach, and have so marked it on the map (Plate VI, Fig. 2). 11. On the north side of the stream (Fort river) the terraces are more nume- rous than on the south side, and in general they do not correspond in height. I have, therefore, been obliged to give another section (No. 11), extending from Fort river, in Amherst Hast Village, to the sandy sea-beach above described, 546 feet above Connecticut river. The course of this section, and also that on the south side of the stream, are indicated by the succession of figures on the map. On the north side the terraces rise highest at the southeast point of Mount Hygeia, evi- dently because there was once a barrier at this spot, at least a partial one, which would cause the materials drifted by the current to accumulate. The depression shown by the section, still further east, was doubtless made by the action of the small stream, as it wore away the barrier. In other words, it was a pond which was gradually drained, and so the terraces were formed. It is not easy to say whether No. 17 be a terrace ora beach. It is coarse sand and gravel, and is somewhat level-topped: yet it passes into a decided beach further south, and I have marked it as such. When the ocean stood as high as 546 feet above Connecticut river at this spot, it must have produced a small bay opening to the north; Mount Hygeia forming the right hand side and Pelham Hill the left. Nearly 400 feet higher, we find another beach, which, on the general map, | have represented as extending through Shutesbury, several miles to the north. It can be traced a great distance, and probably might be found extending into New Hampshire. In Shutesbury it is very distinct, and more sandy than in Pelham, where, at its highest line, the rolled fragments are sometimes a foot in dia- meter. By carrying a level from Packard’s Hill, in New Salem, the height of which has been accurately determined in the Trigonometrical Survey of Massachusetts, I found the most distinct beach in Shutesbury to be 1082 feet above Connecticut river. This corresponds nearly to a third beach on the east side of Pelham Hill, half a mile south of the Congregational Meeting-house, on the road to Enfield, which is 1049 feet above Connecticut river. Between these two highest beaches in Pelham, most of the surface is covered by ordinary drift, with rocks in places (gneiss) occa- sionally shooting through. Drift, also, appears between the lowest and the second beaches. This section across the Connecticut valley I am convinced gives us a good idea of the character of a large part of the valleys of New England and New York, and perhaps of the whole country, with the exception of drift. Wherever I have travelled, since my attention was turned to the subject, I find terraces in the lower part of the valleys, and similar though usually coarser materials arranged beach- wise, on the flanks of the mountains and hills, especially where spurs of the ridges form spots that might once have been bays, in which sand and gravel would natu- rally be accumulated on the shores of a lake, or the ocean, by winds and waves. There are scarcely any mountains of New England so high that this work has not reached their summits. But further on I shall have occasion to point out other particular examples. The section of terraces on the north side of Fort river, passing most of the way 3 18 SURVACH GEOLOGY, through thick woods, I used barometers for getting their heights, except Nos. 11, 12, 13, and 14, which were obtained by levellings. Along this route the rock often projects through the terraces, and shows decided evidence of powerful erosion by aqueous agency, some hundreds of feet above the present stream. 12. This section is in Whately, on the west bank of Connecticut river, and extends only to the third terrace above the river. Had I followed up the side of the mountain in the west part of the town, no doubt I should have found beaches, and most likely one or two other terraces above No. 38. Indeed I know of one terrace, say 100 feet higher than No. 3, about two miles south of the line followed by No. 12, and I shall in the sequel point out a very high beach in the north part of Whately. The principal uses of this section, thus imperfect, are to show that the lowest terrace along the Connecticut is sometimes quite high (32 feet here), and that the height of the broadest terrace in the Connecticut valley, which is No. 3, 1s less than it is nearer to the gorges; a fact which shows the influence of those gorges in the accumulation of the materials of the terraces. As already stated, there are two branches to this second basin, one extending north through Deerfield and Greenfield, and the other south through Hast Hamp- ton, Westfield, Southwick, &c., nearly if not quite to Long Island Sound. These branches are separated from Connecticut river by an almost continuous ridge of trap and sandstone, as may be seen on the large accompanying map of the surface geology of the Connecticut valley. This ridge is breached in Deerfield by Deerfield river, in Westfield by Agawam river, and in Simsbury by Farmington river. On the two first of these rivers are two remarkable sub-basins, sunk some 80 or 100 feet below the general level of the valley, and exhibiting on their margins fine examples of terraces. As these cannot be well shown upon Plate III, I have devoted separate ones, but on a larger scale, to their exhibition. (See Plates 1V and VII.) They both extend a considerable distance along the rivers, and show the surface geology, especially the terraces and old river beds. The Deerfield Basin. 13. Where Deerfield river emerges from its long Ghor, between Shelburne and Conway, into the Connecticut valley, it has formed several terraces; a section of which No. 13 exhibits; though on the south side of the river I have failed to measure two small terraces. But on the north side of the stream a tongue of four or five terraces has been thrown forward, perhaps a mile long, forming a ridge a, little over a hundred feet high, with regular terraces on its south side. The stream here descends rapidly, and so do the terraces slope in the same direction, although I did not measure the rate of descent. It is so obvious to the eye that I thought a measurement hardly necessary, especially as I find the same fact almost every- where upon lateral terraces. ‘They always have as great a slope as the stream on which they occur, and sometimes greater. Until I discovered the tongue of terraces above described, I was of opinion that the basin of Deerfield was once occupied by terrace materials to the height of No. 3 (yellow) on Map No. 1, Plate III, which is the usual level of the Connecticut valley DETAILS OF SECTIONS. ig) in that region, and is upon an average 173 feet above Deerfield river. This amount of sand and gravel (as I estimate it, 135,000 cubic yards) I supposed had been cut away by Deerfield river, and sent forward into the Connecticut. But I can hardly see why this ridge of terraces should in that case have been left. Yet some other facts seem to indicate strongly that most of the whole basin has been thus exca- vated; and upon the whole, I think this tongue of terraces has been formed by the river after it had excavated the basin, and sent its contents down Connecticut river. The tongue of terraces above described was undoubtedly at first a delta terrace, though formed by the rapid stream as it issued from the mountains into the estuary, which is now the Connecticut valley. At present, the ice-floods in that stream, and at this very spot, exert an amazing power of erosion. In early times, such floods must have crowded along great masses of crushed and rounded mate- rials, and piled them up along the margin just as lateral moraines are produced by glaciers. As the bed of the stream sunk, and also the waters of the estuary, successive terraces would be formed, looking like so many moraines, although of ‘ finer materials than the moraines of glaciers, and sorted too. 14. This section extends across the Deerfield basin, though not exactly on a right line. The eastern part starts at Deerfield river, just south of the village, - and the western part from the meadows, a little north of the village. Yet there is no error in representing them as connected, since at their starting points they are nearly on the same level, differing in height only as the banks of the river differ. The terraces are very distinct till we reach the third, over which the railroad passes, on the east side of the valley. Above the third, the top of the deposits is only imperfectly level, and they may be regarded perhaps as beaches; for I am confident that such beaches may be traced all along the flanks of the Connecticut valley, at about the same height. But I have not measured them, save in a few places, as they did not attract my attention when I measured the terraces. The three lowest terraces on both sides of Deerfield river, were measured by levelling; the two highest, by the syphon and aneroid barometers. Yet the latter, on the west side of the river, have not been measured at all. ‘As I saw them from the east side, they appeared to be at about the same height as those on the east side; still I know well how difficult it is to judge accurately in such cases by the eye alone, and actual measurement might show a considerable discrepancy in the heights. Hence, I have added an interrogation point to the heights on the west side of the river. 15. This section, of no great importance, shows the terraces at the north end of Deerfield meadows, to the top of Pettee’s Plain, which lies southwest of the village of Greenfield, and corresponds to the general level of the Connecticut valley. The meadows, or lowest terrace, are here worn away, and the lowest terrace remaining is mostly clay; the upper one sand. The river would encroach still further upon this hill, had it not struck a ledge of red sandstone, which will at least retard its lateral erosion. 16. Pine Hill is an insulated eminence, apparently composed of two terraces, in the northern part of Deerfield meadows. These terraces do not correspond in height, as far as I can see, with any on the margin of the basin; yet they must have been once continuous, as I know of no instance where terraces have been formed 20 2 SURFACE GHOLOGY. so perfect upon a small hill. This fact goes strongly to show that at least a large part of the Deerfield basin was once filled with terrace materials, which the river has subsequently worn away, and the reason why those on Pine Hill remain, I find to be that they rest on a protuberant mass of red sandstone. On the west side of the hill, as shown in the section, is an ancient bed of Deerfield river (crossed twice by the section), which was prevented from making any further lateral encroach- ments by the underlying rock. I shall have more to say hereafter concerning the ancient beds of Deerfield river, shown in such numbers upon Map No. 2 (Plate IV). A few other terraces on Deerfield river, out of the Connecticut valley, will be noticed further on. The Westfield Basin. 17. The major axis of the Deerfield basin lies north and south; that of the Westfield basin nearly east and west. The present section starts from Agawam river, near the east end of the basin, on the north side, and runs northerly. The height of the four lower terraces was obtained by levelling; that of the highest by estimation. All of them, except the lowest, which is loam, are sandy. The most elevated brings us to the general level of the Connecticut valley, though it is for the most part lower towards the east side, and not a little irregular on its top. 18. This section was but imperfectly measured, and only with the arenoid barometer; which, although very valuable where an error of twenty or thirty feet is not of much consequence, does not answer well for such small elevations as our river terraces. By looking at Map No. 6, it will be seen that between Westfield river and Little river, a tongue of terraces extends easterly from Middle Tekoa Mountain, almost to the village of Westfield. In one place on the north side of this tongue, perhaps a mile west of the village, I noticed five terraces, reckoning that on which the village stands as the lowest, although generally the highest terrace around Westfield is reached by three steps from the river. Commencing on the high sandy plain north of Westfield basin, I have carried this section southwesterly across these five terraces and over Little river to the plain of nearly equal height on its south bank; in other words, across the entire basin. I think the barometer has made the central terraces considerably too high. But the sec- tion will give an idea of this interesting valley. The materials of which all these terraces are formed are clay, sand, and gravel, though the red sandstone shows itself occasionally near the river. 19. On this section I have attempted to give an idea of what I suppose to be the remnants of gorge terraces, where Westfield river issues through the deep gorge between Tekoa and Middle Tekoa. The height (measured by the Aneroid), is very great for a stream of no larger size. Near the river on the same section are shown two other narrow terraces, produced at a vastly later period. On both sides of the river the mica slate ledges show themselves frequently as we ascend the mountains. : 20. This section commences on the east side of Westfield river, opposite the station house of the Western Railroad, in Russell, and crosses the river, passing westerly through the flourishing village which has lately sprung up there. Its DETAILS OF SECTIONS. 91 western extremity is very near the place where an old river bed, about a mile long, unites with the present bed. Ido not feel much confidence in the accuracy of the heights, since they were taken by the aneroid barometer. For the view of the terraces on which this village stands, accompanying this paper (Plate IX, Fig. 2), 1 am indebted to Mr. Franklin P. Chapin, who took it with his pentagraphic delineator from the east side of the river. 21. This section extends from the present bed of Westfield river over the hill on its west bank, and across the old river bed referred to in the last paragraph. The heights were obtained by the aneroid barometer; and, therefore, are liable to some uncertainty. Many other terraces are shown along Westfield river on Plate VII, with three old river beds to be described in my paper on erosions. The heights of the terraces I have not measured, and therefore do not give sections of them. 3. In the Basin extending from Mettawampe to the Mouth of Miller's River. 22. This basin, though small, has many terraces, but none of them seem to me of special interest. I have measured only one section in it, and not the highest terrace upon that; as it lies at a distance from those which were measured. I commenced on the narrow alluvial plat just above Turner’s Falls, on the Montague shore, and ascended the sandy hill that lies southeasterly. This was reached as the third terrace; and, except along its eastern margin, it constitutes the general surface of the basin. At its southern part, in the south part of Montague, I judge the surface to be higher than on the section, as is usually the case near gorges. 4, Sections in the Basin extending from the Mouth of Miller's River to Brattleborough. T ought to repeat here, and make more general, a remark elsewhere made, that the upper terraces usually extend more or less from one basin into another; that is, these higher terraces were formed when the waters extended from one basin into another, and what now seem to have been barriers, were then only narrower places in the estuary. On the east side of the river, in this case, terrace No. 4, and perhaps No. 3, on Map No. 1, Plate III, were continued into Northfield from the basin next south. 23. This is in Northfield, two miles south of the village, running eastward from Connecticut river. The fourth terrace, or beach more properly, is irregular on its top, and was not measured. 24, This runs from the same river eastward in the north part of Northfield, only a short distance south of the State line. 25. At the mouth of Ashuelot river, in Hinsdale, the terraces are numerous and instructive. This river is a small but rapid stream, and where it debouches from the hills into the Connecticut valley, it has brought forward a large mass of terrace materials, mainly of gravel, which originally constituted a delta terrace ; that is, the stream threw forward these materials into the lake, or estuary, and formed a bank along its mouth. But as the waters drained off, so as to bring this 22 SURFACE GEOLOGY. bank above them, the Ashuelot cut through them, and formed lateral terraces along its margin. On the northern side of the stream, at its mouth, a rocky hill extends nearly or quite to the Connecticut, which is thereby forced at this spot to make a curve westward. The section No. 25 passes across the Ashuelot near its mouth, directly through the village, northwesterly over the hill, and then descends towards the Connecticut; so that all the terraces on it to the right of this hill belong to the Ashuelot; while those to the left belong to the Connecticut. The difference in their height and size on the two rivers affords a good illustration of the fact that the larger the river the higher the terraces. The character of the materials, too, illustrates another fact, viz., that they are coarser on small and rapid streams than on larger and more tranquil ones. Excepting the lowest, which are narrow, the terraces on the Ashuelot are all gravel, mixed with sand, and often the fragments are quite large; while on the Connecticut are no pebbles of consequence, but sand underlaid by a thick bed of clay. A third circumstance deserves notice: On the Ashuelot the terraces have a rapid slope towards its mouth, corresponding to that of the river, which here falls so much as to afford a good site for manufactories ; whereas, on the Connecticut, the eye cannot perceive that the terraces are not strictly horizontal. Indeed, they probably decline but little from Brattleborough to this place, and the two higher ones are nearly continuous between the two places. The higher terrace along the Connecticut, not measured, is sandy and irregular, and more properly deserves the name of a beach. 26. This section (Plate II) is on the west side of Connecticut river, in the north part of Vernon, and differs but little from that already described on the same river in Hinsdale. The height of the fourth terrace, however, is greater; but the spot is not a great distance south of the gorge in the river at Brattleborough, and hence we should expect a greater amount of terrace materials. 5. In the narrow Basin from Bratileborough to Bellows Falls. So narrow is the valley between Brattleborough and Westminster, that it deserves the name of a defile rather than a basin. And yet terraces are found nearly the whole distance, though usually quite narrow. Opposite Brattleborough, on the east side of Connecticut river, West River Mountain rises very precipitously to the height, above the river, of 1050 feet, as I ascertained by a not very accurate mode of observation. On the west side of the river, the hills rise more gradually, yet the rocks press closely upon the bank. Within a distance of not over half a mile, two tributary streams empty into the Connecticut; the most northerly called West river, of considerable size; and the one at the south end of the village, small, and called Whetstone brook. Such streams, debouching in such a spot, and at right angles to the course of the Connecticut, are sure to produce numerous terraces. So numerous are they, and so complicated, that I judge it necessary to devote a map to them alone, so far as I have traced them out (see Plate V;) for I have not obtained quite all the facts in respect to the sections that would have been desirable, yet I have enough to be very instructive as to river terraces. 27. This section (Plate II) commences on the west bank of the Connecticut and DETAILS OF SECTIONS. 93 wa the south bank of Whetstone brook, and runs southwesterly to the top of the elevated sandy plain that passes into the Basin No. 4, just considered. (See the line of the section on Plate V.) The terraces appear to be the joint result of Whetstone brook and of Connecticut river. They are, therefore, more numerous than is usual on the Connecticut, and less so than on this same Whetstone brook, a mile from its mouth, as the next section will show. The Connecticut valley was probably occupied originally by terrace materials as high as the uppermost of the above terraces on this section, and when the waters gradually subsided, both the Connecticut and Whetstone brook formed channels through these materials, and produced the successive terraces. Why terraces, rather than a continuous slope, were formed, I shall endeavor to show in another place. 28. This is a quite instructive section, commencing on the south bank of West river at its point of junction with the Connecticut, then extending southwesterly across the village of Brattleborough to the high bank of Whetstone brook, a little west of the village, opposite Burge’s factories; thence across the brook, and up the opposite bank, so as to cross the successive terraces, ten in number. The upper - one was not measured, on account of the rain. Nor did I ascertain the height of the brook, where the section crosses it, above Connecticut river. It will be seen that No. 5, on the left hand part of this section, consists in part of an insulated hillock, crossed a little north of the village; and in the main, part of a broad terrace, on which stands the upper and northwest portion of the village. This terrace, as I found by levelling, slopes towards Connecticut river at the rate of 20 feet in 50 rods. Possibly this might have been in part the result of rains for a long pericd, bringing down from the hill by which the terrace is bounded, deposits of sand. More probably the terrace was formed by the conjoint action of West river and Whetstone brook as a delta terrace, and that its slope was produced by the rapidity of the currents. All these terraces are underlaid by argillaceous slate, which shows itself all along the banks of the streams. It is doubtless this solid rock that has determined the present channels of the tributaries to the Connecticut, and caused them to enter that river nearly at right angles. The mere sand and loam of the terraces would soon be washed away in time of freshets, were it not for this rocky foundation. In this section we see a good exemplification of the statement made on a pre- ceding page, that the smaller the stream the smaller are the terraces, and often more numerous too. Here we have ten on Whetstone brook, and nine on West river, yet they do not rise so high as the fourth, on the Connecticut, in Vernon. Had I explored the hills by which the valley at Brattleborough is bounded on the west, I might have found beaches, or imperfect terraces, at a much higher level. But when I examined that region my attention had not been called, as it was subsequently, to the subject of beaches. The same remark will apply to nearly all the terraces of which I have given sections on the Connecticut. Tregret that I did not measure a section across Whetstone brook through the middle of the village of Brattleborough, along the track marked by the figures 1, 2, 2, 3, 4, on Plate V. Here it would seem are fewer terraces than at the mouth 24 SURFACE GEOLOGY. of the stream. Possibly more careful examination might have detected others, and probably also the original surface has been here somewhat altered by the grading of the streets. 29. This section commences with the highest distinct terrace in Westminster, a little south of the village (which stands upon the second terrace, reckoning up- wards), and crosses Connecticut river into Walpole. But unfortunately I was unable to measure the terraces on the east side of the river, and have marked them only as they appeared from the west side. They are very distinct on both sides, and perhaps they correspond in height, though I usually found in such cases, that actual measurement showed considerable difference in elevation where the eye could discern none. 30. At the upper end of the basin under consideration, the terraces are numerous and distinct, just below, as well as above Bellows Falls in the next basin. No. 80 crosses Connecticut river at the mouth of Saxon’s river on the west side, and of Cold river on the east side. Of course the terraces are compounded of the effects of the three rivers. It will be seen that there is no correspondence in their height on opposite sides of Connecticut river, except that the upper terrace very probably once filled the valley; for the difference in height between the opposite terraces (17 feet) is not greater than we might expect on the supposition that the materials were drifted into a former lake, or estuary, by the adjacent streams. These mate- rials are, for the most part, Coarse sand, sometimes mixed with gravel. On the east side ledges of rocks appear on the slope of the third terrace. As an illustration of this paper, I have given a sketch (taken by Mrs. Hitchcock) of the general aspect of the terraces of the above section, as they appear about a mile south of where it crosses Connecticut river, on the road to Walpole. (See Plate IX, Fig. 1.) The view from this spot of the gorge with its terraces, and of some of the principal buildings in the romantic village of Bellows Falls, is very fine, and deserves the attention of the artist. for its scenographic beauties. My object in giving its outlines was to exhibit the terraces as a good example of the very arti- ficial appearance of many spots along the rivers of New England. Certainly it does seem, as we look at these terraces, as if they were the work of man. 31: On the preceding section, on the west side of Connecticut river, I have represented two glacis terraces. On No. 31 Ihave shown them on a large scale, and laid them down accurately, so as to give a good idea of this kind of terrace. It will be seen that they constitute merely undulating portions of the lowest ter- race, and perhaps ought not to be reckoned as distinct terraces. Yet they are sometimes of considerable height, and certainly deserve notice, because they show us one of the modes in which water accumulates terrace materials. How they are formed I will consider in another place. But there are certain laws concerned in their production. Thus, the depression between them always corresponds in its longest direction with the course of the current that produced them. One side, also, and I believe always that next the stream, is steeper than the other. In almost all extensive meadows this sort of terraces may be seen more or less distinct. Excellent examples occur in Hatfield and Hadley, not merely in the meadows, but they are seen in crossing the villages, from street to street, in an DETAILS OF SECTIONS. 95 east and west direction, or at right angles to the course of the stream that made the deposits. It was from such examples as this section exhibits that I first got the type of a glacis terrace; but in passing subsequently through some of the higher valleys of the Alps, I sometimes observed the terrace materials arranged so as to form one continuous slope from the rocky side of the valley to the stream. I noticed this most distinctly on the Eau Noire, in the pass of Téte Noire. Here the materials were quite coarse, the fragments often large enough to be called boulders, though I fancy most geologists would be puzzled to say just how large a pebble may be, or how small a boulder. The same sort of terrace I saw in other places in the Alps, and I have observed them in the mountainous parts of our own country, though but seldom, and they were imperfect. They perhaps furnish a better type for the glacis terrace than that already described. If, however, we regard the gentle slope on one side as a characteristic of this terrace, then both the above descriptions of terrace will belong to it. 6. In the Basins extending from Bellows Falls to Wells River. The mountains at Bellows Falls crowd closer upon the river than at any place south of this spot, except perhaps at Holyoke and Tom. Kilburn Peak, on the east bank, rises almost perpendicularly, over 800 feet. On the west side, as at Brattleborough, the mountains recede further, and have an escarpment less steep; yet the rocks show themselves almost everywhere in the gorge, and form a ridge which produces the falls. All the circumstances here are favorable to the formation of terraces. Sections 30 and 31 are only a mile and a half south of the village of Bellows Falls, and the highest terraces extend through the village into the sixth basin. So remarkably are they grouped together here, that a distinct and separate map seemed indispensable. (Plate VI., No. 1.) 32. This section crosses Connecticut river directly through the village of Bellows Falls and a few rods above the principal cataract. The heights are given from the foot of the falls. The depression on the left was evidently once occupied by the river when at a higher level. I regret that I was not able to measure all the terraces—none, indeed, on the east side of the river; but I am not aware that they are peculiarly instructive. It was my intention for a long time to continue to get the heights of terraces through the whole course of Connecticut river, at least as frequently as they are given above. But I began to be convinced that I had already measured enough for all important purposes in relation to river terraces. The phenomena of beaches arrested my attention more and more, and it seemed a very important point to ascertain how high they could be found upon the sides of our mountains. To this problem I addressed myself, both in this country and in Europe, and shall briefly give the results. But something more needs first to be said concerning the terraces. As to those above Bellows Falls on Connecticut river, I have but little to state ; for although I have passed over the region several times, it has been rapidly, and I can only say that at least three terraces may be traced nearly all the way to 4 26 SURFACE GEOLOGY. Wells river. Sometimes I noticed four, or even more. But with one or two exceptions, I have marked only three on the map, and I fear that I have but very inaccurately represented the position and relative width of these. Neither do I suppose thatthe basins above Charleston, are accurately laid down. In some places, as at Wethersfield, and above Haverhill, the terraces are very perfect and beautiful. 33. My son, Charles Henry Hitchcock, measured this section at White river junc- tion, with the aneroid barometer, and I have thought it worthy to be added in this place, especially as I know from my own observations that its outlines are correct. It commences at Connecticut river, and passes west, near the railroad station. The old river bed, on its west part, was probably formerly occupied by White river, which entered the Connecticut, a little below its present junction. I am not certain, however, that this was the case. Terraces chosen as the Sites of Towns. It is a curious fact that the most attractive villages in the valley of Connecticut river, owe their chief beauty to being placed upon terraces. Among these towns we may mention Wethersfield, Ct.; Hartford, Hast Hartford, Windsor, Hast Wind- sor, Springfield, West Springfield, Northampton, Hatfield, Deerfield, Greenfield, Northfield, Hinsdale, Brattleborough, Westminster, Walpole, Bellows Falls, Charles- ton, Wethersfield, Vt.; Windsor, Hanover, Oxford, Haverhill, and Newbury. Pro- bably but few of the inhabitants have ever thought as to what they are indebted for the beauty of their towns. Terraces and Beaches out of the Connecticut Valley, but in New England or New York. I have already described the terraces on Westfield river, among the mountains west of the Connecticut valley. But they occur on almost all the rivers of New England, and I have not attempted the Herculean task of measuring or even mapping but a small part of those which I have visited since engaged in these researches. After finding the features of them to be essentially alike on all rivers, I became convinced that the measurement of great numbers was not important. I will only refer to those on a few rivers, which I have observed with special interest, as well as to beaches, which I have noticed on the adjoining hills. Merrimack river abounds with terraces, the most perfect of which are in New Hampshire. They give great beauty to many of the towns along that river. From the south line of the State to Franklin I have traced them, and with some interruptions, two or three of moderate height may be seen on one side or the other, or both sides, nearly the whole distance, as I have shown without much accuracy on Plate III. Near the mouth of the river I found terraces, but could rarely find more than one well defined, and so have I represented them on the same map. Plum Island, stretching along south of the mouth of the Merrimack, is a good DETAILS OF SHCTIONS. Dil example of a modern beach. (See Plate III.) Some other features of the surface geology of that region I have delineated, and shall notice further on. A slight examination led me to the conclusion that the terraces are of unusual interest upon Ammonoosuck river, which comes from the White Mountains and ~ empties into the Connecticut. I have followed up the Waterquechee river in Vermont to a considerable distance, and find some interesting terraces a little below the village of Quechee, where is a wild gorge. Above this not less than seven terraces occur on the southwest side of the stream, and four on the opposite side, as I have indicated simply by lines upon Plate III., connected with my paper on the marks of drift and glaciers. On the same map I have sketched most of. the terraces on Deerfield river above Shelburne Falls, where the Ghor terminates. Generally, we have along this stream only two terraces, as represented, though sometimes more exist, as section 34 shows, to be described below. But where small streams enter Deerfield river, I have noticed fine examples of the Delta Terrace, and several of these are marked upon the map, and will be more particularly described further on. I now proceed to describe Section No. 54, just referred to, as well as several others, mostly of beaches out of the Connecticut valley. 34. Beyond the barrier across Deerfield river a little west of Shelburne Falls, commences a rather broad: valley, which must have been once a lake, extending perhaps fifteen miles, to the foot of Hoosac mountain. Here, as we might expect, we find good examples of terraces. I have measured, however, only a single series, lying on the south side of Deerfield river, and at the mouth of a small tributary coming in from the south through Buckland. It will be seen from the section, No. 34, that the terraces are all of them low. ‘They seem to be the result of the joint action of both rivers. 35. In the southeast part of Heath is a mountain, to which the Indian name of Pocumtuck was formally given in 1855, by the Senior Class in Amherst College who graduated in 1856. It was used as a station in the trigonometric survey of Massachusetts, and consequently its height above tidewater is known to be 1888 feet. From this point I levelled northwesterly about two miles, till I struck a deposit of water-worn sand and gravel, of limited extent, but which I must regard as an ancient beach; for I know not how else to explain the occurrence of commi- nuted and sorted materials in a spot so elevated and open to the surrounding country. The section will give an idea of its position. 36. The summit-level of the Western Railroad, in Washington, is 1456 feet above the ocean; the cut in the rock being 60 feet. On all sides of this cut I find deposits of sand and sometimes gravel, at least to the height of 134 feet above the original rock. This would give 1590 feet above the ocean as the highest mark of distinct sea action at this place, although very probably similar deposits can be found in the vicinity at a higher level. But Iam a little doubtful as to some of these banks of sand; for the rock here is a variety of gneiss easily disintegrated, and the result of the disintegration is coarse sand. I cannot thus explain, however, the thicker deposits, certainly not those with pebbles, and these are seen nearly at the height above named. 28 SURFACE GEOLOGY. This spot was doubtless one of the lowest, if not the lowest, pass through the dividing ridge between the Hudson and Connecticut rivers, and therefore we should expect marks of sea action here, if the ocean once stood above the mountains of New England. 37. French’s Hill, in Peru, on Hoosac Mountain, is one of the highest peaks in Massachusetts, and as its height was ascertained in the trigonometric survey, I visited the spot in the hope of finding beaches or terraces in the vicinity, whose height, also, above the ocean, could be easily determined. The section No. 37 exhibits the result. By carrying a level downward from the top of French’s Hill we strike what I conceive to be an ancient beach, 217 feet below the summit, or 2022 feet above the ocean. It is level like a terrace, but the materials are not very thoroughly rounded, like those of the lower beaches and terraces; yet they are more worn than drift usually is, and I can impute the level top of the deposit to water only. Passing eastward from this beach, we cross a brook, which rises in a pond, and then go over a hill of considerable height. In descending it easterly, I fancied the existence of another beach; but, going onward, nearly three miles from French’s Hill, and descending about 470 feet, we reach a small stream, where are at least three terraces, made up of coarse materials, sand, gravel, and bowlders, the highest on the west bank being 85 feet above the stream, and 1852 feet above the ocean. This is the highest river terrace I have yet met with in New England; but I see no reason why they may not be found at a higher level in some of our mountains, since, as I conceive, they are mainly the result of the action of the stream itself. In this instance, however, it is rather difficult to imagine the former existence of any barrier high enough to shut in the water, so that it would overflow these ter- races: so that probably the sinking of the waters of the ocean may have had an important influence on their production. On the east side of the stream are three terraces of about a corresponding height, but I did not measure them. Proceeding eastward from this elevated region, I met with other deposits at a lower level, more obviously once constituting the shores of an ocean; but not then having barometers with me, I could not measure their height. In going westward, also, from Peru, or any other culminating point of Hoosac Mountain, into the valleys of Berkshire County, we meet with many examples of comminuted and rearranged drift, in the form of beaches, and in the valleys of terraces. But I have not measured the height of these, save a single example on the Western Railroad in Dalton, which I find by the aneroid barometer to be 1228 feet above Hudson river. In the west part of Whately, on the ridge between that town and Conway, I found a distinct beach of sand and gravel, which by the aneroid and siphon barometers I ascertained to be 697 feet above Connecticut river, and 802 feet above the ocean. In the northwest part of Conway, called Shirkshire, I found another, of coarse gravel and sand, 935 feet above the river, and 1040 above the ocean. ‘Two miles further west, in Ashfield, is another, mostly of sand, 976 feet above Connecticut river, and 1081 above the ocean. A mile further north, an im- perfect beach shows itself, 1216 feet above the river, and 1321 above the ocean. DETAILS OF SECTIONS. 29 Still further northwest, on the opposite side of the ridge, is another sandy beach, nearly as high, but I did not measure its elevation. Tn all the above cases, and, indeed, wherever I have discovered the most distinct beaches, they occupy such a position among the hills, that if the country were covered by water a few feet above the beaches, they would become inlets or har- bors, and I fancy that if our present harbors, either along the ocean, or the shores of our larger lakes, were to be left by the waters, the surface would be no imperfect counterpart to these ancient beaches. Indeed, when standing on these beaches, and looking in the direction which must have been seaward, if my suppositions are correct, I have often felt that it required no great stretch of imagination to see the ancient waves rolling in upon the beach, and silting up the harbor. Upon Map No. 1, 1 have marked beaches at Franconia Notch and the White Mountain Notch, which are two passes through that gigantic range of mountains. In those passes, a little west from their narrowest part, we find accumulations of water-worn detritus, stratified and laminated, which I doubt not were left there by the breakers of an ancient ocean. At least it is certain that no existing streams could have formed them, and yet water must have been concerned in their pro- duction. By my aneroid barometer, I found the highest point in the road, which passes westerly from the Franconia Notch house, to be 2665 feet above the ocean, and 2259 above Connecticut river. This is not so distinct a beach, however, as is shown at the height of 2449 feet above the ocean. Gibbs’ hotel, at the White Mountain Notch, which occupies the top of a beach, in my opinion, is 2018 feet above the ocean by a mean of the two barometers, and 1612 above Connecticut river. But I fear this measurement may vary somewhat from the truth. 38. This is a very imperfect section, from the mouth of Connecticut river to that of the Thames, at New London, or a little north of the city. I had no intention of making such a section when I crossed that district in the road nearest to the coast, not far from the route of the New London and New Haven railroad. But having taken a few barometrical observations, and finding the two barometers to agree unusually well, I thought it best to put down the different terraces and beaches which I observed, although I have given the heights of only a few; and probably some terraces, at least, are omitted. Perhaps all should be called beaches, as they lie open entirely to the ocean. But the rivers seem to me to have had more to do in their formation than the ocean. The beach marked 17 feet high, on the west bank of Connecticut river, seems to me of the same height, as the very distinct one, commencing on both sides of the Thames, and extending as far as Norwich. This, however, is in fact a terrace, and at New London there is a rocky barrier, which doubtless had something to do with its formation. I regret that I could not spend a longer time along this section, and make more measurements. At the time, I thought the terraces and beaches too low to be measured accurately by the barometer, and I had no level with me. I think it would be instructive to run such a section along much of the coast of New England; yet I think the one given is an epitome of what we should find in the whole distance. 39. In passing from Schenectady to Albany and Springfield, I took observations with the aneroid barometer at certain places, which I had often observed to be 30 SURFACE GEOLOGY. the tops of terraces and beaches, and have given the result on this section, which commences at the highest part of the sandy plain lying between Albany and Schenectady, and, following the railroad, terminates at the highest point on the road of the Hoosac range. The horizontal scale is so small compared with the vertical, that the section is very much distorted, and gives but a poor idea of the country passed over. On the east side of the Hudson, after rising to the third broad terrace, the ascent is gradual most of the way to the State line between New York and Massachusetts, a distance of 38 miles. Between that point and Pitts- field, eleven miles, the surface is chiefly covered with unmodified drift. Thence eight miles to Hinsdale, the drift is frequently covered by re-arranged drift, which I suppose to have been modified by the ocean, beating against the side of Hoosac Mountain. The same is true of the remaining five miles, which brings us to Washington, on the summit level, and, as already explained, I have regarded the sea action there as extending upwards above the railroad 200 feet. Though at each of the railroad stations where I took observations, I have repre- sented a distinct beach on the section, it must not be supposed that such is the fact at those places, while between them no beaches exist. I mean only to indicate that beach materials exist at those places, but exactly how many distinct beaches exist along the route, Iam unable to say. That the whole of this inclined plane once constituted the shore of a retiring ocean, I cannot doubt; but how many pauses there might have been in the vertical movement, so as to form marked beaches, is a point I have not determined. At some of the stations of medium height, say at Chatham and Hast Chatham, I noticed those irregular elevations and depressions of sand and gravel, which I have already described as occurring among the highest of the perfect terraces, and below the most distinct beaches. From this fact we must infer that at that par- ticular level of the waters some peculiar action must have taken place, necessary to produce these modified effects. I refer to those accumulations which I have denominated Moraine Terraces. 40. This section was taken by the aneroid barometer, on the west side of Genesee river, in Mount Morris, which lies at the lower end of that remarkable gorge cut by the river from Portage to that place. There is nothing very instructive in the section. We see, however, that the terraces here are of great height, and they are, also, in general quite broad. An enormous quantity of detrital matter has in past ages been brought into the Genesee valley, and there are some quite instructive facts in relation to former changes of river beds. But this subject I shall reserve for my paper on Hrosions. Terraces on Rivers and Lakes at the West in our Country. I have not had much opportunity to examine our western rivers and lakes with : reference to the surface geology of their banks. The Ohio did not seem to me remarkable for its terraces, nor did the Great Kanawha. On them both we meet occasionally with two terraces, sometimes three. The horizontal position of the sandstone and limestone strata in the Western States, exposes one to error in this TERRACES AND BEACHES AROUND LAKE SUPERIOR. 31 matter, by mistaking a terrace of rock for one of sand or gravel. There is no danger of such a mistake in New England. The terraces and beaches around a considerable part of Lake Superior have been described with great scientific accuracy by Professor Agassiz, in his work on Lake Superior, and by Messrs. Desor and Whittlesey in the Reports of Foster and Whit- ney on the Lake Superior Land District. The latter gentlemen have, also, included a considerable part of the shores of Lake Michigan. From the details given by these gentlemen, I judge that surface geology in the regions of these great lakes corresponds essentially to that of New England. Though the different forms assumed by the materials may in their writings often be given under names different from those I have used in this paper, the things described appear to be identical. There is a coarse drift underlying all the other forms of detritus, and above this lie deposits of clay, sand, and loam, overspread in many places and mingled with blocks of various sizes, generally more or less rounded. M. Desor considers the lowest deposit of the clay some 60 feet thick, and those of the sand and gravel above, some 360 feet thick, to belong to the drift, because mixed with, and covered over, with boulders. He divides all the superficial depo- sits into three parts. I. Drift proper, with the above four subdivisions. 2. Ter- races belonging to a later epoch—a part of the terraces he includes in the drift. 3. Alluvial deposits, embracing all those forms of detritus that have accumulated since the continent began to rise from the ocean, such as beaches, terraces, nooks, belts, bars, marshes, flats, and subaqueous ridges. As to the number of terraces, M. Desor speaks of as many as seven in some places, and Professor Agassiz says that “six, ten, even fifteen, may be distinguished - on one spot.” The number, all agree, varies very much in different parts of the same lake. Professor Agassiz thinks that “these various terraces mark the suc- cessive paroxysms or periods of re-elevation” of the shores of the lake. Desor adopts the same view, certainly so far as to say that the terraces indicate pauses in the vertical movement, which, however, he would make. general over the conti- nent; for he finds the drift deposit at the top of the highest parts of the country around these lakes, not less than 1000 feet above their present level. Now it will be seen that while I agree with these gentlemen in regard to the essential facts of surface geology, we differ as to the mode of stating them, and somewhat in the theory of the whole subject. We all agree in supposing the phenomena to require vertical movements in our continent, or its submergence and emergence since the tertiary epoch. But while they suppose that there were pauses in the vertical movement, long enough to form the different terraces, I have been led to suppose that most of them, certainly river terraces, must have been formed without such pauses, and simply by uninterrupted emergence or drainage of the country. We agree as to the occurrence of a deposit of coarse drift at the bottom of the series; but while they regard the superimposed clay and sand as true drift, I suppose them modified drift, and produced almost entirely by water, save that floating icebergs have dropped the large boulders. ‘They, certainly M. Desor, sup- pose the drift period to have terminated when the continent began to emerge, and the alluvial to have then commenced; but I regard drift proper as the result of 32 SURFACE GEOLOGY. several agencies—icebergs, glaciers, landslips, and waves of translation—which, indeed, operated most powerfully in the earliest periods, but have ever since con- tinued to act and are still acting. And so of alluvial agencies: we find evidence of their operation from the close of the tertiary period; nay, much further back; but they have gone on increasing in power to this time. Thus the drift and allu- vial agencies have had a parallel operation from the first, and hence the difficulty of separating drift and alluvium, and the propriety of regarding the whole as one prolonged period, with synchronous deposits. These views will be more fully developed in the subsequent parts of this paper, and I mention them now to avoid misapprehension. In Professor Owen’s Report on the Geology of Wisconsin, lowa, &c., many inte- resting facts in surface geology are mentioned; such as terraces and old river beds. On the St. Peter’s river he describes two terraces above the meadows, one 130 feet, and the other 230 feet high—the latter of coarse materials. On Red river, according to Captain Marcy (Zeport, p. 35), are three, the lowest from 2 to 6 feet above the stream; the second from 10 to 20 feet; and the third, from 50 to 100 feet; forming the most elevated bluffs along the river. On the River Jordan, in Palestine. Dr. Anderson, geologist to the exploring expedition sent out by the United States Government to the Dead Sea, has given us an account of the terraces in the valley of the Jordan, a river so remarkable for its tortuosities and rapid descent. He says: “There are almost everywhere in the Jordan valley, distinct traces of two independent terraces. ‘The upper terrace extends to the basis of the rocky barriers of the Ghor, both on the east side and the west, and appears to have been due to a geological condition long preceding the existence of the actual river, yet subsequent to the removal of the material which once occupied the space between the two opposing cliffs.” We understand him to mean that there are two terraces besides the meadows, or lower bank of the river; so that I should speak of the river, according to the views presented in this paper, as having three terraces. Near Beisan, or Scythopolis, Dr. Anderson says there are three terraces—four I suppose by my nomenclature. He does not make an estimate of the height of the two great terraces of the Jordan, though in one place he speaks of banks of stratified gravel rising sometimes 100 feet. Dr. Robin- son, in his Biblical Researches in Palestine, &e., describes the valley of the Jordan near the Dead Sea, and says that the immediate valley, which is usually nearly a mile wide, is bounded by a terrace (the first or lowest of Dr. Anderson I suppose) 50 to 60 feet high at its southern part, but not more than 40 feet further north. He also describes a small terrace near the Dead Sea, only 5 or 6 feet above the meadow, which does not extend far up the stream. The width of the whole ghor or valley to its rocky sides varies from 5 to 10 or 12 miles. Delta and Moraine Terraces. Very distinct delta terraces may be seen near the mouths of most of the tributa- ries of the Connecticut and on the branches of those tributaries; but they do not occur usually at the present mouths of the streams, but rather at the point where MORAINE THERRACES. 33 they formerly emerged from the mountains, into what is How a valley with terraces, but was then an estuary, or lake, or broad river. The materials, brought down from the mountains by the tributaries, were pushed forward into these expansions of water, and spread, in part at least, over the bottom. As the drainage went on, these subaqueous deposits gradually emerged in the form of deltas, and were sub- sequently cut through by the streams. ‘The result would be, as I shall shortly attempt to show, that a new set of lateral terraces would be formed in the delta terraces. Hence at present, several of the sections of terraces that have been described on the preceding pages, cross from one side of an eroded delta terrace to the other. This is the case in No. 13, in which the right hand terraces were all formed upon a delta terrace of Deerfield river. The same is true of the left hand portion of No. 25, which crosses the Ashuelot river in Hinsdale, New Hampshire, as also of No. 28 in Brattleborough, which crosses the original delta terraces of West river and Whetstone brook. On Deerfield river, in Charlemont, I noticed good examples of delta terraces on at least three small streams, that come in from the mountains of Coleraine, Heath, and Rowe, on North river, Mill brook, and Pelham brook, as is shown on Plate IV. The Moraine Terrace is certainly one of the most remarkable of all the forms of surface geology, as it is one of the most difficult to explain. It is now more than twenty years since I first attempted to describe this phenomenon, and though I have called in the aid of drawings, I feel that I have yet given but an imperfect idea of it to those who have not seen it in nature. Wherever I have travelled, however, these singular elevations and depressions of sand and gravel have awak- ened my attention, and the localities have multiplied beyond the power of memory to recall. Ido not, however, recollect to have met with them anywhere, save in such circumstances that in the drainage of a country the spot must have formed a shore sufficiently steep to have arrested and stranded floating icebergs. I will refer to a few localities. To begin with the eastern part of Massachusetts, we find these terraces near the extremity of Cape Cod, in Truro, of sand, very strikingly piled up and gouged out. At Plymouth they are more gravelly. In passing west from the coast, we meet with the first general rise of the country. In about twenty miles, and all along this ancient coast line in Connecticut, Massachusetts, and New Hampshire, we find these terraces, not quite so high, however, as in more mountainous regions. In the valley of Connecticut river, all along its eastern side, where the alluvial plain abuts against the bounding hills, they are very common. Still more striking are they along the western foot of Hoosac and Green Mountains, in Massachusetts and Vermont. Let any one pass from Dalton, in Berkshire county, to Cheshire, along the Gulf Road, and he will be a witness of this phenomenon in its grandest form. It is very striking, also, in the east part of Granville, in Hampden county, at the west foot of Sodom Mountain, in a region scarcely penetrated by roads. These singular forms of the surface do not occur in the lowest and most perfect terraces, but generally as a part of the highest in a district. The materials are always rounded and sorted, and water has most unquestionably played an important part in their production. But I am sure that no logical mind, accustomed to geo- 5 34 SURFACE GEOLOGY. logical reasoning, will doubt that some other agent must be called in to explain their formation; and their position and relative elevation, as stated above, are important elements in forming a theory of their origin. But more on this subject in the sequel. 2. SURFACE GEOLOGY IN HUROPE. It is not my intention to give even a summary of the facts collected by Mr. Chambers and others upon surface geology in Europe, except perhaps to refer to a few of them; but, having travelled through several European countries since my attention was turned to this subject, I could not but have my eyes open to it as I passed over the surface. The results of my hasty observations I will now give, though aware that they may be comparatively of little importance. Wales. It happened that the first country which I visited after landing at Liverpool, was North Wales, and not expecting to go there when I left home, I had not refreshed my memory with the statements of English geologists respecting its surface geology, and, therefore, I passed over its lofty mountains and through its rugged passes, with no hypothesis in mind, or expectation of what I should meet. In going from Car- narvon to Llanberris, I thought the detritus, to the height perhaps of 300 feet above the sea, indicated sea action; that is, the detritus was not coarse drift, but had been worked over by the action of water. Above that height I found occasionally small accumulations of rounded and comminuted materials, in some partially sheltered spots on the sides of the steep mountains. The highest spot of this kind on Snowdon, my barometer made 2547 feet above the ocean; but in the higher, or rather midway heights of Snowdonia, my attention was arrested by the marks of ancient glaciers. I had not then seen a glacier, but the marks were so obvious that I could not hesi- tate to refer them to that agency, and the conviction is still stronger since I have been among the Alps of Switzerland, and especially since I have learnt the opinion of Professor Ramsey, who has charge of the geological survey of Great Britain. He finds drift in those mountains 2300 feet high, and thinks that there have been two periods of glaciers there, one before and the other since the drift period. But I will give more details on this point in my paper on the Ancient Glaciers of Hoo- sac and Green Mountains. I ought to add, that I saw scarcely any terraces in Wales, nor were the ancient beaches at all striking. On Cader Idris I saw none; but east of that mountain, on the road to Machynleth, is a pass, 762 feet above the ocean by my barometer, and there I saw some evidence of a beach. Although there is proof enough that Wales has been again and again, and for vast periods beneath the ocean, and expe- rienced deep denudation, I did not see there as much evidence of its last drainage as in Scotland or New England, TERRACES IN IRELAND. 30 England. I traversed England in various directions, and yet generally over its more level parts, and did not see much evidence of drift agency, nor many terraces. The latter I did not expect to find well developed, save in regions where rivers are bordered by hills of considerable elevation, so arranged as to form basins. Yet I did expect to see them on the romantic banks of the Wye, but was disappointed; though materials exist, they are not well formed into terraces. And the same is true of all the streams of England where I passed them. Beds of gravel and sand do, indeed, occur extensively, but they seemed to me to be beaches, or rather old sea bottoms, and not terraces, and many of them sandy and gravelly bottoms of former seas, belonging to a period anterior to the drift, being the beds of tertiary strata. Very probably good examples of terraces may be found in the more hilly parts of England; and geologists describe deposits of drift derived from Scandinavia and Scotland. But they generally make no distinction between drift and remodelled and comminuted drift, which last forms deposits of far posterior date. I think I see in their descriptions, however, marks of what I call ancient beaches and sea- bottoms of postdiluvian date. Treland. I visited only the northeast of Ireland, passing from Dublin to Belfast, through Dundalk, Castleblayney and Armagh; from Belfast, along the coast, to Fair Head, and the Giant’s Causeway, and from thence back to Belfast, through Ballymoney, Ballymena, Antrim, and Carrickfergus. A little south of Castleblayney, I met with genuine unmodified drift, scattered over the slate and silurian rocks, and I saw striz and embossed rocks; the direction of the striz being from northwest to south- east nearly. Here, also, were frequent examples of what I suppose to be the Swedish Osar, viz., ridges of sand and gravel running northwest and southeast, the rounded summit sloping very gradually, especially at its southeast extremity. At the other end the slope is not so distinct, and indeed the ridge is sometimes termi- nated by some obstruction. In Col. Portlock’s “Report of the Geology of Londonderry, Tyrone, and Fer- managh,” which lie north and northwest from the region I am describing, he states “that these trains of sand and gravel are found at an elevation of nearly 1000 feet.” He says, also, that “in the eastern parishes of Derry the form of detritus is peculiar and beautiful. It appears like so many streamers attached to each basaltic knoll, and directed from north to south.” These ridges are somewhat dif ferent from any that I have observed in the United States; or rather, they seem more distinctly to be the result of a current heaping up materials behind some obstruction; precisely, in fact, what we see in the beds of our large rivers, or smaller lakes. Whereas, with us, similar ridges, which I denominate Moraine Ter- races, are often curved, have steeper escarpments, and do not seem connected with obstructions. 36 SURFACE GEOLOGY. They do not seem to correspond to the descriptions given by authors of Osars. Yet M. Desor, who is familiar with such deposits in Scandinavia, describes them as occurring around our western lakes; and he refers to the gravelly ridges at An- dover, Mass., as of the same kind. As to the latter, taking Sir R. Murchison’s de- scription of Osars (Russia, vol. i. p. 547) as a guide, I have doubted very much whether they could be Osars, since they are tov crooked, too narrow, and to long, to be produced by a current sweeping past some obstruction, either a rock or an iceberg. Seffstrom regarded the Osar as peculiar to Sweden, though probably wrong in such a view. But I ought perhaps hardly to give an opinion adverse to such authority on the subject. As remarked on another page, I have represented Osars in four places in New Hampshire on Map No. 1, Plate III, viz., at the Pot-hole Gorge in Union, near Fabyan’s tavern, in the White Mountains, and a few miles south of Conway, on the road to Centre Harbor, and just within the bounds of the town of Eaton. These may be Osars, yet my doubts as to the fact are not all cleared up. Along the northeast coast of Ireland the streams are little more than brooks, yet the glens are numerous, and I looked into them with interest, expecting to see perfect terraces. But they are infrequent and imperfect. Soin the gently undu- lating region from the Giant’s Causeway, through Ballymoney and Ballymena to Belfast, although rocks seldom appear in place, and a coarse detritus covers the surface; yet it does not assume the form of distinct beaches or terraces. They doubtless exist, however, in other parts of the island; and yet, although in the able papers and volumes of Berger, Weaver, and Portlock, on the Geology of Ire- land, I find decided evidence of ancient beaches, I have not met with any descrip- tion of distinct terraces. Scotland. I entered Scotland by the way of the Frith of the Clyde, and soon noticed the general resemblance of its banks to those of American rivers. A few miles below Glasgow, two, and sometimes three, terraces were obvious from the steamboat. They were of small elevation, however, not more, I judged, than 20 or 30 feet, and there is no barrier between them and the ocean. Subsequently I passed through the Highlands by the way of Loch Lomond and Glencoe, and thence to the Parallel Roads of Glen Roy. On this route the surface geology bears a strong resemblance to that of New England. At the foot of hills great quantities of modified drift appear in the form of beaches, rather than of terraces. Some- times, as in the valley near the lead mines of the Marquis of Breadalbane, the coarse gravel is piled up in those irregular masses with deep depressions, which I have called Moraine Terraces. These, both in Scotland and America, have been regarded as the moraines of ancient glaciers. Once I was prepared to adopt this opinion, but since I have seen undoubted moraines in the Alps, I feel compelled to dissent from it. The fatal objection to such an opinion is, that the materials, composing these supposed moraines, have been modified and in a measure sorted by water—a condition never seen in genuine moraines, at least to any great TERRACES IN THE HIGHLANDS. 37 extent. Fragments of all sizes and shapes are crowded along ‘promiscuously by glaciers, and though some of them are rounded and others ground to powder, there is no separation of one sort and size from another. Wherever we find such separation, however imperfect, we may be sure that the materials, even though originally produced by glaciers, have been remodelled by water. And such are most of those cases which I have seen of supposed moraines in the United States, which I thought strongly to resemble those above alluded to in Scotland. In passing from Fort William to Glen Roy, along the northwest side of Ben Nevis, vast accumulations of such materials occur, which appear to me to have once been sea-beaches or sea-bottoms. In descending towards the Spean on that road, we meet with very fine terraces, sometimes three or four tiers of them. They are, also, seen along the Roy, even beneath the Parallel Roads, where they have been long since figured by Dr. Macculloch, in the Transactions of the London Geological Society. These Parallel Roads are certainly the most remarkable terraces I have ever set my eyes upon: peculiar from their narrowness and from their perfect horizontality and parallelism. The first fact may perhaps be explained from their occurrence on hills so steep that they could not retain wide platforms of loose materials. The other facts lead the mind almost irresistibly to the conclusion that the body of water, which once filled these glens, must have paused for a time at the successive roads, as it was drained off. But was it the sea, or a lake, whose barrier towards the ocean has disappeared? Did not the markings extend towards the ocean below that point on the Roy river, a mile or two above its mouth, where such large quan- tities of detritus lie upon its west side, we might say that the valley at that spot was once choked up with detrital matter to the height of the roads, and subse- quently eroded. But since the terraces can be traced far down the valley of the Spean, where it becomes quite broad, such erosion never could be accomplished by the river. Nothing but the ocean could have opened such a broad valley. To suppose the space to have been choked up by a glacier, descending from Ben Nevis, does not relieve the matter, because the materials now occupying the valley have been most evidently worn and comminuted by water, and are not the simple moraine of a glacier. Moreover, I noticed that in some places at least, the side of the mountains above the highest road, was covered by such sand and pebbles as constitute the terraces. I did not ascertain whether the same is true to the very top of the hills; yet such was my impression, and if correct, it destroys the idea of lakes and obliges us to admit the presence of the ocean. But I fear that I am affording ground for the charge of vanity in venturing an opinion on questions which have divided the judgment of so many able men, who have devoted much more of attention to the phenomena than I have. The new suggestions I have made, in respect to the nature of the materials forming the parallel roads and spread over the sides of the valleys, is my only apology. In ascending towards the higher parts of the Highlands, especially on approach- ing Glencoe—that most romantic of all the Highland glens—I found the detritus becoming coarser, and the fragments more angular, with slight evidence of being sorted, very similar, indeed, to the unmodified drift of New England. Just at the 38 SURFACE GEOLOGY. entrance of Glencoe, I noticed striz upon the ledges running nearly N. W. and S. E. At Oban, on the western shore of Scotland, I observed similar markings, having a direction N. 50° to 60° W., and 8. 50° to 60° E. A good example, also, I observed upon the railway track at the Rath station, between Glasgow and Kdin- burgh—to say nothing of the examples pointed out around the latter city by her eminent geologists. Perhaps it may be superfluous to mention that, on the hill lying directly east of the village of Oban (where I was detained by ill health), Mrs. Hitchcock found detrital accumulations of recent shells from 200 to 250 feet above the ocean. Prof. James Nicol, in his Guide to the Geology of Scotland, mentions that a raised beach occurs not far from Oban, but only some 30 feet above the sea. Others, however, may have described the higher beach to which I allude. Inoticed among the shells those of Ostrea, Mytilus, Mya, &c. Valley of the Rhine. In travelling through Belgium, the most of which appears as if recently reclaimed from the sea, and is, in fact, probably a not very ancient sea-bottom, I saw no terraces nor beaches till I reached its northeast part. In the vicinity of Liege, beds of gravel appear which I regard as beaches; and, as we approach the Rhine, the railroad is tunnelled through a high deposit of this material. merging into the broad valley of the Rhine, we find distinct, though not high, terraces. They are such as are sometimes produced by the slow alteration of a river’s bed, by the wearing away of one of its banks and depositing a lower bank on the opposite side. Such a terrace, some miles long and 15 to 20 feet high, I saw on the right side of the rail- way between Cologne and Bonn, near the latter city. The beaches are composed of sorted gravel and sand, but I observed no genuine drift in passing through the Ardennes mountains. A little above Bonn, is one very distinct terrace, on the south sidé of the river, above the meadow, with deposits like beaches above. Before reaching the Siebengebirge, or seven mountains, are remains of terraces, some of which have a rapid slope down the stream. But possibly these are rocky platforms covered by detritus. Between the Siebengebirge and Aldernach, we pass occasionally narrow meadows, on one side or the other, with terraces, and sometimes beaches, higher up. Generally there are only two terraces besides the meadow. The lower ones at least are composed, as I was told, mainly of Léess. One of these terraced basins I noticed opposite Linz, at the mouth of the Ahr; another opposite Niederbreisig. But I think it useless to particularize, as the terraces all have the same general characters. They are usually of rather mode- rate height and not wide. Above Aldernach the valley expands, with at least one terrace above the mea- dows. From Coblentz to Bingen, the river is crooked, and the banks crowd so closely upon it that terraces hardly exist. Above Bingen, terraces appear, espe- cially on the- north side. The Chateau of Johannisberg, the property, as I was told, of Prince Metternich, stands upon one of these, not less than 100 feet above the river. Above this place, the mountains recede far from the river, and the TERRACES IN SWITZERLAND. - 39 country is undulating, seeming like the bottom and shores of an ancient sea. But the river terraces are few and imperfect. Near Heidelberg, on the north bank, a few are placed along the foot of the hills. At Wiesbaden and Frankfort, the detrital matter appeared to me like old sea-bottoms, and the long sandy plain passed over between Frankfort and Heidelberg, is probably a terrace of similar origin. For the next 200 miles, between Heidelberg and Basle, I can only say that the valley of the Rhine is broad most of the way, and I saw but a few well-marked terraces, with now and then a beach above them. But I doubt not that examina- tion would show them both to be numerous, though probably not so distinct as in narrow valleys. Upon the whole, I may say that the phenomena of surface geology on the Rhine, as far as I observed them, correspond entirely with those upon the larger rivers of our country. Switzerland. We next reached Switzerland, but in passing towards Zurich, through Bruges and Baden, we continued for a time along the south bank of the Rhine. A little beyond Basle, near the mouth of the Birs, terraces are very fine; and, in fact, they continue to be exhibited along the Rhine as far as I followed it, viz., to Mumpy. The two lowest are very distinct, and then we frequently have irregular ones still higher, which I should call beaches. Near Basle, | measured a terrace, the third in height—and, so far as I saw, the highest—which I found, by the aneroid barometer, to be 228 feet above the Rhine, and 983 feet above the ocean. At Rhinefelder, I took the approximate heights of three successive terraces, and observed at least one other below the lowest of these, and also what seemed to me to be beaches above the highest; these are represented on section No.41. The highest, it will be seen, is 306 feet above the Rhine, and 1226 above the ocean. Further up the Rhine, near Mumpy, I measured what seemed to me a beach, 696 above the river; and found the highest part of the road between Mumpy and Bruges to be 941 feet above the Rhine at the former place, and 1915 feet above the ocean. At this summit, the detritus was perhaps drift, though I thought it had been modified by water subsequently. After leaving the Rhine at Mumpy, we followed up a small stream with terraces, but they slope rapidly towards the stream, and are, properly speaking, glacis terraces. Around Bruges, where the Reuse and Limmat join the Aar, the terraces are very fine, and may be seen extending down the river several miles. Between Bruges and Zurich, through Baden, we see some terraces on the small streams, but they are not striking. Most of the detritus seemed to be drift, yet somewhat modified. The northern part of Lake Zurich I found to be fringed by three or four terraces, which are often chosen as the sites of villages and scattered houses. Leaving the lake at Horgen, on the west shore, we ascended the ridge separating Lake Zurich from Lake Zug. Section No. 42 will give some idea of the terraces on that route. Two of the terraces I measured; and the beach represented as 843 feet above the 40) SURFACE GEOLOGY. lake may be only drift, yet it seemed to me to have been modified by water. If so, this gives us a beach 2185 feet above the ocean. Crossing Righi, I went to Lucerne; next to Bern, and from thence to Vevay, on Lake Leman; thus passing lengthwise through the greater part of the great valley of Switzerland between the Alps and Jura. North of Lake Zug is a wide plain, but little above the lake, and appearing like an ancient bottom of the lake, as I doubt not it was. On the east shore of the lake, I thought I saw one or two imperfect terraces. Around the western part of Lucerne lake, I saw none that I recollect. In going from Lucerne to Bern, we ascended the Little Emmen as far as Scups- heim, and then passed over to a branch of the Great Emmen, which, however, we left ere many miles, and passed over an undulating country, where are numerous accumulations of water-worn materials which constitute what I call beaches, or perhaps, more properly, ancient sea-boftoms. Along all the rivers on this route, terraces are common and often quite perfect; for example, a little south of the village of Langnan, in the Emmenthal. I ought, however, to mention that the sandstone along this route sometimes assumes a terrace form, and, where covered by soil, I might have mistaken such a terrace for one composed of detritus. Yet Iam sure that many unconsolidated postdiluvian terraces exist on these rivers. On the Reuss, a little out of Lucerne, I measured one that is 267 feet above the lake, and still further on another that is 825 feet above the same. Towards the summit level of the route, near Scupsheim, I measured a detrital accumulation— which, with some doubt, I call a beach—894 feet above the lake, and 2274 feet above the ocean. The summit I found to be 1287 feet above the lake, and 2667 feet above the ocean. Around Bern, and wherever I travelled on the banks of the Aar, the terraces are well characterized. They consist mainly of gravel and sand; but as we recede from the river, and come to the beaches, the materials are coarser and pass into drift, the boulders rarely exceeding two feet in diameter; yet they are mainly of the older crystalline rocks, while those in place are sandstone. From Bern towards Vevay, the detritus, till we reach Bulle, beyond Freyburg, is evidently water worn and sorted into terraces and beaches. Some distance beyond Bulle, genuine drift (perhaps the old moraine of the Rhone glacier) began to appear, and continued, so far as I could judge in the fading twilight, nearly to Vevay, where we strike some lake terraces—which Robert Chambers has described as delta terraces—at the heights of 108, 165, and 442 feet above the lake. The highest terrace, or beach more probably, which I passed on this route, my barometer indicated to be 981 feet above Bern, and 2640 above the ocean. From Lausanne to Geneva, the west shore of Lake Leman is fringed with terraces. In some places I noticed three or four, though not so many are continuous; probably none of them are all the way. Back several miles from the lake, the country appeared to me to be covered with such materials as terraces or beaches are usually composed of. Some of the terraces near the lake I could see, from the steamboat, to be composed of laminated sand and fine gravel. In entering the harbor of Geneva, I noticed several large Alpine boulders. TERRACES IN SWITZERLAND. 41 From Geneva I turned eastward and followed the Arve nearly to its source, on the route usually taken to Chamouny. On looking over Mr. R. Chambers’ paper on the valleys of the Rhine and the Rhone, since my return home, I find that he took the same route, and has anticipated some of my observations. I shall, how- ever, give the few which I collected as they appeared to me. At the south end of Lake Leman, where the Arve from the region of Mont Blane unites with the Rhone, a mile below Geneva, as it comes from the lake, is a deep accumulation of detritus, through which both the rivers have worn a passage. It was mainly brought down by the Arve, a rapid and tumultuous stream, almost always loaded with matter mechanically suspended. It is in fact the delta terrace of that river and the Rhone, and extends back to the Saleve Moun- tains. A mile or two east of the city we reach its highest part in that direction, before crossing the Sardinian frontier. I found the terrace there to be 137 feet above the lake. Passing from this level towards the Arve, we find one or two lower terraces: which are composed of pebbles and boulders mixed with clay, not unlike the “boulder clay” of Scotland. ' There can hardly be a doubt that Lake Leman owes its existence to this delta terrace of the Arve. But this point will be better understood when I have treated of analogous cases in my paper on Erosions. As we proceed along the Arve towards its source, we find terraces more or less distinct most of the way to Sallenches, which is 36 miles from Geneva. These terraces for the most part slope with the stream, and they, also, usually slope towards the river, often rapidly, so as to form the Glacis Terrace. \ In some places, especially where the valley is narrow, there is only a single slope, as is very com- mon in the higher Alpine valleys, where the river runs at the foot of one of the hills. The materials of the terraces are usually coarse, though sometimes we pass alluvial meadows. But the higher terraces are very coarse, often like unmodified drift. A few miles below Bonneville, I measured a terrace, not the highest, and found it 314 feet above Leman, 1544 above the ocean, and about 154 above the Arve. A little beyond Bonneville, I measured another, which was 372 feet above Leman, and 1603 above the ocean. At Sallenches, I found one which is 581 feet above Leman, 1811 above the ocean, and about 120 above the “Arve. Around Sallenche the terraces are fine, but on the north side of the river I suspect the existence of a portion of a former terminal moraine. Still lower on the stream I thought I discovered another, and when we had gone a league or so beyond St. Martins, and began to ascend the enormous masses of coarse detritus unmodified, I could not doubt that we had reached the terminal moraines of former glaciers. Four or five miles before reaching Chamouny, we pass a long and narrow defile, and as we might have expected, found terraces above where the valley opens, in which Chamouny is situated. A few of them may be level-topped; but they mostly slope rapidly towards the Arve. Chamouny (Union Hotel), according to my barometer, is 3270 feet above the ocean: 3425, according to Johnston’s Dic- tionary of Geography, and 3190 French feet, according to Keller’s map. Some distance above Chamouny, and just beyond the termination of the Mer de 6 42 SURFACE GEOLOGY. Glace, the Arve valley is blocked up by an enormous mass of coarse detritus, which was probably the right hand lateral moraine of the glacier, when it for- merly extended across the valley. It is nearly 200 feet high, as I judged, save that on the north side of the valley the Arve has worn a passage to its bottom through the moraine. Above this barrier was once a lake, and the result has been, that at least three terraces have been formed on both sides of the river. The highest of these terraces I found to be 670 feet above Chamouny, and 4100 above the ocean. Still higher up the stream, just beyond the glacier, called Argentiere, is another similar moraine, which produced some terraces, less distinct, however, than in the lower basin. I did not pass into the bed of this ancient lake, but took an obser- vation, towards the hamlet of le Tour, on a level with the terraces, as near as I could judge with the eye, and found the height to be 926 feet above Chamouny, and 4351 feet above the ocean; the highest point where I have ever seen terraces. After passing the summit between the valleys of the Arve and the Rhone, on the Téte Noire Route, we came upon the Hau Noire, which descends into the hone. The highest terraces I noticed on the Eau Noire, which are small and of quite coarse materials, are 793 feet above Chamouny, and 4218 feet above the ocean. But the valley of this stream, for several miles on the Sardinian side of its course, affords a fine example of that sort of glacis terrace, which consists of one broad slope towards the stream from the mountain side. The materials are quite coarse, yet rounded, and evidently the result more or less of aqueous agency. Yet along this stream the erosions of former glaciers are quite manifest, high up on the precipices that bound the gorge. As we descend towards Martigny, on the Rhone, we have a view of the valley of that river some dozen miles up the stream, traversed by the Simplon road. It looks very much like an estuary recently abandoned, and I could see no terraces. The detritus is spread, with nearly an even surface from one steep side of the valley to the other, having a downward slope equal to that of the rapid stream. Such, for the most part, is the character of the Rhone valley half way from Martigny to Lake Leman. Frequently, however, the alluvial sides of the valley slope towards the river in the glacis form, and sometimes I noticed more than one of this kind of terrace, arranged in successive steps, like the level topped terraces. At St. Maurice, where the river goes through a narrow gorge, and the road passes from the Valais into the Vaud, we meet with terraces of the common form, which I found to be 250 feet above Leman, and 1480 feet above the ocean; or on a level with the surface at Martigny. The Rhone, however, at St. Maurice, is 70 feet lower than at Martigny, according to Keller’s map.! + In several of the valleys of the Alps, I was struck with a singular optical deception, which I have not seen noticed by travellers. In ascending valleys with steep and lofty sides, the road sometimes descends slightly for some distance, in consequence of the detritus, which spreads out over the whole valley. In some cases of this sort, I felt a little anxiety to see the postilion urging on his horses at so furious a rate, down what appeared to me a quite steep hill. But on looking back, I found that we were scarcely descending at all. And, indeed, I found that a great part of the way we seemed to be THRRACED ISLAND IN HAST INDIAN ARCHIPELAGO. 43 France. I passed from Geneva to Paris, through Dijon and Tonnerre, and from Paris to Boulogne: also from Calais to Lille, in the north of France, but I have not much to say of the terraces. The country generally is too flat and free from mountains to make their occurrence probable. On the route from Geneva to Paris, terraces are uncommon, though the limestone, which I believe underlies the whole country, sometimes assumes this form: as for example, in the hills surrounding Poligny. Around Campanogle river, terraces are well characterized, and at a higher level I saw some beaches. As to drift derived from a distance, I saw no good example; however, I crossed the Jura mountains in the night. In many places the limestone is worn into a thousand fantastic shapes at the surface, and appears extremely jagged; showing that drift agency has not smoothed it down. Scandinavia. This country I did not visit, and I allude to it here for the purpose of quoting a remarkable fact, mentioned by Mr. Robert Chambers, in his description of some of its terraces. These he traced at least to the height of 2162 feet above the ocean, and found the highest bearing a strong resemblance to the Parallel Roads of Lochaber, in Scotland. But the fact to which I allude, is this: “that there is a district in Finmark, of 40 geographical miles in extent, which has sunk 58 feet at one extremity and risen 96 at the other.” (Hd. New Phil. Journ., Jan. 1850.) If the terraces there are as irregular as in this country, and as much wanting in continuity over wide districts, this would be a very difficult fact to determine. ‘But I cannot doubt that one so familiar with this subject as Mr. Chambers, would be on his guard against confounding different terraces. 8. TERRACED ISLAND IN THE HAST INDIAN ARCHIPELAGO. Rev. Charles Hartwell, American missionary in China, on his passage thither, took a sketch of Sandalwood Island, on account of its terraced appearance. For- merly my pupil, and knowing the deep interest I felt in terraces, he sent the sketch to me; and in the dearth of information respecting terrace phenomena in that part of the world, I have thought it ought to be preserved. I have accord- ingly added it to the illustrations of this paper in Plate XII, Fig. 6. It was taken at the distance of eight miles. a, is a projecting point of terraces; 0, the S. EK. point of the island; c, detached isle west of the point 6, and near the southern descending, when in fact there was a slight slope upward. I observed, also, that when we were on one side of a valley, say 80 or 100 rods wide, and where in fact the two sides sloped somewhat rapidly towards the river in the centre, it seemed as if there was a continuous slope to the opposite side, where the steep rocky mountains rose. I shall not attempt to explain these phenomena, though confident that they are not the result of anything peculiar in my own perceptions. 44 SURFACE GEOLOGY. shore. This was the only terraced island seen by Mr. Hartwell during his voyage. He says it is volcanic in part, and the terraced margin may be coral reefs. It is covered with vegetation, sandalwood being abundant. Other Forms of Surface Geology. In the commencement of this paper I have enumerated other distinct forms of detrital matter coming within the province of surface geology. I have not studied these so carefully as the terraces and beaches, and, therefore, my descriptions will be short, though I trust they may deserve the attention of observers. 1. Sea-Botioms. If we find evidence of the existence of shores of ancient seas, we should expect to discover the remains of their bottoms; and if I mistake not, New England, especially in its less elevated portions, does present the gravelly and sandy plains and low ridges, which can be explained only by the former presence of the ocean above them, with its waves, tides, and currents. In the vicinity of Connecticut river, they are less obvious, because in the lower parts of the valley drainage has, in a measure, obliterated the marks of oceanic action, and the materials have heen converted into terraces and beaches. The sides of the valley also rise too rapidly to expect many such accumulations of detritus as form sea-bottoms. But when we get into the comparatively low region, within twenty or thirty miles of the coast, in Massachusetts, Rhode Island, and Connecticut, the surface is in a great measure covered with such materials, and in such forms as the ocean must have produced. Though I am not prepared to mark these definitely upon a map, yet I have ventured to define a few of them near the mouth of the Merrimack, and also in Berkshire valleys, in Plate IIL; I have likewise marked a strip as of this character, along the route of the New London, Palmer, and Amherst Railroads, and from Merrimack river to Saco river, along the northwest side of Lake Memphre- magog. 2. Submarine Ridges. I agree with Mr. Whittlesey in the opinion that the ridges which encircle Lakes Ontario and Hrie, were probably formed beneath the waters. These lake ridges— the lowest certainly—may not have been swhmarine in the strict sense of the term, though as it is certain the ocean once stood above the western lakes, it is not easy to say at what altitude the waters became first brackish, perhaps, and then fresh. T have ventured to mark one submarine ridge near the mouth of the Merrimack, on its south side, and to extend it southerly along the_coast at least to Ipswich ; beyond which I have not attempted to trace it. The highest part of the city of Newbury- port occupies the summit of this ridge, which has a slope both towards the ocean and towards the country. This ridge preserves a pretty uniform height, nearly to Ipswich. DELTAS AND DUNES. 45 This ridge may prove to have been an ancient beach, but its slope towards the interior and its singularity have led me to refer it to a submarine origin. Others, doubtless, will be found along the coast. 3. Osars. I have perhaps already said all that is necessary as to the existence of Osars in this country. I cannot see why they should not occur here as well as in Europe, since all the other forms of modified and unmodified drift are so similar on cis- atlantic and transatlantic shores. But what I call Moraine Terraces cannot be referred to accumulations of detritus by a current sweeping past an obstruction ; and, therefore, they are not osars, if such a mode of formation be essential. I should be inclined to refer to osars those remarkable trains of blocks, starting in Richmond in Berkshire county, and extending southeasterly several miles, de- scribed by me in the American Journal of Science, XLIX, 253; but they are too long to answer Murchison’s description. I will mention one or two cases, how- ever, in the vicinity of the White Mountains, which seem to me more like osars than any examples I have met with in this country, though not satisfied that they are so; but I have placed them on Plate III, in order to call the attention of geologists to those spots. One is a remarkable mound of gravel, near Fabyan’s Tavern, five miles from the notch in the White Mountains. Its height cannot be less than twenty or thirty feet above the surrounding surface; and its top (mea- sured with the aneroid barometer) is 1537 feet above the ocean. (See a sketch and description of it in Vol. I of the Transactions of the Association of American Geologists and Naturalists, Plate viii, Fig. 10.) The other case presents us with several ridges of sand, nearly straight, in a val- ley lying southwest from Adams’ Tavern, in Conway, New Hampshire, towards Eaton. The principal ridge may be a half a mile long, terminated on the north by apond. These ridges seem to me to differ from those in Andover, in being nearly straight; but they need further examination. 4, Deltas and Dunes. Connecticut river has, of course, made some delta-like accumulations at its mouth, but they are not extensive, being probably swept away by tides and cur- rents. The same is true of the smaller rivers of New England, but as I have not studied any of these with care, I pass them by. The dunes of southeastern Massachusetts have long since been described. They are sometimes quite high and large, requiring vigorous and expensive efforts to arrest their progress. Along the Connecticut valley small ones exist in Hadley, Granby, Montague, and Enfield, Ct., which are slowly advancing southeasterly, in consequence of the predominance of northwesterly winds. These dunes are derived from the sands of one of the higher terraces of the valley. 46 SURFACE GHOLOGY. 5. Changes in the Beds of Rivers. 1. On Connecticut River. On the maps which I have given of Connecticut and Deerfield rivers, I have marked numerous ancient river beds. These are of two kinds, the most ancient, showing a deserted rocky gorge, where once the stream flowed at a higher level than at present; and the other, a depression in alluvial meadows, once the bed of the stream, and from which it has been generally slowly deflected by the wearing away of a bank. Changes of the first sort probably present us with old river beds of the antediluvian period, as I shall attempt to show in my paper on Erosions; but the latter class are postdiluvian, and sometimes occur in our own times; one good example of which change may be seen along the Connecticut, at the foot of Mount Holyoke. I was surprised to find how numerous these ancient river beds are, and I doubt not that time and further research would bring to light many more than I have exhibited on the maps. I will briefly describe such as I have found. Of some of them I am not quite sure, but generally they are distinct. The antediluvian river courses it is sometimes difficult to distinguish from erosions by the ocean; and the alluvial ones may be confounded with the troughs between glacis terraces. The most southerly deserted beds of Connecticut river are in Portland, opposite Middletown. The present bed of that stream through the first range of moun- tains, appears to me to be in a measure postdiluvian. It curves around two hills of considerable height, between which, as it appeared to me, is a former bed of the stream. I feel quite confident, also, that it once ran on the east side of both the hills, at a considerable elevation above the present level. j On the west side of the river, I think I can trace an ancient, though postdiluvial bed of the river, through Wethersfield, passing a little west of the village, and also through the west part of Hartford, so as to unite with the present bed a little above the city, bringing the city upon the east bank, had it then existed. Along the east bank a depression commences on the east margin of the meadows, in East Hartford, and continues as far as the south part of Enfield. I have not, however, followed the old bed through the whole of this distance, and may be in error. In the town of Springfield, a similar appearance is exhibited along the foot of the highest terrace on which the United States Armory stands, from a small stream at the south end of the town, to near the mouth of Chicopee river. I think the river once ran where we now find the principal street of the place. An isolated terrace, a little north of the town, marks the west bank of the former stream, as shown on Section No. 3, Plate I. Commencing in the west part of South Hadley, an ancient bed is marked on the map, passing to the east part of Granby, through a part of Ludlow, thence into the west part of Belchertown, where it passes through the gorge between the east end of Mount Holyoke (or Norwottuck, as the eastern part is called), and the OLD RIVER BEDS. 47 \ gneiss hills of Pelham; thence through the east part of Amherst, into Leverett, where it runs along the east base of Mettawampe (Toby), and thence along the east part of Montague, to the mouth of Miller's river. In the south part of Amherst, at a later period, when the waters had sunk below the gorge at the east end of Norwotiuck, I suspect that the current ran along the north base of Hol- yoke, and entered the present bed of the Connecticut, opposite Northampton. Ata period somewhat later, I think another bed ran from this same place along the west side of Amherst; thence to Sunderland, at the foot of the higher terraces, where, at the north of the village, it coalesced with the present bed. In Hatfield, somewhat north of the village, is a distinct ancient bed of postdilu- | vian date, but of no great extent. In the east part of Leverett, is a valley which was probably once the bed of Connecticut river, earlier, without doubt, than the bed so distinct along the foot of Mettawampe. The two unite at Amherst on the south, and in the north part of Leverett on the north. In Vermont and New Hampshire, I have not examined the Connecticut with care enough to discover its ancient beds, save in two places. In Claremont, I think it formerly ran about two miles east of its present bed, from which the old bed is separated by a hill of considerable height. In the southwest part of Piermont, also, I thought I discovered an abandoned bed, but had not time to explore it carefully. Opposite Mount Holyoke, in Hadley, is an example (referred to above), of a recent change in the bed of the Connecticut, of considerable extent. Formerly the river made a curve here of three or four miles long, while its actual advance towards the ocean was only about 100 rods. Ten or twelve years ago, during a freshet, a passage was cut through this neck, and since that time, the stream has left its old channel, which is fast filling up, and across which Connecticut River Railroad now runs. 2. In Orange, New Hampshire. On Plate III, a distinct ridge of mountains is represented as running from Bellows Falls, in New Hampshire, to the White mountains. It is not intended to convey the idea, however, that such a continuous ridge exists: but only that it is the summit between Connecticut and Merrimack rivers, from which tributaries of those rivers run in opposite directions. In that summit, in the town of Orange, is a depression in the range, through which the Northern Railroad passes, at an elevation above Connecticut river, at West Lebanon, of 682 feet, and of 830 above the Merrimack. Here pot-holes of great size indicate the former passage of a stream of water for a long time, from the Connecticut into the Merrimack valley. In other words, it seems to have been one of the outlets of the waters of the Con- necticut valley, where they stood at that height. But this is hardly a case of the change of a river’s bed, since no correspondent stream now exists. Two small brooks, commencing in the peat swamps lying on each side of the ridge, and run- ning, one easterly and the other westerly, are all the representatives remaining of 48 SURFACE GHOLOGY. the powerful current that once crossed this spot. It will be more particularly described in my paper on Hrosions. 3. In Cavendish, Vermont. On Plate III, Black river and William’s river, in Vermont, are seen to run nearly parallel courses. It appears that they were once united: at least the prin- cipal branch of Black river formerly ran southerly into the present bed of Wil- liam’s river. Whoever will pass through “ Proctorsville Gulf,” in Cavendish, shown on Plate III, as an old river bed, will be satisfied that it was indeed once the channel of Black river. Its present summit, raised considerably by detritus, is (by the aneroid barometer) 792 feet above Connecticut river, at the top of Bellows Falls, and about 100 feet above the Black river at Proctorsville; so that if this river were 100 feet higher at that spot, it might run through the gulf. The sides of the “eulf” are quite steep and high, resembling the banks of many of our mountain streams that have been worn deeply by water. At Duttonville, in Cavendish, two miles lower down the stream than Proctors- ville, is another more obvious ancient bed of the Black river. This, also, is filled with detritus where it branches off from the present bed, but within 100 rods of that spot, on the route of the Rutland and Burlington Railroad, we find large and distinct pot-holes; the infallible mementos of a former rapid current. This old bed may be traced some six or eight miles towards Connecticut river, where it unites again with the present channel of Black river. By the detritus which chokes up the old bed, at Duttonville, that river was compelled to turn to the left, where it has worn out a gorge through the rocks nearly 100 feet deep, producing a romantic cataract, called Great Falls; the foot of which is 183 feet below the old river bed. These two cases, belonging as they do in part to antediluvian agencies, will be described again in my paper on Hrosions. 4. On Deerfield River. One of these occurs near Shelburne Falls, in Buckland, where pot-holes exist in the sides of the old channel, 80 feet above the present stream, as may be seen on Plate IV. But a description of the spot is reserved for my paper on Erosions. Where Deerfield river debouches into the valley of Connecticut river, from its mountain gorge, it has formed an alluvial plat of unrivalled fertility. And here is displayed the best example of changes in the bed of a river by alluvial action that I have ever seen. As all the early part of my life was spent in that valley, I became familiar with these ancient river beds, and I have sketched them in Plate IV. Some others, less obvious, perhaps, might have been added: but it will be seen that not less than fourteen are put down on this spot, only four miles long and one mile broad. Nay, from the manner in which rivers in alluvial spots change their courses, viz., by the gradual wearing away of one of their banks, I cannot doubt that every part of these four square miles, save Pine Hill, in the INFERENCES. 49 northern part, and perhaps some limited spots where the village stands, has once constituted a part of the channel of the stream. In the extreme northern part of Deerfield, only a mile south of the village of Greenfield, occurs an old rocky bed of Green river, a tributary of Deerfield river. Here are pot-holes in the red sandstone, and a gorge in the same, while the pre- sent river runs in a channel worn in sand and clay, several rods further west, and at a considerably lower level. (See Plate IV.) 5. On Agawam River. I have traced out three examples on this river of antediluvian date. One is in Russell, on the west side of the present stream. The old bed is filled to a con- siderable height with sand and gravel, compelling the river to find its way through a rocky barrier. A second of these beds may be seen to the east of Chester village, at the junc- tion of its east and west or principal branches. A third is some three miles above this point on the east branch. (See my paper on Hrosions.) T might refer to many other examples of ancient beds of rivers, not connected with the Connecticut. But since most of these are older than the alluvial pericd, they will more properly be noticed in my paper on Hrosions. They would not be mentioned here at all, were it not that the accumulation of detrital matter during the last sojourn of the continent below the waters, seems to have been the means of commencing many of those defiles in which rivers now run. Feespilis, or Conclusions jrom the Facts. I shall now proceed to state the conclusions at which my own mind has arrived from the facts which I have observed respecting surface geology, especially ter- races, beaches, and drift. And as these conclusions are not based altogether upon the details above given, I shall present a summary of the arguments by which they are sustained, and the collateral facts and considerations on which they rest. 1. Postdiluvian terraces and beaches all lie above the coarse unstratified and unmodified drift, as well as above the stric, furrows, and roches moutonnes, con- nected with drift. Hence the terraces and beaches are the result of operations subsequent to the drift period. I wish not to be understood as maintaining that no genuine drift shows evidence of stratification and other modifying effects of water. Such effects do present themselves sometimes in the midst of detritus, which generally, in position and character, affords unequivocal evidence of being true drift. Limited beds of sand and clay are met with sometimes in the midst of such materials, and sometimes we find masses of coarse irregular detritus and scattered blocks above deposits that are distinctly sorted and stratified. But, as a general fact, the sorted and stratified materials lie above the drift. I wish, also, to add, that it is no easy matter always to draw a line between Ks 50 SURFACE GHOLOGY. unmodified drift and the modified materials of beaches and terraces. The eradua- tion of one into the other is often so insensible, that we cannot tell where the one ends and the other begins. But I shall refer to this again in another place. 2. The successive beaches and terraces, as we descend from the highest to the lowest, in any valley, seem to have been produced by the continued repetition of essentially the same agencies by which the materials—originally coarse drift— have been made finer and finer, and have been more carefully sorted and arranged into more and more perfect beaches and terraces. This seems to be the general law: at least such is the conviction produced in my own mind. Yet occasionally we meet with limited deposits, as already remarked, of fine materials in the midst of, or beneath those very coarse. This only shows that in certain places the comminuting and sorting processes were carried on at an early date as perfectly as afterwards when they were extended to large areas. 3. By far the largest part of the materials constituting the beaches and terraces is modified drift, in other words, fragments torn from the rocks in place by all the eroding agencies down to the close of the drift period. This position is proved by the occurrence of drift scratches and furrows over most of the rocks in place, in the valleys as well as on the hills. Indeed, I expect to show in my paper on EHrosions, that some rivers have made deep and long cuts through the rocks since that period: for instance, the gorge of Niagara river, from the Falls to Ontario, and the still deeper cut between Portage and Mount Morris, on Genesee river. But in the valley of Connecticut river no such gorges have been worn, since we find the drift stris in many places almost as low as the surface of the present stream, even at those points where once gorges were worn out. Thus, at Bellows falls, the rocks at the top of the falls, even to the water’s edge, exhibit distinct and beautiful examples of furrows and protuberances produced by the drift agency, although the cataract has undoubtedly receded con- siderably at this spot since that force acted. At Brattleborough the slate on the west side of the river shows drift furrows only a few feet above the river. Here too was once a gorge: but it was worn out earlier than the drift period. At Sun- derland, where Mettawampe and Sugar Loaf, between which the Connecticut now runs, were doubtless once united, drift scratches now show themselves almost on a level with the stream. The same is true on the trap rocks at Titan’s Pier, in the gorge between Holyoke and Tom, which were once still more certainly united. As to the gorge a little below Middletown, I am not able to speak certainly, yet so far as I could judge, in passing upon a steamboat, I do not doubt the occurrence of drift erosions at a low level. 4. Hence on such rivers as the Connecticut, wherever, indeed, we can find marks of drift agency low down on the rocks at gorges, we cannot suppose that rocky barriers closed those gorges during the period when the terraces were forming; and, therefore, we cannot call in their aid to explain the formation of the terraces. 5. The highest distinct terraces which I have measured above the rivers on which they occur, are as follows: On Connecticut river, at Bellows Falls, 226 feet; on Deerfield river, 236 feet; on Genesee river, at Mount Morris, 848 feet; on the BEACHES AND TERRACHS. 51 Rhine, near Rhinefelder, 306 feet. Some of the accumulations of gravel and sand above these might perhaps be called terraces; but I think they are more appropri- ately called beaches. So far up the sides of the valleys as these banks appear to have been formed mainly by the rivers that now run through them, when at a higher level, and forming a chain of narrow lakes, thus high should I denominate them terraces. But when we reach such a height that the waters producing the banks must have overtopped most of the hills and communicated with the ocean, or constituted a part of it, then they ought to be called, as they undoubtedly were, beaches—it may be the shores of a bay, or estuary, or frith; but still produced more by breakers than by currents, and, therefore, have not a level top. 6. The most perfect beaches in New England vary in height from 800 to 1200 feet above the ocean. (In Pelham, Shutesbury, Whately, Conway, Ashfield, &c.) Others occur less distinct, as we might expect they would he, from 1200 to 2600 feet above the ocean (at Dalton, Hinsdale, Washington, Peru, White Mountain Notch, and Franconia Notch). I can hardly ‘doubt that further examination will discover others at a still greater altitude. On Snowden, in Wales, I found a few traces of sea-beaches at several altitudes, the highest 2547 feet above the ocean. Still more distinct marks of a beach occur a little east of Cader Idris, 762 feet above the same level. In the north part of Switzerland, near Mumpy, I measured what I called a beach, 1670 feet above the ocean; on the west side of Lake Zurich, another, a little doubtful, perhaps, 2105 feet; between Lucerne and Bern, near Scupsheim, another, 2274 feet; and between Bern and Vevay another, 2640 feet, above the present ocean level. 7. The number, height, and breadth, of the river terraces, vary with the size of the river, the width of the valley, and the velocity of the current above the place where the deposits are made. Generally the number is greater upon small than large streams, while the height is less. This may be seen upon the subjoined sections. Thus the terraces on the Connecticut rarely exceed three or four; but on its tributaries, where they enter the Connecticut especially, the number rises sometimes as high as ten, as on the Ashuelot, in Hinsdale, Whetstone brook, and West river in Brattleborough, and Saxon’s river, at Bellows Falls. In these cases the terraces on the tributaries are formed in the terraces of the principal stream ; yet though the former are more numerous they rise no higher than the latter. 8. The river terraces, excepting the delta terraces, rarely correspond in number or in height on opposite sides of the stream. The delta terrace, whenever worn through by a stream, will, of course be of equal height on both sides of the river. When the valley is wide, and several terraces exist on opposite sides, by the eye alone we are apt to imagine an exact correspondence in height. But the applica- tion of the level usually dissipates such an impression, as nearly all the subjoined sections, which extend across the stream, will show. Had I carried these sections across the river more frequently, it would have appeared that sometimes no terraces exist on one side, while there are many on the other; or that the number differs much on opposite sides. 9 River terraces usually slope toward the mouth of the stream, to the same 52 SURTACEH GHOLOGY. amount as the current descends, and sometimes more. It is on the smaller and more rapid streams that we see this slope most conspicuously ; indeed, on these it is so obvious that I deemed measurements urinecessary. I have made only a single one, and that shows the slope in a delta terrace in the west part of Deerfield, which terrace was produced by a small stream called Mill river, which, as it entered the former estuary, thrust forward a quantity of sand marked as a terrace on Plate IV. This deposit would of course be thickest nearest the shore and diminish outwardly. The amount as I measured it by the aneroid barometer, is thirty-nine feet, in less than half a mile, a slope which of course had no reference to that of the current. I have said that the slope in some cases is greater than that of the stream. To illustrate this, let us refer to the wide and long basin from Mt. Holyoke to Middle- town, in which the current of the Connecticut must have been gentle, nor could the tributaries have brought in materials sufficient to fill up the broad valley as high as where it is much narrower. Hence we should expect, that as we pass south from Holyoke, the upper terrace would become thinner and thinner. Such I suppose to be the fact, as stated in my description of the sections in the part of Connecticut valley above alluded to. In a distance of forty or fifty miles, I have thought we have evidence of a descent of more than 140 feet, besides the descent of the river. The only doubt I have in the case, arises from the difficulty of determining whether the upper terrace, to which my sections extend, is continuous throughout this whole distance. 10. Terraces are usually the highest about gorges in river courses. Such is the fact at Bellows Falls, at Brattleborough, at Montague, at South Hadley, and a little above Middletown, where Rocky Hill on the west side of the river pro- duces a narrow gulf for the river. Also between Tekoa and Middle Tekoa, on Agawam river (Section No.19.) The materials are not accumulated around these narrow passes because they were then closed, for we have shown that since the drift period most of them have not been closed. But the narrowness of the valley at these spots would, to some extent, retard the streams when swollen, and cause it to deposit more of its suspended matter than in the middle part of the basin. In general it is on the lower side of the gorge that the accumulation is the greatest, because there the waters would spread out laterally and produce eddies or ponds. But sometimes it is above the gorge where the terrace is highest, as on Tekoa. 11. The chief agent in the formation of terraces and beaches appears to have been water. The following facts establish this conclusion beyond’ all reasonable doubt. 1. The materials have been so comminuted and rounded as no other agent but water can do. Glaciers and stranded icebergs may, indeed, crush and some- times partially round abraded fragments of rock, but they do not produce deposits of rounded and smoothed pebbles, such as form most of the terraces and beaches. 2. The materials are sorted, so that those of different sizes occupy distinct layers. This effect water alone, of all natural agencies, in the form of waves or currents, can produce. The size of the fragments indicates the strength of the breaker, or the current. 3. The deposition of the layers in horizontal or nearly horizontal position, can be effected only by water. In order to produce the level tops of the terraces water must have once stood above them, while currents strewed the mate- THEH WATERS OCHANIC. 53 rials along the bottom. So too, though we find more irregularity in the beaches, yet along what was by the supposition once the line of a coast, they are level, while seaward they are rounded and sloping, like beaches now forming. In the case of moraine terraces, however, I think it unquestionable that some other agent, besides water, must be called in to explain their formation. If masses of ice were stranded for a long time on the spot where they occur, and currents of water had accumulated the sand and gravel around them, and afterwards the waters had retired and the ice melted, it seems to me that the surface would be left in that peculiar condition which the phenomena under consideration present. I can, however, conceive how strong eddying currents alone might pile up sand and gravel to some extent in a similar manner. But when I meet with these ridges, knolls, and depressions, over wide surfaces, and a hundred feet in height and depth, I have strong doubts whether we must not call in the aid of stranded ice. Water, however, even in this case, must have been the principal agent. But more on this subject in a subsequent paragraph. 12. If the preceding conclusions be admitted, it will follow, that at as high a level as we can find accumulations of rounded and sorted materials, we may be sure of the long continued presence of water, since the drift period, or during the alluvial period. Hence I feel sure from the facts which I have stated, that over the northern parts of this country, this body of water must have stood at least 2000 feet above the present sea level; and I might safely put it at 2500 feet: for up to that height I have found drift modified by water. At an equal height have I observed it on the continent of Europe. 13. The water that stood at such a height on the continents, must have been the ocean. For most of the mountains in the United States are below that level, and consequently must have been enveloped by the waters. Not a few instances occur, indeed, nearly all the examples of beaches which I have described are of this character, in which Plate XII, Fig. 4 represents their situation. Between the old beach and the present ocean there are no barriers high enough to prevent the water that covered the beach from communicating with the ocean: and the fact that the surface, almost everywhere, is smoothed, rounded, and striated by the drift agency, even to the bottom of the valleys, precludes the idea that rocky barriers existed when the beaches were formed high enough to shut out the ocean: for those beaches were formed since the drift period. I know of no way of avoiding the conclusion that these waters were oceanic, unless it be by supposing barriers to have been formed by vast accumulations of detritus and ice, which subsequently disappeared, after having formed and sus- tained lakes and inland seas long enough to form the beaches. But this must have required barriers, sometimes perhaps a hundred miles long, and in some places at least 1000 feet high. If they once existed, and were formed of detritus, what can have become of it? Was it carried into the ocean? This would have been impossible by the breaking away of the barrier, even though ruptured in several places; and we may not, by the very supposition, call in the breakers of an ocean to wear it away. Was it an icy barrier? Is it not incredible that an embankment of this material, so many miles long, and so many hundred 54 SURFACE GEOLOGY. feet thick, should have been able to sustain for centuries vast bodies of water, while it was comminuting and depositing extensive beaches. I am fully satisfied, that even though the geologist may, in his study, conceive of such icy or detrital barriers, he could not maintain his opinion, were he to stand upon these beaches, and turn his eyes towards the present ocean, and see what an immense mass of materials must be required to fill up the country to the level of his eye, so as to cut off all communication with the ocean. Certainly nothing like such piles have been witnessed in any place on earth. It is true of some Alpine valleys, that their lower ends have been choked with ice and detritus, so as to form ponds above; but where do we find an example, in which the sides of such valleys, many miles long, are formed by the same materials? Some, I know, consider no evidence of the presence of the ocean decisive, unless it have left marine remains, and such we find in the United States only among the more recent beaches and terraces, for example the clays around lake Champlain, and along the St. Lawrence, at Montreal, &., which are only a few hundred feet above the sea. Why they do not occur among the more ancient pleistocene strata, I mean the terraces and beaches, I know of no more probable reason, than that animals and plants were not then living in the waters that made these deposits. But that the beaches and terraces were formed by water, no one, who will examine them, can doubt. This being admitted, I am forced irresistibly to the conclusion that this body of water must have been’ oceanic, for the simple reason that a sheet of water thick enough to reach such spots, must have spread on all sides far enough to form a sea. It is possible that some may resort to the supposition, that though no high rocky barriers have been worn down since the formation of the beaches and ter- races, yet there may have been great changes of relative level since that time, so that places, which are now lifted high above the general surface, may then have occupied depressions where lakes existed. I can hardly believe that any one practised in surface geology would adopt such an opinion, for he will see that nowhere have terraces or beaches been disturbed by any such movements, but retain exactly the contour and levels which they had when deposited. This they could not have done if there had been any appreciable changes of relative level: and to meet the case, such changes must have been very great. The hills, too, that were rounded by the drift agency, present their stoss, or abraded sides, to the north, just as they must have done when struck by such agency: and at the foot of other hills, boulders are accumulated, just as they would be, if those hills stood there during the drift period. In short, though there be evidence that the land as a whole has either risen, or the water has retired from it, since the drift period, in thirty years’ examination I have never met with a single example of any change of relative level in different parts of the surface by vertical movements since that time; nor have I seen any such changes described, save that sort of see-saw movement which Mr. Chambers found in Scandinavia, and which may have hap- pened, also, in our own country, but which has never disturbed the relative levels in the sense above supposed. 14. It is hardly venturing beyond a legitimate conclusion, in view of the pre- A) FORMATION OF BHACHES. 50 ceding facts, to say, that all the northern part of this continent, at least all east of the Mississippi, has been covered by the ocean since the drift period. For admit that these waters rose 2000 feet above the present ocean, and how few mountains even, would project above the surface. A few rocky islands only would be seen, the largest around the White mountains and in the northern part of New York, while the chief portions of the land would have disappeared: nor in the opinion of many geologists is the evidence wanting, in the marks of drift agency everywhere, save at the very top of Mount Washington, that all the hills, higher than 2000 feet, save that single peak, were at that period beneath the waters. 15. Admitting the existence of the ocean over the whole, or the greater part of North America (and the same may be said of other continents, with similar phenomena), and a gradual elevation of the land, or a depression of the ocean to commence and continue to the present time, we can see how, by the drainage of the uneven surface, and the action of waves, tides, and oceanic and fluviatile currents, the whole system of beaches and terraces, as well as other forms of sur- face geology, were produced. 16. Let us begin with the beaches, which must have been formed the earliest. As the elevated portions of the surface began to emerge from the waters, covered probably to a considerable extent by drift detritus, the waves would act upon the shores and comminute the materials, causing them to accumulate in bays and friths. Yet at first the quantity. must have been small, both from the limited extent of coast, and deficiency of materials; and if the elevatory movement was rather rapid, the fragments would not be reduced very small, nor thoroughly rounded. Hence the highest beaches might be difficult to distinguish from the drift, especially as the drift, while beneath the waters (I say nothing here of the time or mode of its origination, save that the period was earlier than the rise of the land), would most probably be made to assume a beach-form in some places. If the elevation proceeded equably, the wave-worn detritus might be strewed some- what evenly over the sloping surface, and not form distinct beaches. But if there were pauses in the movement, we might look for beaches at successive levels. Yet there would doubtless be great inequality in their position and character, nor should we expect, unless the pauses were long, and the quantity of detritus great, that they would form regular fringes around the islands: but rather that they would be found in the successive bays that would be formed in different places, as the irregular bottom of the sea emerged. I have supposed pauses in the vertical movement: and these doubtless would produce beach deposits at successive levels. But when enough of land had emerged to give rise to rivers, I think we can see how similar beaches might be formed without paroxysmal movements. A river would carry detritus into the sea, which might be spread along the coast by oceanic currents, and form a bank beneath the waters. Gradually would this be raised by new depositions, and by the uniform rise of the shore, until it would reach the surface, forming a marsh at first; and as the process of elevation went on, a dry and raised beach, modified by the breakers while within their reach. But when the river could no longer deposit its sediment upon this bank, it would be carried forward into the water 56 SURFACE GHOLOGY. beyond, and there begin to form a new bank, which in like manner, would at length reach the surface; and then a third bank would be formed, all the while the vertical movement proceeding without pause or paroxysm. It may be thought that in such a case the sediment would be deposited in one continuous slope or talus: and it would be without a current along the coast to wear away the successive banks on the outer margin; and thus, it seems to me, the result might be terraces, or rather successive beaches, at different levels. And thus might the lower beaches, that now fringe the coasts of North America, have been formed by a secular and perfectly uniform elevation of the continent. Until rivers existed, however, I should expect the beaches to be very irregular and indistinct, unless there were pauses in the upward movement: and so I do find them near their upper limit, while the lowest beaches on our present shores, are almost as perfect as river terraces, especially at the mouths of rivers, where per- haps, they should be called terraces. 17. Let us now take a bird’s-eye view of the continent, raised high enough to bring nearly all the surface above the waters, which is now above the level of the highest terraces. We see the valleys occupied as arms of the sea, in the forms of friths, estuaries, and bays, and in some places, bodies of water exist, cut off entirely from the ocean. Some of the estuaries, too, are so narrowed in particular places, by the approach of barriers on opposite sides of the estuary, as to form, as it were, a chain of lakes, connected by straits. Such would be the aspect at the time supposed of the Connecticut valley. Along the shores, we see on a diminished scale, those rivers which are now its tributaries, emptying into the lake-lke estuary, and thus producing a current towards the ocean. Their waters, acting on the drift over which they run, would comminute and carry into the estuary the smaller particles, and thus form shoals, or banks, along their mouths. Meanwhile the ocean is sinking, and at length these banks will come to the surface, and con- stitute small deltas to the rivers. The streams, too, will wear down their beds, as the estuary sinks, and hence they must cut passages through their deltas, and urge forward a new mass of sorted materials into the now diminished estuary. Thus another delta may be formed, and even a third, or fourth, in the same manner; and even though the vertical movement be perfectly uniform, the current towards the ocean, produced by the tributaries, will so act upon the outer margin of the embankments, as to form terraces, rather than a simple talus. In this manner, it seems to me, may the delta terraces have been formed by the slow drainage of the country, and without supposing pauses in the vertical move- ment. These are in fact, among the most usual and striking of the terraces. Though formed in essentially the same manner as the beaches above described, they would be more regular on their tops, because not exposed as the beaches were, during their emergence, to the action of the breakers. Mr. Charles Darwin, I believe, first suggested the mode in which delta terraces were formed, as described above, in his paper on the Parallel Roads of Glen Roy. Mr. Robert Chambers, however, has pointed out a case in Switzerland, which fully confirms these views. In the canton of Unterwalden, the lake of Lungern has been artificially lowered within the last sixty years. Where the head of the lake FORMATION OF THRRACES. 57 formerly was, and into which a number of small streams formerly emptied, several deltas are laid bare by the draining cff of the water, and they are cut through by the streams, which have worn deep chasms through the loose materials, and are still wearing them backwards towards the Alps. 18. We will now inquire, how, in like circumstances, lateral terraces may have been formed. As the comminuted and sorted materials are projected into the main valley, now an estuary, which, as it sinks, is putting on the characters of a river, they will be swept towards the ocean by the current, a greater or less dis- tance, according to the velocity of the stream. Thus will the delta terraces of the tributary, become in part lateral terraces to the principal valley. 19. There is another mode in which lateral terraces may be formed, as suggested by Robert Chambers, in his paper on the Valleys of the Rhine and the Rhone. In the successive basins that form the chain of lakes produced by the drainage of a country, the detritus brought into the basins by their affluents, will more or less be spread over their entire bottoms, although, as above suggested, banks may be formed, also, along the shores. The materials there spread over the bottom, may accumulate to a great depth, if the straits connecting the several expansions of water are narrow, and the water not so deep as in the basins.. At length, however, as the drainage goes on, the bed of the basins will be brought to the sur- face, and the waters, narrowed into a river, will cut a passage through the detritus, leaving probably on each shore a terrace of the same height. The current, how- ever, might crowd so closely upon one side of the valley as to sweep away all the detritus there, and leave a terrace on one side only. 20. There is a third mode in which lateral terraces might be, and doubtless have been formed. In the case last supposed, the river is represented as simply cutting a chasm through its sandy, clayey, or gravelly bottom. But powerful freshets occur not unfrequently on all rivers: and in their swollen condition, and with increased velocity, they act powerfully upon their banks, especially if of alluvial materials. And if the course of the stream be tortuous, as is always the case, one bank will be acted upon more powerfully than the other. This action will produce a meadow on one side of the stream, but little raised, it may be, above the river in its ordinary state. Successive inundations will eat away the bank more and more, and thus widen the alluvial flat. The stream will thus be spread out over a wide surface during its floods, and of course its velocity will be lessened. This will cause a deposition of suspended matter to take place, whereby the meadows will increase in height. Meanwhile the stream will continue to wear its channel deeper, the supposition being that the drainage is still going on. At length the channel will become so deep, and the meadows so high, that even in freshets the waters will not spread over the meadows. They have now become a permanent terrace, bounded by the river on one side, and by a steep escarpment on the other, that leads to the higher terrace. As the river no longer rises over the meadows in time of floods, the process already described is repeated, and a third terrace is the result; and so a fourth, a fifth, &., may be formed, if the river sink deep enough and time be given, 21. A modification of the above process may in some cases be witnessed. The 8 58 SURPFACE GHOLOGY. stream sometimes wears away one of its banks to such a depth, that the channel eradually changes towards that side, while the back water produced on the other side causes a deposit, which is increased by freshets, and although its upper surface becomes nearly level, it yet forms a terrace which properly deserves the name of a elacis terrace. After this process of lateral change has gone on for some years, it not unfrequently happens that the river suddenly deserts its old bed, in consequence of having found a new channel. Successive floods fill up the deserted bed, some- times so as to make a level-topped terrace: but in other cases, it is only partially filled, and exhibits, at least for centuries, evidence of the former presence of the stream. Such are the old river beds in Deerfield meadows, shown on Plate IV. In the short one directly west of the village, the whole process has been gone through since my boyish days, and I have watched its progress with interest from year to year. 22. It is I apprehend, by modifications of this process, that that variety of elacis terrace exhibited on section No. 31 was produced. Sometimes they may also have resulted from the accumulation of sand and loam on one shore, by the lateral influence of a strong current. I am not prepared to say exactly how that variety of glacis terrace, found in the Alps and other mountainous districts, con- sisting of rather rapid slopes of the whole alluvial formation of a valley towards the stream, was produced. It may, however, have resulted from the sliding down of detrital matter towards the stream from the steep adjoining hill-sides, during the semi-fluid condition of the surface in the spring, or after powerful rains. 23. On the supposition above made, that during the drainage of a valley like the Connecticut, it assumed the condition of a chain of small lakes, we can see how it is, that around the gorges or straits between them, the terraces should be higher than in the wider parts of the valleys. For the contraction of the stream at the gorges, would check the current there, and thus cause more of the sus- pended matter to be deposited. Very probably it might so fill up the gorges, that, as the continent rose, it would require a great length of time to wear them down to their present depth. 24, We see then that the various forms of river terraces, whether called delta, lateral, gorge, or glacis terraces, may be formed by the simple drainage of the country, as the surface emerges from the ocean. Nor need we, as has generally been thought necessary, suppose that there were pauses in the vertical movement. That such pauses may have occurred I admit, and that in this way some terraces and beaches may have been produced; but to form the river terraces we need not call in their aid. 25. I now proceed a step further, and will state certain facts, which prove that river terraces in general could not have been produced by pauses in the vertical movement of the land. 1. If thus produced, they ought to be the same in number and height in the different basins of the same river, and on different rivers not very remote from one another. For, even though we might admit some small difference in their height if thus produced, their number must correspond, since the water would sink equally in the different basins. Buta reference to the sections attached to this SUPPOSED PAUSES IN THE UPLIFTS. 59 paper, and to the tabular heights of the terraces, will show that the facts are widely diverse from this supposition. Along the Connecticut, indeed, the most usual number is three or four: but on some of its tributaries they rise as high as eight or ten. Which number, in such a case, shall we assume as indicating the pauses in the vertical movement? If the smallest, then how are we to explain the excess? If the larger number, then why did not the waters leave traces of their influence alike numerous wherever they acted an equal length of time. 2. On this supposition, the terraces ought to agree essentially, at least in height, on opposite sides of a valley. Circumstances might, indeed, erase all traces of their action in particular spots, but such great irregularity as exists in this respect, cannot be thus explained. ‘Terraces thus formed would leave evidence of their existence, as the Parallel Roads of Lochaber have done, on the steep flanks of the Scottish Highlands; which I am willing to admit were produced by succes- sive uplifts of the land, or subsidence of the waters. 3. The difference in the number and height of the terraces upon the principal stream and its tributaries at their debouchure, affords decisive proof that said ter- races were not the result of the paroxysmal elevation of the land. Here we find two sets of terraces formed in the same bank of detritus; one set, usually the smallest in number, on the main river, and the other set, formed by the erosion of the tributary through the first. Of these, the maps and sections appended, afford numerous examples. Thus, at the mouth of the Ashuelot river, in Hinsdale (No. 25), we have five terraces on that river, and three, or perhaps four, on the Con- necticut. Just below Bellows falls, we find at the mouth of Saxon’s river (No. 30), as many as six terraces, while on the Connecticut, a little to the south, in Westminster (No. 29), are only four. In the north part of Vernon (No. 26), are only four on the Connecticut: but on West river, in Brattleborough, perhaps two miles north, we find nine, and on Whetstone brook, ten (No. 28 and Plate III). Moreover, the latter rise no higher than, if as high, as the former. And since both sets are found in the same bank of sand and gravel, it is certain, that if one set were produced by pauses in the retiring waters, the other set could not be: since no possible reason can be assigned, why in the same bank of materials the terraces on one stream should be twice as numerous as those on the other, if pro- duced by pauses in the retiring waters. 26. These facts, especially the last named, afford almost equally strong evidence that river terraces could not have been produced by the sudden bursting of bar- riers. In the valley of the Connecticut, if such barriers existed, they must have consisted of sand and gravel, choking up the gorges, and not of solid rock, since the traces of drift agency occur so low down at those gorges. That detrital barriers may have existed to some extent, perhaps with the addition of ice, I will admit. But that they had little to do with the formation of terraces, is clear from the above facts; since if suddenly lowered they could not have produced a different number of terraces on the principal stream from those on the tributaries, nor such irregu- larity as we find in their height and number upon opposite sides of the river, although they might have formed more in one basin than in another. 27. In a former paragraph (11) I have given an intimation of the views which 60 SURFACE GEOLOGY. I have been finally led to adopt, as to the formation of moraine terraces. I regard them as mainly deposits by water, urged in currents through the sinuosities of stranded icebergs. The subsequent melting of the ice, as the surface was drained, would leave it with those convolutions and anfractuosities, so like those upon the human brain. That powerful currents occur among stranded icebergs, we have the testimony of Sir James Ross, who “ mentions that the streams of tide were so strong amid grounded icebergs at the south Shetlands, that eddies were produced behind them; so that as far as such streams were concerned, they acted as rocks. Navigators have observed icebergs sufficiently long aground in some situations, that even mineral matter might be accumulated at their bases in favorable situa- tions, while tide currents may run so strongly between others, that channels might be cut by them in bottoms sufficiently yielding, and at depths where the friction of these streams would be experienced. Much modification of sea bottoms might thus be produced by grounded icebergs, &c.” (De la Beche’s Geological Observer, p. 254.) Such masses of ice are liable, at some seasons of the year, to be crowded forward by other ice, so as to plough furrows in the loose materials, and grind down and striate the rocks in place. Sir Charles Lyell quotes an interesting case, in which mounds analogous to moraine terraces were produced “by the pressure of ice.” From the account given by Messrs. Dease and Simpson, of their recent Arctic discoveries, we learn, that in lat. 71° N. long. 156° W., they found “a long low spit, named Point Barrow, composed of gravel and coarse sand, in some parts more than a quarter of a mile broad, which the pressure of the ice had forced up into numerous mounds, that viewed from a distance assumed the appearance of large boulder rocks.” (Lyell’s Principles of Geology, p. 230.) Such statements, especially the last one, give great plausibility to the theory which I have adopted. It is still further strengthened by the fact, that these moraine terraces occur in spots, which must have been the shores of the ocean, or of estuaries, or of lakes, as the waters were retiring; and, therefore, just the spots where icebergs might be expected to get stranded. They are found, also, as a part of the earlier terraces, not long posterior to the drift, while as yet we may presume the temperature was low enough to allow of the long continued presence of ice along the shores. But though the preceding views may explain the rounded hillocks and inter- vening depressions of the moraine terraces, something more-seems necessary to account for those remarkable ridges of sand and gravel, usually more or less ser- pentine, that accompany the mounds in some instances, as at Andover. Now in high latitudes the shores are found sometimes to be composed of layers of sand, gravel, and ice, more or less interstratified; that is, the waters throw up gravel and sand upon and among the ice along the shores. As the ice melts away, we might expect ridges of sand and gravel to remain, being crooked or straight as the shores were. It seems to me that this may have been the origin of such ridges of this kind, as have fallen under my observation, the most striking of which are in Andover, Mass. I have seldom been so much perplexed to find a name for any natural object as Se a a LAKE TERRACES. 61 for these moraine terraces. Without some new term they cannot be referred to, without much circumlocution. In my Reports on the Geology of Massachusetts, and in a paper on the subject, in the first volume of the Transactions of the Ame- rican Association of Geologists and Naturalists, I called them, in the first work, Diluvial Elevations and Depressions; and in the other, Iceberg Moraines, but these terms are quite unsatisfactory; and after having ascertained that these objects are connected with, and frequently form a part of, one of the higher terraces, I have named them, merely on the ground of some external resemblances, Moraine Ter- races, which I shall use only until I can find a better term. I have not gone into minute details respecting these curious forms of modified drift, because they are given in the works above referred to, and in my Elementary Geology. By recurring to those details, the reasons will be obvious why we can- not explain the phenomena by water alone, nor by ice alone. Their conjoint agency, it seems to me, may do it. I ought to add, perhaps, that I have sometimes seen appearances in the bottom of an old river bed, somewhat analogous to the moraine terraces. As such a bed was being filled, when beneath the waters, with sand and gravel, spots were left here and there, several feet deep, which were not filled for want of materials, or from the direction of the currents. But I cannot believe that depressions so deep and numerous, and separated by ridges so narrow and steep, as. some of the moraine terraces exhibit, could be the result of mere currents of water. 28. As to lake terraces I can say but little with much confidence. I cannot doubt, however, that those around most of the small and narrow lakes, such as those of New York and of Switzerland, fall into the same category as the river terraces, while yet the water was high enough to form chains of small lakes. For the drainage of the modern lakes appears to have been going on in the same man- ner as the estuaries, that become ultimately converted into rivers. Such seemed to me to be the case with Lake Zurich and Leman; and such, I am told, is the fact in respect to the smaller lakes of New York, so that they do not seem to require us to call in any new principle besides those already applied to river terraces. As to the larger lakes, I have had no opportunity to examine any of them, save the one called the Ridge Road, of Ontario, which has more the appearance of a beach, or rather a submarine ridge, than a terrace. Professor Agassiz describes those around Lake Superior, as varying very much in number in different places, “six, and rising from the height of a few feet, to several hundred. He says, that ten, even fifteen such terraces may be distinguished on one spot, forming, as it were, the steps of a gigantic amphitheatre.” He distinguishes between these lake terraces and the delta terraces, at the mouths of rivers, which he also describes: and he states also, that the lake terraces “present everywhere undoubted evidence, that they were formed by the waters of the lake itself’ He supposes that the shores of the lake have experienced vertical movements; first a depression and then a rise, and that “these various terraces mark the successive paroxysms or periods of re-elevation” (p. 104, Lake Superior, &c.). He supposes the terraces to have been formed, and of course the last elevation of the land to have taken place, subsequent to the drift period: for he remarks, “It is clear that the formation 62 SURFACE GHOLOGY. a of the terraces was subsequent. They overlie the grooved and rounded rocks” (p. 103). Yet, if I understand Prof. Agassiz, he ascribes these vertical movements to the injections of trap veins, so common along the shores. “ ‘This process of inter- section, these successive injections of different materials (in the veins), have evi- dently modified at various epochs, the relative level of the lake and land, and probably also occasioned the modification which we notice in the deposition of the shore drift, and the successive amphitheatric terraces, which border, at various heights, its shores” (p. 424). Now, with so little personal knowledge of lake terraces, it may be presumption in me to call in question any of these conclusions. But a few suggestions may not be improper. i Were Lake Superior, itself an ocean, alone concerned, we might have less diffi- culty in admitting these views, and in supposing that its terraces mark the pauses in the uplifts of its shores. But I apprehend that scarcely a lake exists in our country that does not show distinct terraces, nay even ponds, covering only a few nundred acres, exhibit them distinctly. I know of some such in New England. Now surely we cannot suppose that the shores of each of these smaller lakes and ponds have undergone any such elevation since the drift period: I mean to say that they have been elevated only as a part of the continent, and not by a local move- ment, as must have been the case if the shores are raised above the waters. So that if we could dispose of the Lake Superior terraces in this manner, those of other lakes would still remain unaccounted for. Moreover, as to the cause assigned for this rise of the shores, viz., trap dykes, I do not see how these could have been concerned in the last movement which produced the terraces. For the surface of these dykes is smoothed and striated by the drift agency, which shows them to have been injected long before the drift period, whereas the terraces have all been formed since. I agree with Professor Agassiz in the opinion, that subsequent to the drift period, our continent has been beneath the ocean, and has subsequently risen. But it seems to me that it came up bodily, or as a whole; at any rate, I have not met with any evidence of local elevations. Supposing it was the ocean that spread over all our continent; as that was gradually raised, the waters might have left evidence of their recession, and of their successive pauses (if any prefer that view), in the form of terraces around all our lakes. I think that a rise of the land, unattended by paroxysms and pauses, may more easily show us why the number and height of terraces differ so much on different bodies of water, and that the unequal number which we find on the same lake, or river, may thus be more satis- factorily explained. Tor if there were such pauses to any great extent, I do not see why the number and height of the principal terraces should not correspond everywhere, even though we leave out of the account the irregularities of the minor terraces. Yet I admit the occurrence, occasionally, of such pauses. I could not, for instance, look on the Parallel Roads of Lochaber, in Scotland, with- out feeling that probably they mark paroxysmal movements of the waters. But it cannot be denied that men, even geologists, are too prone to resort to paroxysms and irregular action to explain phenomena; and I look upon the labors of Sir ANTIQUITY OF THE TERRACKHS. 63 Charles Lyell as of great value in this respect; although I might suppose that his views of uniformity are sometimes carried too far. The rule which I theoretically adopt, is, to admit paroxysms wherever there is evidence of their action, but not introduce them for the sake of eking out an hypothesis. For we ought ever to remember, that in nature, uniformity is the law, and paroxysm the exception. I will only add, that if it be admitted that the facts adduced in this paper prove the presence, since the drift period, of the ocean at the height of 2000, or even 1200 feet, above its present level, then it must have extended over nearly all of our western country; and unless Professor Agassiz says that he had his eye upon this matter along the shores of Superior, I cannot avoid entertaining the expecta- tion, that what I call beaches will yet be found at a much higher level there, than the 331 feet terrace, measured by Mr. Logan. 29. The period when the formation of beaches and terraces commenced was immensely remote. The proof of this position will more appropriately be given in my paper on Hrosions. I trust there to prove, that the whole of the gulf between Niagara falls and lake Ontario has been worn out by the river since the drift period: as well as the gorge between Portage and Mount Morris, on Genesee river, and several analogous gulfs in other parts of the country. I expect also to show, that some of the old river beds, pointed out in this paper, were beds through which rivers ran before the continent went down beneath the ocean the last time. Such facts, if admitted, give an antiquity to the drift period little imagined heretofore ; and may excite astonishment that the drift strize should be so fresh and distinct 30. The facts and reasonings that have been presented, exhibit to us one simple, grand, and uninterrupted series of operations, by which all the changes in the superficial deposits since the drift, have been produced. We see the continent slowly emerging from the ocean; rivers commencing their wearing action on the islands; waves and oceanic currents meeting the detritus of rivers and comminut- ing, sorting, and arranging the same, in the shape of beaches and terraces, while it may be that icebergs and glaciers modified the whole. It may be, too, that paroxysmal movements occasionally accelerated, retarded, or modified, the effects. The period over which the uninterrupted operation of these agencies can be traced, may be regarded as the alluvial, and we can refer them back at least to the tertiary epoch. 31. It is obvious, however, that it is only the present form and admixture of the loose materials on the earth’s surface, that can be referred to the post-tertiary period. We infer that their present arrangement is post-tertiary because they lie in some places above the tertiary. In others, however, they lie upon older rocks—some- times upon the oldest known. And in such case, though the presumption is strong that their present disposition and mixture are not older than the tertiary, yet the time of the abrasion, comminution, and rounding of the fragments, may have been vastly earlier—as early, indeed, as the consolidation of the rocks on which they now repose. They may have formed other terraces and beaches on other conti- nents; and it is quite possible that in some cases those old terraces and beaches may still remain, not having been remodelled by the last vertical movement of the continents. In an important sense, therefore, the alluvial period may have been 64 SURFACE GHOLOGY. contemporaneous with all other periods; or rather, each period had its alluvium, and sometimes the same alluvium may have belonged to successive periods. These ‘ facts give a peculiarity to the alluvial formation possessed by no other. 32. It appears that the time since man came upon the globe, has been only a small part of the alluvial period. For we find none of his remains, nor works, except in the superficial portions of the terraces. The lowest of these, save alluvial meadows, are often the seat of his most ancient works—his habitations and forts. The remotest epochs of history rarely, if ever, reach back to the time when the most recent terrace, save overflowed meadows, was formed. Even if it be admitted, which yet requires proof, that his remains are found with those of extinct animals, this by no means throws back his origin, as has been supposed, to what is usually understood by the drift period, for many races of animals have disappeared since alluvial agencies have been at work. 33. A large proportion of those superficial deposits in high latitudes, that have been usually included in drift, appear from the views that have been presented, to have been the work of agencies greatly posterior; analogous probably to those that produced the lowest and coarsest drift, but still greatly modified. These agencies have taken the drift and worked it over, and though the same kind of drift as the oldest is still produced in some parts of the globe, yet it is undesirable to confound modified with unmodified drift, since it embarrasses our reasonings as to the origin of that coarse deposit which usually lies beneath all others that are un- consolidated, and which all geologists agree in regarding as drift. The super- imposed beds of gravel, sand and clay, demand only water to explain their origin; whereas all geologists at this day would agree that the coarse drift must have been the result, in part at least, of glacial action. Besides to blend drift proper and modified drift is almost as much of an anachronism as to regard the conglomerates of the triassic or carboniferous period, as contemporaneous with the fragments of which they are composed. 34. But after all, the idea so long and generally maintained, that the drift agency operated for a certain length of time after the tertiary epoch, and then ceased, and was succeeded by alluvial action, which did not operate during the drift period, I find myself compelled to abandon. For I find evidence that both these agencies have been in parallel operation from the close of the tertiary epoch, to say nothing of earlier periods. They have varied only in the amount of their action. During the earlier part of the period, drift agency largely predominated, as the alluvial agency has since done. Hence the attempt to fix upon a certain definite time when drift agency ceased and alluvial agency commenced, has so signally failed, and scarcely no two geologists have drawn the line in the same place. But I shall recur to this point again after laying down a few more posi- tions. 35. It appears that the organic remains which have been referred to the drift, do, in fact, belong to modified drift, and generally to a very late stage of the allu- vial period. The marine remains are the oldest, such as are found on the shores of Lake Champlain, and on the banks of the St. Lawrence, at Montreal; on Long Island, at Brooklyn; at Portsmouth, New Hampshire, and at Portland and other ANCIENT GLACIERS. 65 places in Maine, only some four or five hundred feet above the present ocean; and they occur in clay or gravel that has been thoroughly rounded. These remains (along our coast) belong altogether, I believe, to existing species, and the molluscs even yet retain the epidermis. They must, therefore, have been deposited at a period vastly posterior to the drift. The Delphinus Vermontanus, described by Professor Thompson, from the clays near Lake Champlain, was found only one hundred and fifty feet above the present sea level, and hence we should not think it strange that he found it difficult to distinguish it from an existing species. Still more recent are the remains of extinct land animals, which have often ina general way been referred to the drift. I mean the mastodon, elephant, horse, &c., for they occur most usually in peat and marl swamps, and these may have been quite recent. Such is the case at Newburg and Geneseo, New York, and at the summit-level of the Burlington and Rutland railroad in Mt. Holly, Vermont. In Wales, marine shells were found nearly 1400 feet above the sea, in what, though called drift, was most probably modified drift, which I saw at even a greater elevation in that country. 36. So far as this continent is concerned, I think we may as yet safely say, that there is no evidence of the existence of life in the seas that covered it during the period of unmodified drift; and, indeed, we might say the same of a considerable part of modified drift and alluvium. I mean that the lowest drift and most of the terraces have not furnished any example of fossil animal or plant. And when we find such proof of glacial agency, especially in the oceans, during those periods, we do not wonder that life was mostly absent. Sir Charles Lyell has also assigned some other reasons for this paucity of organic remains, in the pleistocene deposits, which are probable. (Manual of El. Geol., p. 136.) 37. With such views of the climate in regions now temperate, we should expect, that as mountains emerged from the ocean, glaciers would be formed upon their crests and slopes. Those descending towards the ocean, would produce strize upon the rocks, radiating from the highest points, or directed outwardly from the axes of ridges, and more or less obliterating the traces of the drift agency, where, as in our country, the striz that have resulted from it, run nearly in a north and south direction over the whole continent. As far down the mountains as the glaciers extended, they would obliterate, also, the beaches and terraces that may have been formed by the retiring waters. In Wales, as I have already stated, the marks of ancient glaciers seem to me most manifest, and they have erased most of the marks of the former presence of the ocean, though they do not prove that the country was not all once beneath the ocean, but only that the glaciers have since occupied its higher parts and so changed the surface that the proofs of oceanic agency are less obvious. And, moreover, the ragged aspect of the highest peaks, makes it probable that they never were rounded, as nearly all the mountains in our country are, by drift agency. In Switzerland, I think we can easily find proofs of the action of water from 2000 to 3000 feet high: but all the regions more elevated, show marks of ancient 9 : 66 SURFACE GEOLOGY. or of existing glaciers. And here, also, the lofty summits have not been truncated by glaciers or drift agency. In America the evidence of ancient glaciers is less striking. I think, how- ever, that I have discovered them upon some of our mountains, and the subject is of such importance, that I have devoted a separate paper accompanying this, to the details of my observations relative to them. 38. Countries corresponding in their modified drift, or rather their beaches and _ terraces, may be regarded as having occupied about the same length of time in their last emergence from the ocean, and consequently are of nearly the same sub- aerial age. Perhaps I ought to add, that this principle would require that there should be a general correspondence, also, in the outlines of the surface, and the nature of the rocks, as well as in the rapidity with which the waters withdrew. For, since in my view the terraces and beaches were produced by the drainage of the country, the length of time occupied would depend very much upon the contour of the surface, and the character of the rocks. All these circumstances being the same, I do not see why the time occupied by the drainage should not be the same. In the northern parts of the United States, in Scotland, and Scandinavia, so far as my observation in the two first countries, and information concerning the third, extend, all the above circumstances are essentially alike, and hence I should regard their postdiluvial ages as nearly equal. The facts mentioned elsewhere as to the terraces of the river Jordan, would lead to the conclusion that Palestine and Syria, regarded by so many writers as having experienced great vertical move- ments, have remained essentially unchanged nearly as long as New England; and the facts respecting the Arabah and its Wadys, south of the Dead Sea, confirm this opinion. This point I have discussed more fully in the first volume of the Transactions of the American Association of Geologists and Naturalists. 39. It is a well known question of great interest, whether the drainage of con- tinents, since the drift period, has been effected by the elevation of the land, or the depression of the oceans. The able expositions of the latter hypothesis, by Professor James D. Dana, in the American Journal of Science, incline me to adopt it, at least partially, some of the facts, concerning beaches and terraces, affording a presumption in its favor. It is not very easy to conceive how a broad conti- nent can be lifted up, and permanently sustained, to the average height of nearly a thousand feet. Still more difficult is it to imagine how this can be done so as not to rupture or disturb the superficial deposits upon it. We should expect that in some places the elevation would be much greater than in others, and conse- quently the lines of level of the beaches and terraces would be changed, and the materials in some places be disturbed, as they are in regions subject to earth- quakes. But I have never met with a single example of such disturbance. And the only case I know of, is the one described by Mr. Chambers, in Finmark, where a seesaw movement, of more than two feet in a mile, has been traced over an extent of 40 miles. Such cases may be discovered in our country; but, so far as I can judge, the change of level has been effected here in the most quiet manner, and the surface has risen in every part alike, and its whole contour remains as when DRIFT AGENCIES. 67 the waters left it. Such a fact corresponds better with the idea of a retiring ocean than of arising continent. And upon the whole, though I cannot doubt that lateral pressure and internal volcanic force have produced limited vertical movements; I am more and more inclined to believe that the waters have in a great measure withdrawn in the manner suggested by Prevost and Dana. 40. The phenomena of drift, in distinction from terraces and beaches, although an important part of surface geology, I have not dwelt upon in this paper, because they are now generally known, and, so far as North America is concerned, I have _ published them elsewhere. But some suggestions upon the theory of drift seem important in this place, in order to bring out my views fully upon surface geology. I have endeavored to show that a large proportion of what has been usually regarded as drift, has been the result of subsequent alluvial agencies. There still, however, remains an irregular coarse deposit’ beneath the modified beaches and terraces, whose origin is a matter of great interest. The subject is narrowed, but not disposed of. There yet remain the great boulders, mixed with rounded frag- ments and sand and clay, as well as the striated and embossed surfaces, to be explained. And in respect to the agency by which the phenomena have been produced, the following positions, which are most of them essentially those taken by Professor Naumann, appear to me most unquestionably true :— 1. The eroding materials must have been comminuted stone. 2. They must have been borne along under heavy pressure. 3. The moving force must have operated slowly and with prodigious energy. 4, It must have been nearly uniform in direction, yet capable of conforming somewhat to an uneven surface, and of some divergence when meeting with obstacles. 5. The vehicle of the eroding materials cannot have been water alone. 6. It must have been a firm and heavy mass, yet somewhat plastic. 7. The grinding and crushing mass must have been impelled by such a vis a tergo, as would urge it over hills of considerable height. 8. A part of the phenomena can be explained only by the presence and agency of water in some places, at least to sort out, arrange, and deposit layers of sand, clay, and gravel, which are sometimes found beneath the large boulders that are scattered over the surface, or sometimes mixed with the finer stratified deposits. Were this the proper place, I would quote a multitude of facts to sustain these positions. But since to do this would be less original than the other parts of this paper, I will refer only to a single observation, made by me in the White Moun- tains, in 1851, and which I have described in the 14th volume, 2d Series, of the American Journal of Science, p. 73, to illustrate the fifth of the above positions. On the southwest side of La Fayette Mountain, near the Franconia Notch, I fol- lowed the track of a recent summer slide, which had never been explored. The perils which I encountered in this attempt, greater than I have ever met in a mountain excursion, are detailed in the Journal of Science, but will here be omitted, and I shall give only a part of the facts. I found a path several rods wide ploughed out by an immense mass of coarse 68 SURFACE GEOLOGY. drift, some of the boulders being from 10 to 20 feet in diameter. They still lie along the borders of the gulf in ridges that correspond exactly to the lateral moraines of Alpine glaciers, and at the end of the slide we have a terminal moraine. The rock in place is laid bare most of the way, and although consider- ably smoothed, it is not striated to any extent. I cannot conceive of a fairer opportunity to test this matter than on this spot. The size and quantity of the moving mass of detritus, and the rapidity with which it must have descended on a slope of 10° to 38°, were all favorable to the production of an exact counterpart of drift action, if water only was the transporting agent. But it failed just where we should expect it to fail, viz.: in the formation of strie and furrows. Where now, save in glaciers, icebergs, and ice-islands, can we find agencies that meet the conditions of the above principles respecting drift? Glaciers, as every one knows, who has observed their effects in the Alps, do produce phenomena corre- sponding to those of drift in northern regions, in almost every respect. Nor can we doubt that icebergs and ice-floes, large enough to grate along the bottom of the sea, would do the same, although the proof is more difficult to obtain, because the scene of the operation is beneath the ocean. But such icebergs and floes as I sup- pose, would, it seems to me, operate almost precisely like glaciers. For I assume that they are so large and thick that they reach and press heavily upon the bot- tom: such icebergs and icefloes in fact, as northern voyagers have described, whose surface was so large that they travelled for days upon them, or their vessel was frozen into them, without their suspecting that they were in motion, till an observation for latitude and longitude showed them that they were upon a drifting mass. Let such masses be put into motion by currents and winds, ever so slowly, and how powerfully would they scour the rocky bottom, wherever they reached it, especially if their under side were armed with fragments of stone. To which phase of this glacial agency, then, shall we refer the phenomena of drift? Before attempting to answer this question, I shall make a few remarks upon another point, viz.: whether in such a country as the United States and Canada, we can fix upon the geological period when the drift agency operated ? Was it previous to the last submergence of the surface, or during its subsidence, or while it was emerging ? i There is one fact that leads to the conclusion that the greater part of this work was done before the continent had emerged very considerably from the waters. In my paper on Erosions, I point out several instances in which the beds of rivers, that existed before the submergence of the continent, apparently became so filled with detritus, while beneath the ocean, that the postdiluvian rivers were forced to leave these old channels and wear out new beds, sometimes through solid rocks. True, this detritus is often made up of materials much comminuted, and formed into terraces, and, therefore, may not have accumulated till the continent had been lifted considerably from the ocean. But since these old beds of rivers often show drift scratches beneath the detritus, they must have been made previous to its accumulation, and, therefore, before the drainage had proceeded very far. On the other hand, there is a fact that leads the mind to the conclusion that the PERIOD OF THE DRIFT. 69 work of erosion went on for some time after the continent began to emerge. A careful examination of the rounded and striated rocks at different altitudes, will satisfy any one that in the valleys the work is considerably more fresh and less affected by decomposing agencies than on high mountains. The erosions are also deeper in the valleys. Sometimes, as on Holyoke, in Massachusetts, a succession of valleys crossing a mountain ridge, have been excavated, to a considerable depth; but I never saw any such drift valleys on the tops of high mountains. All this looks as if the work at high altitudes was completed first, and continued in the valleys after the emergence of the mountains. Yet, in this country, such anachronism could not have been long continued, for in that case, the emergence of the high mountains would have changed the direction of the abrading force into the valleys, from a north and south direction, and this appears to have been the case only to a limited extent. While only the higher parts of the mountains were above the waters, as islands, they would not very much affect the direction of the force, if it consisted of large icebergs. Some may imagine that rocks much elevated are more liable to surface disinte- gration than when in valleys. This may sometimes be true, but I doubt whether, with most rocks the reverse is not the fact. The best example of freshness in rocks rounded and striated at high levels, that I have met with, may be seen on the top of Monadnoc, in New Hampshire, 3000 feet above tide water. Yet appa- rently it is not as recent there as in the bottoms of some of the valleys. Upon the whole, I think that we must throw back the drift period with the exception above named, at least as far as the time when this and other countries were sinking beneath the ocean. But did the work take place during that sub- sidence, or previous to it? My own conviction is, that we have evidence that the work extended into both those periods. If before the time of subsidence, it was accomplished by glaciers on a former continent. If we find evidence, as I think we do, in Wales, in Scotland, in some parts of Switzerland, and in New England, that glaciers existed before the last submergence, the detritus accumu- lated by them, although modified somewhat by oceanic action, ought to be regarded as a part of the drift deposit. We know, also, that since the emergence of the land, glaciers, in some countries, have been producing genuine drift. It is well known that eminent men have referred the whole of the drift to glaciers, and they seem to me to have proved uncontrovertibly, that the smoothing, rounding, and striating of the rocks in northern regions, have been the result of large heavy bodies of ice, foreed along the surface by a vis a tergo. Now did the glacier theory apply to other countries as well as to Switzerland, so far as my slight examination of that country enables me to judge, I could not well resist its adoption. But in Great Britain, and especially in this country, there are peculi- arities in the drift phenomena, that lead me to hesitate, and inquire whether they are not better explained by the passage over the surface of large icebergs and ice- floes, whose effects scarcely differ from those of glaciers. Some of the reasons for such an opinion are the following :— 1. The occurrence of striz upon the northern slopes of mountains, even to a 70 SURFACE GEOLOGY. considerable height, is better explained by icebergs than by glaciers. In some in- stances the grinding body must have been forced upward, above the general sur- face, which is also striated hundreds if not thousands of feet, as on Mt. Monadnoc and the White Mountains. Now a glacier, descending as a whole in every known instance, is able to force portions of its mass over obstacles a few feet only in height. But here we must suppose one not on a slope, but moving over a level surface for hundreds of miles, to be able to crowd large portions of its mass hundreds of feet over opposing mountains. If we could suppose a huge iceberg, suspended in an ocean rising above the mountains, to impinge against its top, with an immense momentum, it might force a portion of its mass over the top; especially if at the same time the mountain were sinking; though perhaps this descent would be too slow to meet the case. 2. Iceberg action explains better than that of glaciers, that sorting of materials and of laminations, which we sometimes find in the drift. I know it is customary to speak of drift, (I mean the lowest and coarsest variety,) as a mass mingled in perfect confusion. But I have rarely seen a section in it, of very considerable extent, in which I could not discover some marks of the action of water in the parallel arrangement and separation of the materials into finer and coarser. I have often been struck with this evidence of a tumultuous and quiet action in close juxtaposition; and we know that not unfrequently the aqueous action appears to have predominated. But if huge icebergs tore off and accumulated the detritus, we might expect that the currents which bore them onward would, to some extent, separate and arrange the materials, especially where masses of ice were stranded; and that sometimes the icebergs would be absent altogether. Glaciers, however, have no such power, save that the stream which usually issues from them, will cause some alluvial accumulations in the valley below the terminal moraines, but not in the midst of the moraines. 3. The facts concerning the dispersion of boulders can be more satisfactorily explained by icebergs than by glaciers. It appears that the work of scattering these boulders continued till after the time when a large part of the beaches and terraces were formed, for they are scattered over the surface of these sandy deposits. (See Mr. Desor’s account of the Drift of the Lake Superior land District, in Moster and Whitney's Report, p. 190.) Now glaciers could not have done this; for they would have ploughed a track through the stratified deposits of sand and clay beneath, if they had transported these boulders; and so would such icebergs as I have supposed might have produced the drift below the terraces and beaches. But such icebergs as now traverse the Atlantic might have carried boulders over the beaches and terraces and dropped them from time to time, as we now find them scattered over the western prairies. By the same agency, also, we can explain the intermixture of coarse angular blocks in any of the beach and terrace deposits. 4, The supposition that a glacier once existed on this continent, wide enough to reach from Newfoundland to the Rocky Mountains, is the grand difficulty in the way of the glacier theory. All known glaciers occur in valleys, not many miles GLACIER THEORY. ial wide, and so did the supposed ancient glaciers, of which traces now exist. But the North American glacier must have extended uninterruptedly almost over hill and valley, for at least 2,000 miles; nor even with that width could it have found higher ground on its borders, unless it were the Rocky Mountains on the west, con- cerning whose drift phenomena we know but little. Again, all known glaciers are situated upon slopes, greater or less. Indeed, how could they advance, if not upon slopes? For though expansion by freezing mieht have some influence in urging them forward, as maintained by authors, yet the facts and reasonings of Prof. Forbes seem to show very conclusively, that gravity is the principal cause of their onward march. At any rate, I know of no example where a glacier does advance upon a level surface—certainly where hills oppose its progress. It is surely, then, a great demand upon our faith, to ask us to believe that the broad North American glacier has crowded southerly 500 or 600 miles, over a highly uneven but not sloping surface, and that simply by expansion. Even should it be proved that we have centres of dispersion in the White Mountains, or the mountains of northern New York, we must still admit a great movement from the north sweeping the whole country, save a few peaks. Nor does it relieve the difficulty to suppose an enormous thickness of the sheet of ice in the arctic regions, from which the great glacier proceeded ; for its movement was on the surface of the earth; and this had no greater average height to the north than in the United States. As to those supposed traces of ancient glaciers, to be described in my paper on that subject, as occurring in New England, the probability is, that they were made earlier than the drift scratches. At any rate, the latter are altogether the most obvious phenomenon, and the principal thing to be accounted for; and it is their characteristics that are reconciled with so much difficulty with the effects of glaciers. 5. I find some difficulty in reconciling to the glacier theory, the diversity of direction taken by the drift agency in different parts of the country. Over the mountains of New England the course was south and southeasterly. But in the valley of Lake Superior, it was nearly southwest. What could have determined different glaciers in directions so diverse, especially as they must have ascended rather than descended, both in New England and to the southwest of Superior, I am unable to conceive. But supposing icebergs to be driven forward by currents in the ocean, and there is no difficulty in accounting for such diversity of direction in the striae and boulders. Upon the whole, those difficulties seem too formidable to admit of the adoption of the unmodified glacier hypothesis. I lean, therefore, at present, toward that which imputes most of the work on this continent to immense icebergs, icefloes, and shore ice; not because that view is free from difficulties; for I acknowledge them to be many; but they appear less to me now than in the other hypothesis. Perhaps, however, the iceberg hypothesis, as I have stated it, falls but little short of that of the glaciers. For I agree with Professor Agassiz, that to sustain the former, “we must assume an ice period—nothing less than an extensive cap of ice 72 SURFACE GEOLOGY. upon both poles.” “This,” says he, “is the very theory which I advocate; and unless the advocates of that theory go to that length in their premises, I venture to say, without fear of contradiction, that they will find the source of their ice- bergs fall short of the requisite conditions which they must assume upon due con- sideration, to account for the whole phenomena as they have really been observed.” (Lake Superior, p. 406.) I think that could we get access to the floor of the Arctic Ocean, where the icefloes probably occupy more space than the water, that par- tially bears them up, we should find a work going on very similar to that which produced the drift. On such icebergs and icefloes, for the present I take my stand. But as I look toward the shore, and see my neighbor standing upon a glacier, I can hardly tell the difference between the two foundations ; and whenever he will show me that his glacier is advancing southerly over a level surface, as does my iceberg, I will gladly place myself by his side. As to the origin of that more intense cold which once prerailealon over New Eng- land and other countries much farther from the pole than at present, I have no hypothesis to offer. But as to the fact it seems to me that the undeniable former great extension and thickness of glaciers in Switzerland, Scandinavia, Wales, and perhaps Scotland, and the absence of organic remains from drift, in general, make it certain. I have sometimes imagined that the upheaval of the bed of the north- ern ocean, according to De la Beche, or the earthquake waves of the Professors Rogers, sweeping southerly from the same region, might afford an explanation. But such forces would produce only a temporary submersion and icy deposit; whereas the evidence of the long continued presence and action of water and ice, and of the slow emergence of the land from the ocean, evince its permanent sub- mergence. 41. Let me now present a summary of my present views of the origin of that deposit, properly called drift, excluding all which I have described as modified drift. 1. Glaciers.—It seems to me that the moraines of glaciers affords a good type of drift, viz.: a confused mixture of abraded materials of almost every size, driven mechanically forward. I cannot see why we should limit the impelling force to water as does the ordinary definition of the term drift. If these views are correct (and I presume no geologist will dissent), then we have one agency in this work in which all are agreed, and which is still in opera- tion before our eyes. Moreover it has been at work from the earliest times in which we have any evidence of drift action. Certainly it goes back as far as the tertiary period, perhaps further. Before the last submersion of our continents it may have operated long and powerfully; and if the views of some geologists are true, it then accumulated the great body of the drift now before our eyes. And still in northern regions, and even in central Europe, it is adding to the mass daily. 2. Icebergs.— Wherever these reach the bottom and are urged forward, it cannot be doubted that they must produce essentially the same effects as glaciers. And for the reasons already given, I must suppose that in some countries—our own for CAUSES OF DRIFT. 73 instance—most of the drift has been thus produced, and most of the erratic blocks thus scattered. This agency, too, we can trace back to the dawn of the drift period, and it is still in operation on a stupendous scale in arctic and antarctic regions. What we witness of its effects in temperate seas shows only its power in transporting afar blocks of stone which it has torn from the shore. 3. Mountain Slides produced by Aqueous Agency.—If any one doubts whether this should be reckoned among the causes of drift, let him visit the case described in this paper, on what I call Moraine Brook, in Mount La Fayette, at Franconia, and he will see first, that the materials torn off from the ledges and strewed along for two miles, cannot be distinguished from coarse drift; and secondly, that they are so arranged as not to be distinguishable from the lateral and terminal moraines of a glacier. Why then should they not be regarded as drift? 4. Waves of Translation, produced by the Paroxysmal Upheaval of Continental Masses, or Earthquake Undulations.— Whether any certain example of such a move- ment can be pointed out—unless we admit. drift generally to have been thus pro- duced—I exceedingly doubt. But hypothetically we can realize that such waves would tear off fragments of rocks and roll them along and smooth, if they did not groove, the rocks. This action would, indeed, be too short, violent, and irregular, to explain all the features of drift, which were the work of agents acting ages upon ages: yet, from the phenomena occasionally exhibited by earthquake waves along the coast, we may reasonably include this force among those concerned in the production of drift. And in some countries it may have done much of the drift work. 5. Perhaps I ought to add, as a fifth cause of drift, those ice floods that occur almost every winter in the rivers of northern and mountainous countries. Often in these cases, the river is choked with fragments of ice, so that its banks are full. ’ Yet there is water enough to keep it slowly in motion. It differs, in fact, from a glacier, only in being more fluid, so that its motion is more rapid. But it grates powerfully upon the sides and bottom of the stream, and produces miniature moraines. I see not why such detritus should not be regarded as drift as much as the moraines of glaciers or icebergs. 42. According to these views, drift is the result of several agencies that have been in operation upon the earth’s surface, certainly since the tertiary period, and in some countries, from a much earlier date. “They have varied in intensity at different times, and in different circumstances, and each one has had a predomin- ance at certain times. But all of them are still in action in some parts of the globe, and perhaps with as much power as ever. 43. In like manner, alluvial agencies have had an operation parallel to those producing drift, and as far back, though the present forms of alluvium are chiefly posterior to the tertiary epoch. But perhaps the whole formation is not so. 44, Drift and alluvium ought to be regarded as only varieties of the same forma- tion. And since water has always been present and essential in the operation of the other agencies, the whole formation should take the name of alluvium. Chro- 10 74 SURFACE GEOLOGY. nologically, we might divide this formation into the following periods; which, however, must not be understood as completely isolated from one another, but only as marking the times when certain phenomena predominated. 1. The Period of unmodified Drift. 2. The Period of Beaches, Osars, Submarine Ridges, and Sea Bottoms. 3. The Period of Terraces. 4. The Historic Period, or the Period of Deltas and Dunes. Lithologically, Alluvium may be subdivided as follows: 1. Drift unmodified, embracing angular and rounded boulders, gravel, sand, and clay. 2. Modified Drift, embracing the following forms : 1. Beaches, ancient and modern. . Osars. . Submarine Ridges. Sea Bottoms and Lake and River Bottoms. . Terraces. . Deltas. . Dunes. . Moraines. Such views, essentially, have been advanced by previous writers of great ability. Thus, Sir Charles Lyell groups together all the strata above the tertiary, under the name of Post-Pliocene, of which the Recent embraces the deposits coeval with man, and Drift, those anterior to man. We find, also, that the eminent paleeonto- logist and geologist, M. Alcide D’Orbigny, in his Cowrs Elementaire de Paleontologie et Geologie, comprehends in his Terrains Contemporains, ou Epoque actuelle, every thing above the tertiary. Still more specifically like my own, are the views expressed by William C. Redfield, Hsq., at the meeting of the American Associa- tion for the advancement of Science, at Cambridge, in 1850. He remarked, “ that the phenomena of the boulders and drift should be attributed to mixed causes, and that the theories which refer these phenomena to the several agencies of glaciers, icebergs, and packed ice, are, in truth, more nearly coincident than is commonly imagined.” I understand M. Desor, also, who has had opportunities for examining drift phenomena, not inferior to those of any man living, as inclined to similar views. He supposes that “the surface boulders, like many of those buried in the drift, clay, and sand, have been transported by the floating ice :” and he says that since “glaciers in our days occur chiefly in the valleys of the highest mountain chains, it is difficult to conceive how they could exist and move in a wide and level country like the northern parts of the United States and Canada.” (Foster and Whitney's Feeport, p. 215.) 45. Such are the results to which I have been conducted by the facts respecting surface geology which have fallen under my notice. Iam aware that these are subjects of great difficulty, and that I am in conflict with the views of eminent geologists on several points; as I am, indeed, with my own opinions, as held several years ago. And yet for a long time I have stood chiefly aloof from the OID oF oo bP CONCLUSIONS. 15 various hypotheses that have been broached respecting surface geology. But I could not refuse to follow where facts seemed to lead the way. It becomes me, however, to be very modest in urging my conclusions upon others. If they cannot adopt my explications, I hope they will at least find my facts to be of some little service in reaching better conclusions. 16 SURFACE GEOLOGY. Heights of River Terraces and Ancient Beaches above the Rivers to which they are contiguous, and above the Ocean (mean height), as measured by Epwarp Hrrencock tin 1849, 1850, and 1851. Heights in English feet. S. B. prefixed indicates that the heights were obtained by the Syphon Barometer; A. B., by the Aneroid Barometer. In all other cases, they were measured by the common levelling instrument. The figures inclosed in parentheses refer to the sections where the terraces and beaches are represented. 1 2 3 | 4 5 | 5 | 6 U 9 | 9 | 10 | 10) 11) 11 2 |2 ox|od| |: j : 5 : j : : : = eerie (ines ae A We) Se Bessie) 8) el ele) e/F) a) els Bl sl/l S/ E181 Sl elel 8 ae -l S| Sle |/S|/B/S 18) S |e Sle) S |HlSlelo) & lola lo ON THE SHORE OF THE OCEAN. 8. B. 0 14 Lyme, Ct., beach (33) ne B. x 19 are payer beach (ancient) (5. 31 33) ive 31 me Lyme River terrace { 5. ae : 119 (highest) (33) ADB. 7. 102 Flanders (New London) (8. B. . 34 beach (33) ATi 3 On Connecticut RIvER. Glastenbury, Ct., terraces (7) -| 20) 36) 50) 66) 174, 190 East Hartford terraces (6) . -| 15) 36) 40) 61 Wethersfield terraces (8) ° 0 57| 76 Windsor terraces (9). © -| 19} 44) 49) 74) 114) 139 East Windsor terraces (5) . -| 22) 47) 71) 96 Longmeadow terraces (4) . -| 24) 88) 136) 200 Springfield terraces (3) . ° -| 21) 85) 36) 100} 67) 131) 136) 200 ©) Springfield Willimansett do. (2) | 40) 114) 194) 268 South Hadley terraces (1) wi 125 |) dee ioe y A. B. | 193] 298 Northampton terraces (10) . -| 57) 162) 97) 202 Hatfield terraces (10) . 0 - | 22) 130} 28} 136} 38) 146) 53) 161 Hadley terraces (10) . 6 .| 27) 135) 54} 162) 181) 289 : ¢ Whately terraces (12) . 4 32} 146) 46] 160) 92) 206) Turner’s Falls, Montague terraces ; (sg) . 0 18} 212) 97| 291) 175| 369 Northfield (south part) terraces (19) 24) 224) 90) 290) 131) 331 Northfield (north part) terraces (20) | 24) 224) 87) 287) 112) 312 Hinsdale, on south side of Ashuelot River, near its mouth (21) 7| 215} 14) 222) 36) 244| 66) 274) 150) 358 Hinsdale, south side of the Ashuelot GAD) c : 7| 215) 14) 222) 37) 245) 73) 281) 162) 370) Hinsdale, on Connecticut River, be- yond the village (21) ° -| 21) 231) 96) 306) 159) 369} unk. Vernon (22) . : 21| 234) 38) 251) 107} 320) 237) 450 Brattleborough, mouth “of Whet- stone Brook, towards the 8. W. (23) . 20) 234) 74) 288) 86) 300) 118) 332) 165) 379) 200/414 Brattleborough, mouth of West River, across the village S. W. (24)} 25) 239} 47] 261) 58) 272] 70) 284) 80) 294) 100,.314)114) 328 132 246)221)/435 Brattleborough, on Whetstone Brook (24) Q 6 8 14 23 44 56 83 102 138 153 Unk. Westminster (25) . 5 24) 255) 94) 325) 139] 370} 171) 402 Langdon, mouth of Cold River, south side (24) . . 16} 251) 94} 329) 243) 478 Westminster, near Bellows Falls, | opposite Cold River (24). 26| 261} 34) 269) 38] 273] 83) 318) 117} 352) 138'373/161) 396'226'461 Bellows Falls, above the falls (26) 41) 327| 122) 408 Pelham, ancient beaches (8. B. . | 583) 688 (10) ie B+ | B83) bes] 921|1029/1049)1151 | Shutesbury, ancient beaches . « |1053/1167 1103 1217 OMe Amherst, near Mount Pleasant, an- ( cient beach (10) c . | 329) 437 Whately, north part, peach { 5 Be is oe Conway (Shirkshire) beta ES os et Ashfield, N. E. part, beach, A. B. 976 1031 1216 1321 Heath beach (30) g - 1438 1561 \ HEIGHTS OF RIVER TERRACES, ETC. Wi Heights of River Terraces and Ancient Beaches—Continued. 1 1 2 3 4 7 9 | 10 | 10/11 )11 oO Oo Fag |p| Se | amare | eee [ina isaac =| lel OS teh | ere . . . . . . On| © . . . . . . . . BSlEal Gel PEs Ey SE See E BIE Teles Weal a-a/23) & 3 ie Be 8 || da Sed WR El Sei Slel sl 2 lseiels Se] N — 20. s. = WN. Section acrofsa tongue of Terraces tn Westfield. a4. ane (Sand Wg/ / | ~) i Sank y 7a ~» /Sand/ > 326 y pe S / Sand “a Saned el 3 Clay S iN NS asf Yn Vie 8 41 ; E = [ Loum Section acrofs Deegfield River at loots Serry near the entrance x : ne N° 19. oy \ INK Vi Middle \— I op Tekoa \ y J tekow \ \ . i \ hocks N \ 8 Rocks \\ 5 ff Sy L Gorge Terraces on Nestfiell River Noe Zo: = 150 \ ae Grawvel| \ Gravel x / Gravel | < yi 8 San y Gravel N \ 37 = ate = ¥ Gravel Nt h/ Loan field. N of the Village Seclion across Ashuclot Pe, tr east, Hinsdale, N.W to the Connecticut: Connecticut. River s S Gorge Tirrace tn Soule Hadley, near Mt Holyoke Seal al Wilunanselt Man the Raul - road Bridge to he plan eastward Weel eantniad al the North end of ae f- Cmnnectieut Hier” on road to Springfield Section, a Tag Mead Ne park 5 & = 7 8 : ¥ NES. sy x i 1 is 5 gb | é No. No 7, re e 2B. & Ne 9. 3s 5 = SS 3 ee y = Hi a RA x a s an SS & iS g NBS g ‘ N x S Sandy S| RS * : ; < ze f = NS zl iv j k ui a 2 HY _ NS Ae se é 4 Seok in B Wordsor Sec! on Le Hartlord Wel bao De 2 Wap of Clastin- Sect tr Whethershield. C1 7 i ¥ Le ud’ we Ma ‘ D 1 : Seclion- Wa yy a the from Conn ox to Thea! Semn® Spare of Village bury Ct. running E from the th title of’ A ee ra eis autlinef Fars ee Si f * 8 a 3 it s Se zs : SN S$ ony Ss # BS Gravel ej N S ‘ + Gants Died AR = S 210 ae : g 3 y Q ee SS 5 3 = : es x 3 } 3 5 a san) By : NaN N 3 S a 3 Gravel antl Sa) Rae S : = M0. E ire CRSA US & 5 i y Gy BES OR : 2: South Leon’ { Oravel North ee YS 3 x RN x ON me . Seclion in Whately thorn Ch Section acryfc Dersfield Hiver at foots Ferry near the entrance 7 \8 3 ie S N Sy SS go, : Revers west. of the Chor Se EE he J oS 28 fey) | - ————a 2 : es L cet : Present Seu Level 5 - Section of liver Terraces tron 1 the W. Part of Northampton tough Hulfield Vailley and Amherst. to lham. PX e 18 \e7? Ne 14 er N § eat UE Ne 15. Ne 16. Ne 17. \ Tee i a 5 Pettees Plan f 3 159 $ 52300 N x ca g ce g 310! > & pl 10s : N RS pa os x 53 BS y yf = fe ands g 53 . 3 5 ES ; a) cy Na S “. S fu Sj 5 Mhtock: = 25 5 5 waa . Yeriegy \ S 8 / 10 sont Tok y Dives Tee — rao iB Section acrofsa wngue of Terraces tt Westfield. Mie, e BL 3 < ere = = < iS OO 4, 2E § S oi me: Pettees Plan Section across Pine Hill Section in Wesifil on Westfield a Nee é - PPO EO LN EERE MED Deepilaeatloms Worth side, 3 riiles fof the Village. a = ——— We nel a TiN LODEN Wadia \SeePaproce Duara DMea oun | (ssh Den eLUS AEA hres ; N25 Ne 20 Ne 2l Ne 22 Ne 23. NO 24. = . d ; akngen se 150. pears eg : 6 ray, geen = [Greed 18 xv , an DLBER Ss & PES = / ; Ls SSS 3t_ a > ¥e Vi : me x \ Ss I I, SS y 8 F = \ S : Hache = SS _# ae ve RUS ee S “ae Ba s esas 5, les J fe N 5 Bsn fi iritiae s 5, ~AS.s Sal iy of pes AS 4 SS ine 7 = ee oc a A PY, Si Be Al | han , 5 2 oh Sate ; y isd. NOW to the Connecticut Sec! across Westhielil Rin Itusselt Section across Old Kier V ged in Russell. Suction trom Turners Fills Ferry] Southwest Section tn Narlliftedd, Sof Neotron. tn Northfield. N of the Village Section across Ashuelot 2 tn Hinsdale NW ta the Con Villaye MOM, Lftom On Mom @- Hever: est é ‘ ¥ . i ' l 2 s - ’ By rh oe 4 7 3 Bi 4 S Bi S 8 x 3 S Si aes ee, 3s 2% Loam cS) 5 As > 2 Section fron the Connecti! 6 aad, part of Vernon: We. 161 aa ~ Mountarn Section across Connecticut s [above the Falls. 472 bb, _ Section on § side of Deerk Buckland . palareders Beach xs Sse OS NEe S77! i VALE. WE =:: We & 3 3 SI Q BS) 4 N Ss x < S N Ce Ne 29. ff Connecticut River Er / > 8 W Section acrofs Connecticut River trom NW to SE trom Westminster Vt. to Walpole N. H Neos! Nn y Ss Sy : A iS “209 x Pa } § = aN 5 Vi - f > f / Pu y \ Ss Y s eg » iS a i S y “ig ; QQ 3 Rocks > xs J S 63 8 ces — SS We Perm pes Sechon westward from Connecticut River at. White River JSiurcetion. N° 32. Sift above tide water \ Sea Beach 3° Terrace 18: 278 10. Terrace Terrace od A Terrace \ Terrace SLY I G50 = eS = Sea Beach \ BL e miles. | N° 200 S FF = Paes re Sand 3| / » 8 S m7 Ss = SS / Sanc S$ Lanes - rar = no Oe $ MsGrimt\ & a 5 = hy g Sand z ras S FS : a x & s a 3 Tang 7 8 \3 $7 canth Rocky Hill 3 s Ries Ss 5 y 2 oS 2 e* y S Atoam us . foam 3 Sie s = fese 5 : E me fon, from the Cornecticrt Liver NW in the North Section fiom the Bridge over he Connecticut River wn Section i Brallleboro front the mouth of West River across the Village and Svetron acrofs Connecticut River from NW to 8 E from Brattleboro to the Soiithwest. Whetstone Brook. k Westminster Vt, to Walpole N. 1 i | : : } § NO32 : No33 s i ° : 2 Ne 30. 28 Ne 3h é { = Sand S ; § g ‘ : S 3 i yy iy rs; ei 1s § é $ i s 3 we 7 uy = a = , S g * N Eas g Ai x = Mountain s Tall Yountain g = g ; & ——— g fountas i $ ut : et 3 w/e x Se § N { S 3 ® SH = = | Section across Connecticat Haver in Walpole near the mouth of Cold and Savon Rivers. Section of tro Glacts Terraces near the mouth of Saxons River. — N° 36. Section werofe Carinelicul Fiver al Bellows Hales Nabove the ald Barrier’) Maght goer trom the tool of the Kills, } Section westward from Connechout River at White Rue Junction N° 37. S { es ib Walnut Milt Brete Tall 3 nN N° 35 1883 fect above tite. water 2259 fC abive ede water © & : ~ - £ 3 3 é 3 “es Height of Wt above the Urean 3 3 < a zg x 2 g ~ { ry . Ss = . a £ N & < y § t 5 S ‘. S $ als ee 5 a s R 3 5 a “ | | s PI N a Ss | : * ES ae & 3 ‘ F = Sey e ~ = x SE | 5 Section on S stile of Deerfield River in Section tn Heath from Walnut Hill N Gasterly about two Section acryfs the deep cut ut the summit level Df the Western Section frome Frenchis Hill in Peru easterly three niles. \hength of the base about Buckland . miles. % RERS in Washaigton Mass. three miles : s { Washington h ‘Sani 36) ; = (eS Ne39. | a Sine | tes DRS Beaches : 3 S = t 506 3 v ° No 38 Se eae 5 Ne 40 No Ay. 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J 4 Sy ys 5 ~ $ if q \ 8 ue } \ : rs ' \ < VA q \ He 3 if 1 \ 7. \ Q ee } SY ~ S 5 fo i x Dee y S| ies ! y See s ‘. ae NG Bay eae \ Kuthe na, ty f : North \ Seelion acrofs Deerfield hiver al Shelburne ; } Falls & { Heath iq Backlanid gal ZENON TERM fH a = — ~ S| Sy ®& a naiupasmpyayr ~ = in} Q : N O) 6 9th 2 SUL SMITHSONIAN CONTRIBUTIONS TO KNOWLEDGE. OBSERVATIONS MEXICAN HISTORY AND ARCHAKOLOGY, WITH A SPECIAL NOTICE OF ZAPOTEC REMAINS, DELINEATED IN MR. J. G. SAWKINS’S DRAWINGS OF MITLA, ETC. BY BRANTZ MAYER. COMMISSION TO WHICH THIS PAPER HAS BEEN REFERRED. A) URS AO RLS aN ES fa es ‘cea ah iE ED avas uve Dare ia ee (at ak tae ee JosEpH Henry, igi mea Secretary S. I. " T. K. AND P. G. COLLINS, PRINTERS, PHILADELPHIA. MEXICAN HISTORY AND ARCH AOLOGY; ZAPOTEC ARCHITECTURE, ETC., AT MITLA. CAEP APE Hi Bipey el: Durine the last twenty years, the attention of students has been directed with much zeal to the investigation of American Archeology. The peopling of our continent, the romantic ideas attached to the remnants of our Indian race, the strangeness of their architectural remains, and sometimes mere curiosity, have been the motives for this labor; yet it is to be regretted that no very definite historical results have been obtained from these studies, and that it is probable the future will be equally barren of scientific certainty. The works of McCulloh, Schoolcraft, Gallatin, Rafinesque, Bradford, Squier, Davis, Lapham, Whittlesey, and others, in regard to the aboriginal remains within the limits of the United States; and the publications of the American Ethnological Society; the vast repository of Lord Kingsborough’s volumes relative to Mexican antiquities; the admirable work of Antonio Gama; the illustrated publications of Stephens, Catherwood, Norman, and Squier, on Yucatan, Central America, Nicaragua, and Honduras; the Crania Ame- ricana of Morton, and the Peruvian Antiquities of Von Tschudi,—have presented us, mainly, the physical remains of our ancient continent; but, while they serve to stimulate our curiosity and wonder, they have done very little in elucidating the national antiquity or personal story of our aborigines. After a careful study of all these books, the question may still be properly asked: Who were the Indians of this northern continent and whence did they come? Who were the Toltecs, Chichimecs, and Aztecs of Mexico? What was their origin, and what are the facts and exact chronology of their history? Who built and dwelt in the civilized cities of Yucatan? What was the origin of the wealth, refinement, and polity of Peru? Who were the Araucanians? Yn fact, excepting the fanciful traditions of the northern tribes at the period of European occupation, and the few scattered “picture writings” and legends of Mexico, we have very little but architectural, image, and utensil remains, to inform us ‘how far the inhabitants of the western world had advanced beyond the mere supply of animal wants, towards those higher degrees of intellectual and social progress, in which taste, sensibility, and moral feeling expand into civilization. This progress is shown by the traditions or written history of all people who have emerged from barbarism. They hunger, and, at first, allay the cravings of appetite by the fruits of the earth, or invent the simplest instruments to pursue the chase. They suffer from cold, and clothe themselves in the skins of beasts they have 1 Q MEXICAN HISTORY AND ARCHAOLOGY. slain. They are exposed to the rain and frost of winter, or the heat of summer, and, after finding the forest boughs inadequate for protection, they learn to build for temporary or permanent comfort. As the family grows into a tribe, and the tribe multiplies its numbers, they congregate in villages or towns, which, through fear or affection, become affiliated by the bond of nationality. During this process, which often requires centuries, according to the grade of aggregate intellect, all the wants and passions of society make themselves gradually known. ‘They de- velop gradually in the natural growth of a people. Municipalities and states beget police, law, government. The changes of day and night are beheld; the regular motion of sun, moon, and stars is noted; seasons are marked; and the simpler portions of astronomy are developed in the scientific division of time, as chronicled in the dial of the sky. The rivalry of neighboring states begets wars; and thence, protection ensues in the shape of arms, soldiery, arsenals, military experience, and fortifications. The inevitable conviction of a creative and preservative Power im- presses the minds of all with a religious sentiment, which begets worship and builds temples, either for adoration or propitiation, according as the national mind is exalted or grovelling. And, finally, as the people observe the necessity of recurring to the past for facts and principles, they advance from oral tradition to written and monumental records, which modern civilization endeavors to ripen into history. Now, in the absence of explicit records in regard to American nations, the object of antiquarian research, at present, is not so much to pehetrate, by fanciful guesses or resemblances, the periods antecedent to the European occupation of our conti- nent, as to fix the world’s attention on the actual condition of the aboriginal nations at the period of the conquest, and to endeavor, from their remains, to form a fair estimate of their relative status at that time. I consider this the true and best object to propose; because, most of the records—legendary, hieroglyphic, or monu- mental—concerning the antiquity of the chief centres of civilization on this continent, which were rescued from destruction, have been deciphered as far as practicable, “and their valuable facts detailed by investigators. Of all things, the American anti- quarian should, as yet, avoid the peril of starting in his investigations with an hypothesis, for the chances are very great that, in the mythic confusion of our aboriginal past, he will find abundant hints to justify any ideas excited by his credulity or hopes. In the present state of our archeology, all labors should be contributions to that store of facts, which, in time, may form a mass of testimony whence future historians shall either draw a rational picture of ante-Columbian \ civilization, or be justified in declaring that there is nothing more to be disclosed. The ancient history of our own tribes, it is well known, is a matter of tradition alone, for they had no written language; or, if they had, their story was not en- graved on monuments or transmitted on imperishable materials. Their wampum and pictographs may scarcely be entitled to consideration for permanent or historical purposes. Among the Peruvians, the guipo was only a species of memoria technica, and served rather to aid arithmeticians and financiers, than to establish an inde- pendence of individual recollection. The Aztecs, and perhaps their predecessors in the valley of Mexico, possessed a “picture writing,” which was chiefly used for the recording of facts apart from abstract ideas; but the Spaniards who seized Peru MEXICAN HISTORY AND ARCHAOLOGY. 3 and Mexico did not protect these simple archives, flimsy as they were, from destruc- tion by an ignorant soldiery and their superstitious companions. The Mexican “picture writing” consisted of several elements: an arbitrary system of symbols to denote years, months, days, seasons, the elements, and events of frequent occur- rence; an effort to delineate persons and their acts by rude drawings; and a phonetic system, which, through objects, conveyed sounds that, singly or in com- bination, expressed the facts they were designed to record. This imperfect and mixed process of painting and symbolizing thought, was stopped at this stage, for it was the extent of Aztec invention at the period of the conquest, and it is difficult to judge, from the known character of the people, whether further progress would have been made. But this inquiry is of comparatively small importance, as the archives of Mexico and Tezcoco, containing “ picture writings” which were regarded by the Spaniards as the “symbols of a pestilent superstition,” were piled in a heap by order of Zumarraga, the first archbishop of Mexico, and reduced to ashes." ‘This species of literary auto da fé was imitated by other Spanish authorities, so that every painted paper or graven image they found was soon annihilated by the invaders. Still, a few of these relics escaped the general wreck, and were deposited in the Royal Libraries of Paris, Berlin, and Dresden; the Imperial Library of Vienna; the Museum and Vatican at Rome; the library of the Institute at Bologna; and in the Bodleian Library at Oxford. In summing up the character of the most important of these relics, Mr. Gallatin observes that, “whatever may have been the value of the Mexican paintings destroyed by the Spanish clergy, it has now been shown that those which have been preserved contain but a meagre account of the Mexican history for the one hundred years preceding the conquest, and hardly anything that relates to prior events.” The consequence of this is, that the antecedent history of the aboriginal nations inhabiting the territory of modern Mexico must rest upon the reports of early Spanish writers, their monumental remains, and, perhaps mainly, on the questionable authority of Ixtlilxochitl.’ 1 Prescott, Conquest of Mexico, I, 101. See his authorities. 2 Am. Ethnological Soc. Trans., I, 145. * The sources of information in regard to early Mexican history and antiquity are the following :— 'The Codex Vaticanus, No. 3776. a Vaticanus, No. 3738. f Borgianus, of Veletri. Bologna. « Pess Hungary, of Mr. Fejervari. No. 1. The Mexican Paintings, &e. tt Oxford, Arbp: Laud. These are engraved in Lord ee Vienna. Kingsborough’s Ist, 2d, and 3d ie Oxford, Bodleian. volumes of Mexican Antiqui- ef Oxford, Selden. ties. ee Berlin, of Humboldt. ss Dresden. a Boturini. G6 . Paris, Tell: s Tellurianus Remensis. i Oxford, Mendoza Collection. (CONTINUED OVER PAGE.) 4 MEXICAN HISTORY AND ARCH MOLOGY. “Clavigero,” says Prescott,’ “talks of Boturini’s having written ‘on the faith of Toltec historians.2 But that scholar does not pretend to have ever met a Toltec MS. himself, and had heard of only one in the possession of Ixtlilxochitl.* The latter writer tells us that his account of the Toltee and Chichimee nations was ‘derived from interpretation’ (probably of the Tezcocan paintings), ‘and from the traditions of old men; poor authority for events which had passed centuries before.” This depreciation of the sources of recorded and traditionary information in regard to Mexico by Mr. Prescott, has drawn a critical notice from Don José F'. Ramirez, in his notes on the Spanish translation of the history of the conquest, published in Mexico.’ The criticism, though earnest and ingenious, does not seem to improve our sources of knowledge and their authoritative value. Sefior Ramirez was natu- rally anxious to sustain the idea of an extremely ancient civilization, and to destroy as much as possible the fabulous air which some of the Spanish narratives were 2. Torquemada’s ‘‘ Monarchia Indiana.” 3. Bernardino de Sahaguns’s ‘‘ Historia Universal de Nueva Hspania.” 4. Boturini’s ‘Idea da una Nueva Historia General de la America Septentrional.” 5. Fernando de Alva Ixtlilxochitl’s ‘‘ Relaciones, Historia Chichimeca.” 6. Castafieda’s ‘‘ Viaje a Cibola,” 1540. 7. Fray Bartolomé de las Casas, ‘‘ Historia General de las Indias,” &. &c. 8. Antonio de Herrera’s ‘‘ Historia General de las Indias Occidentales.” 9. Torebio de Benavente, ‘‘ Historia General de los Indios de Nueva Hspania.” 10. Pietro Martire de Anglera, ‘‘ Decades de Orbe Novo.” 1587. 11. Gonzalo de Oviedo y Valdes, ‘‘ Historia General de las Indias.” 12. Diego Mufios Camargo’s ‘‘ Historia de Tlascala—pedazo de historia verdadera.”’ 13. Francisco Lopez de Gomara’s ‘‘ Cronica de la Nueva Espania.”’ 14. Bernal Diaz del Castillo’s ‘‘ Historia Verdadera de la Conquesta de la Nueva Espania.” 15. Pesquisia contra “Pedro de Alvarado y Nufio de Guzman.” 16. Don Martin Veytia’s “ Historia Antigua de Mejico.” 17. Clavigero’s ‘‘ Storia Antica de Messico.” 18 Antonio Leon y Gama’s ‘‘ Descripcion de las dos Piedras,” &e. &e. &e. 1832. 19. Lord Kingsborough’s ‘‘ Mexican Antiquities.” London, 18380. 20. Cavo y Bustamante’s ‘“‘Tres Siglos de Mejico.” Alaman’s works on Mexican History, &e. &e. . Nebel, ‘‘ Voyage Pittoresque et Archeeologique 4 Mexique.” . Stephens’s works on Central America, Yucatan, and Chiapas. . Norman’s works on Yucatan and Mexico. Catherwood’s illustrations of Stephens’s works. 3. Bartlett’s ‘‘Personal Narrative.” Mexico: Aztec, Spanish, and Republican. De Solis, ‘‘ Historia de la Conquista de Mejico.” . Robertson’s ‘History of America.” Prescott’s ‘‘ History of the Conquest of Mexico.” Ramirez, Notes on the Spanish translation of the last work ;—Mexico, 1844. The vols. of the American Hthnological Society’s Transactions.” nw pw bo Ww bw bo oe OR 0) bo re -T ga > eo 09 4 bw OW Fe To} Lo t Prescott, Cong. Mex., I, 12, note. 2 Storia de Messico, I, 128. % Nueva Historia General, p. 110. + Txtlilxochitl, Rel. ® Prescott, Conqnista de Mejico, vol. IL; motes, p. 1. MEXICAN HISTORY AND ARCH AOLOGY. 5 calculated to throw around it. He admits, I think with great justice, that Antonio de Leon y Gama “has achieved the first and only rigorously archzeological investi- gation in his country ;”’ and he very properly adds, in regard to these mythic periods, that “historical criticism, notwithstanding the quantity written on the subject, is probably the most difficult and least advanced portion of Mexican litera- ture; for, while some of our writers incur imminent risk from excessive credulity, others are governed by a scepticism which is radically destructive of all scientific investigation. A history may be true and highly instructive, though it contains the most incredible absurdities; for while it states what may be absolutely false, either through invention or insufficient proof, i may faithfully transmit the tradi- tions, beliefs, and customs of the people it describes. * * * * Mexican history, like that of all nations, is made up of two classes of narratives; the usages, customs, and ruling beliefs which present the type of the people, and of the public and private life of its eminent men, together with facts which concern the mass of the commu- nity, and constitute the very life and essence of a people.” Thus, it may be said that the deciphered picture writings found among the Mexicans by the Spaniards, together with the traditions recorded by Ixtlilxochitl, Sahagun, and others, will, in all likelihood, be found to present a typical idea of the individual, tribal, and national character. Some great historical facts may stand out in bold relief; some persons, and certain biographical incidents may appear in shadowy outline through the veil of the past; but the whole antiquity, blurred by dilapidation, looms up dimly, like a noble ruin in the gloom of twilight. 1 Gama’s “ Descripcion historica y chronologica de las dos piedras descubiertas en la plaza principal de esta ciudad.” Mexico, 1832. 2d edition. * Ramirez; Notes to the Spanish translation of Prescott’s Conq. Mex., II, p. 8 (of notes). CREAN TBE is: ° Tux letters of Cortez to the Emperor Charles V., and the writings of Bernal Diaz del Castillo, Sahagun, Torquemada, Las Casas, Oviedo, Boturini, Veytia, and Clavigero, digested as they have been in the valuable work of Mr. Prescott, display a picture of the Aztec people as they existed at the period of European occupation. We are informed, no doubt accurately, as to much of the religion, laws, science, and social life of the conquered. The Spanish exaggerations were thoroughly examined, and the essential, characteristic facts have been preserved for our acceptance. The ancient history of the foundation of the Aztec empire, stripped of most of its myths, may be comprised in a few paragraphs. At the period of the conquest by Cortez, the Vale of Anahuac, with its assem- blage of lakes, levels, and mountains, seems to have been the conceded seat and centre of greatest civilization on the northern continent. Yucatan and the territory of the Zapotecs were doubtless inhabited by a refined people; but they were probably subordinate to the Aztecs by conquest. The received traditions as to the Vale of Anahuac declare that the original inhabitants came from some unknown place “at the north,” and, in the fifth or eighth century, settled at Tollan or Tula, in the neighborhood of the Mexican Valley. This spot became the parent hive of an industrious and progressive people, whose northern frames and charac- ters were civilized and not emasculated by the more genial climate to which they migrated. They cultivated the soil, built extensive cities, conquered their neigh- bors, and, after performing their allotted task in the development of our continent, wasted away in the tenth or eleventh century, under the desolation of famine and unsuccessful wars. The Toltec remnant emigrated southward; and, during the next hundred years, the valleys and mountains of this beautiful region were nearly abandoned, until a rude tribe, known as the Chichimecas, came “from the north,” and settled among the ruins abandoned by the Toltecs. Some years afterwards, six tribes of the Nahuatlacs reached the valley, announcing the approach of another band “from the north,” known as the Aztecs. About this period, the Acolhuans, who bordered on the Chichimecas before their southward emigration, entered the Valley of Anahuac, and allied themselves with their ancient neighbors. These tribes appear to have been the founders of the Tezcocan government, which, in the fifteenth century was consolidated by the courage and talents of Nezahualcoyotl. Thus it was that wave after wave of population poured “from the north” into the valley, till it was reached by the Aztecs, who, about the year 1160, left their mysterious and unknown “northern” site at Aztlan. Their wanderings were slow. It is alleged that one hundred and sixty-five years elapsed before they MEXICAN HISTORY AND ARCH #HOLOGY. 7 descried “an eagle grasping in his claw a writhing serpent, and resting on a cactus which sprang from a rock in the Lake of Tezcoco. This had been designated by the Aztec oracles as the spot where the tribe should settle, after its long and weary migration; and, accordingly, the city of Tenochtitlan was founded on the sacred rock, and, like another Venice, rose from the bosom of the placid waters. “Tt was nearly a hundred years after the founding of the city, and in the begin- ning of the fifteenth century, that the Tepanecs attacked the Tezcocan monarchy. The Tezcocans and the Aztecs united to put down the spoiler, and, as a recompense for the important services of the allies, the supreme dominion of the territory of the Tezcocans was transferred to the Aztecs. The Tezcocan sovereigns thus became, in a measure, mediatized princes of the Mexican throne; and the two states, together with the neighboring small state of Tlacopan, south of Lake Chalco, formed an offensive and defensive league, which was sustained with unwavering fidelity through- out the wars of the succeeding century. The bold allies united in the spirit of conquest and plunder which characterizes a rude, martial people, as soon as they are surrounded by the necessaries and comforts of life in their own country, or whenever the increase of population begins to require a vent through which it may expend those energies which would explode in civil war, if pent up within so small a realm as the Valley of Mexico. Accordingly, we find that the sway of these tribes, which had but just nestled among the rocks and marshes of the lakes, was quickly spread beyond the mountains that hemmed in the valley. The Aztec arms were triumphant throughout all the plains that swept down towards the Atlantic and Pacific, and penetrated, as is alleged by some authorities, even to Guatemala and Nicaragua.” Large, however, as was this dominion of the Aztecs and their allies, it must be recollected that their territorial power did not cover the entire region which was known subsequently as New Spain or Mexico. In addition to the tribes or states I have mentioned in this notice, as constituting the nucleus of the empire at the period of the conquest, there were numerous other aboriginal powers, among which the Cholulans and Tlascalans were the most eminent. SBesides these, there were, on territory now comprehended within the Mexican Republic, the Tarascos, who inhabited Michoacan, an independent sovereignty; the barbarous Ottomies; the Olmecs; the Xilancas; the Mistecas; and the Zapotecs. The Aztec arms had recently subdued the region of Oajaca, and the last-named tribe, with all its civil- ization, had submitted to Ahuitzotl.* There was something, doubtless, in the geographical position and geological structure of this remarkable region, that assisted in making it the seat of empire. History shows that colonial offshoots are modified by climatic change. The great 1 Mexico: Aztec, Spanish, and Republican, I, 96. 2 Ag an illustration of the uncertainty of the early aboriginal history of Mexican tribes and nations, and especially of their chronology, I annex the following tables of their emigrations from the north, and of the duration of the reigns of Mexican sovereigns. They were compiled by Mr. Gallatin from a comparison of Ixtlilxochitl, Sahagun, Veytia, Clavigero, the Mendoza collection of ancient picture writings, the Codex Tellurianus, and Acosta, and inserted in the Ist vol. of our Ethnological Society’s Transactions, p. 162. The tables will be found on the next page. 8 MEXICAN HISTORY AND ARCH AOLOGY. features of Mexico are the same now that they were in the tenth and sixteenth centuries. The waters of the Atlantic, sweeping along the central parts of our continent, and compressed within the gulf by the curving shores of Florida and Ixtlilxochitl.| Sahagun. Veytia. Clavigero. . —— —— — } Tourec Emieration, &c. Arrived at Huehuetlalpallan . 0 387 500 adi Departed from Pe dene G00 596 544 They found Tula 498 713 720 Monarchy begins 510 pos 667 Monarchy ends 959 1116 1051 CuHICcHIMECAS AND ACOLHUANS OR TEZCOCANS. Xolotl, 1st king, occupies the valley of Mexico 963 1120 about 1170 Napoltzin, 2d king, ascends the throne 1075 1282 18 cen. mean 3d king, so called erroneously, ascends the throne . 1107 12638 14 cen. Quinantzin, 4th king, ascends the throne a 1141 a 1298 14 cen. Tlaltecatzin, Ist king according to Sahagun, ascends the throne é0q 1246 000 600 Techotlalatzin 5th (2a Sahagun) ascends the throne 1253 1271 1357 14 cen. Ixtlilxochitl 6th (3d Sahagun) ascends the throne . - 1857 1831 1409 1406 Netzahual-Coyotzin 7th (4th, Sahagun) ascends the throne 1418 1392 1418 1426 Netzahual-Pilzintli 8th (5th, eas dae ascends the throne 1462 1465 a 1470 Netzahual-Pilzintli dies . 5 6 : f 1515 1516 1516 TEPANECS, OR TECPANECS OF ACAPULCO. Acolhua arrives. - 1011 1158 Acolhua, 2d son of ‘Acolhua Ist, arrives 900 1239 Tezozomac, son according to D’ "Alva, gra andson according to Veytia, of the 1st Acolhua, arrives 0 F 6 2 6 1299 1348 13438 Aes Maxtlan, son of Tezozomac, arrives : 5 1427 aes 1427 1422 Mexican or Azrec EMiGRarion. Mexicans leave Aztlan 6 3 5 i 1064 1160 ce arrive at Huelcolhuacan . 003 1168 ce “© at Chicomotzoc . B90 1168 bio a «¢ at valley of Mexico : 1141 1227 1216 i 1248 he ce “at Chapultepec. S . 9 5 : {3976 1245 Menderes Codentels Acosta. | Siguenza. Ee Sahagun.| Veytia. | Clavigero. Mexican or Aztec PowER. Foundation of Mexico or Tenochtitlan | 1324 O00 ae 1325 1220 on 1325 13825 Acamapichtli, elected king Bl ee 1399 1384 1361 1141 13884 1361 1852 Huitzilihuitl, accession . 4 «| 13896 1406 1424 1403 1353 Sb 1402 1889 Chimalpopoca . 3 . 0 .| 1417 1414 1427 1414 1857 1414 1409 Ytzcoatl . 6 . 6 6 . | 1427 1426 14387 1427 142 1427 1423 Montezuma Ist . 0 9 a . | 1440 1440 1449 1440 1440 wes 1486 Acayacatl 5 a . 6 . | 1469 1469 1481 1468 1469 1464 Tizoc b 4 . 4 : . | 1482 1483 1487 1481 1483 1477 Ahuitzol . 9 . 6 : .| 1486 1486 1492 1486 1486 1482 Montezuma 2d . 9 : 5 . | 1502 1502 1503 1502 1503 1502 DURATION OF REIGNS OF Mexican Kinas. | Acamapichtli . , F 6 21 7 40 42, 150 21 cae oe Be Huitzilihuitl . 0 9 9 3 21 8 3 11 50 21 12 20 Chimalpopoca . Sea ° ; 10 12 10 13 70 10 NS il | pel | Ytzcoatl . 5 . q 2 13 14 12 13 13 14 bi | 138 Montezuma Ist . : : 0 ORY Nes DAS) 82 28 29 3 | 28 Acayacatl 0 ° ; 0 13 14 6 13 14 14 |) sal3 Tizoc ce 6 5 ' ¢ 4 3° «| 5 5 3 4 5 Abuitzol . : : 0 0 4d 16 16 11 16 17 8 16 Montezuma 2d . a 0 ; 5 17 ELSE tee, 17 7 19 17 The discrepancies between these authorities, amounting, in many cases, not only to years but cen- turies, show the extremely unreliable and mythic character of the records and traditions of the ante- Columbian period. MEXICAN HISTORY AND ARCH AOLOGY. 9 Yucatan, whirl the shifting bed of the sea in continual eddies at the mouths of the few rivers that pour into it, and create the formidable bars and shoals which make the eastern coast so dangerous an anchorage. But on the west, the shores of the Pacific are favored with tranquil and commodious havens, while numerous indenta- tions break the rugged outline of the coast with landlocked bays. The voyager may sail from the extreme eastern shores of our continent to the very centre of the Mexican Gulf-coast, along a low sandy beach, visible only at a short distance from the sea; but as he advances to that point, the snowy peak of Orizaba, towering seventeen thousand feet above the ocean, looms up in the distance like an outpost sentinel of Mexico, indicating his approach to the dividing ridge of lofty mountains. The vast Cordillera which rises near the Frozen Sea, descends southward in a series of mighty waves through the whole of this continent, until it is lost in the ocean at Cape Horn; while at the Isthmus which lmks the great body of North to South America, it parts the two seas that strive to meet across this narrowest portion of the Western World. Between the 16th and 33d degrees of north latitude, this mountain range sends forth a multitude of spurs and branches, and, within that confined space, piled on a massive base of sverras, rising from the Atlantic till they reach the height of nearly eighteen thousand feet, and thence plunging westward into the Pacific, is the territory of\ Mexico, hung upon these sloping cliffs, and resting among the sheltered recesses of their upland valleys. Two important rivers may be said to form the natwral northern boundary of this region. The snow that melts on the Sierra Nevada, descends, one-half to feed the fountains-of the Rio Grande, which winds through an immense extent of country before it falls into the Gulf of Mexico—and one-half to swell the Colorado of Cali- fornia, before it reaches the Pacific through the Sea of Cortez. The sources of these two streams nearly meet at the same mountain, in the neighborhood of the fortieth degree; but the configuration of the earth essentially varies between the northern and southern sides of these rivers. From their northern banks the land recedes in comparative levels, interspersed with arid wastes and prairies, sloping gradually to the Pacific and Atlantic; while from their southern banks the country almost directly breaks into the steeps of the Sierra Nevada, whose multiplied veins enlace the whole of Mexico with a massive network. Uncertain streams—none of which are navigable, and all dependent on rain for their floods—pour down the pre- cipitous defiles, on their way to the seas. As the centre of this territory is ap- proached, the naked Cordilleras become loftier and loftier, as if to guard, with double security, the heart of the nation; while, in the midst of this sublime congregation of mountains, rise still more majestic peaks crowned with eternal snow, presiding over the beautiful valley of Anahuac, wherein the ancient Aztec capital nestled on the border of its crystal lake. Flanked by two oceans, and rising from both to the rich plateaus of the table-land, Mexico possesses, on both acclivities, all the temperatures of the world, and ranges from the orange and plantain on the sea- shore, to eternal ice on the precipices that overhang the higher valleys. Change of climate is attained merely by ascending, and, in a region where the country rises steeply, the broad-leaved aloe and feathery palm may be seen relieved against the 2 10 MEXICAN HISTORY AND ARCH AOLOGY. everlasting snow of Popocateptl. All these delightful climates produce the fruits and flowers of the tropics on the same parallel of latitude that crosses continual frost, while, over all, a never ending spring bends its cloudless arch. Nor are these the only allurements of this wonderful land, for nature, as if unsatisfied with pampering the tastes of man by crowding the surface of the earth with everything that might please his appetite or delight his eye, has veined its sterile mountains with precious ores in exhaustless quantity. It is not surprising that hardy races from the northern hive, where vigor is gained from toil and where toil wrests existence from an ungenerous soil, abandoned their savage habits and were subdued into a masculine civilization by a country and climate like these. It was a tropical Switzerland. Such a people, by migration, may lose nothing of their energy except its barbarism, and gain nothing from the softer skies but their genial blandness. CREASE Lap By ries Leelee Tr is conceded that, at the period of the first European occupation, all parts of North and South America were peopled; and Dr. Morton, in his elaborate “ In- quiry into the Distinctive Characteristics of the Aboriginal Race of America,” says, “That the study of physical conformation alone, excludes every branch of the Caucasian race from any obvious participation in the peopling of this continent.” _ * * * “Our conclusion,’ he continues, “long ago deduced from a patient examination of the facts thus briefly and inadequately stated, is that the American race is essentially separate and peculiar, whether we regard it in its physical, its moral, or its intellectual relations. * * * * I maintain that the organic characters of the people themselves, through all the endless ramifications of ries or nations, prove them to belong to one and the same race, and that this race is distinct from all others.” Without stopping to discuss Dr. Morton’s opinion, let us now consider the general characteristics of the remains still visible on this continent, and especially of the architectural antiquities of Mexico. “‘ Architecture is one of those massive records, either of intelligence or absurdity, which require too much labor in order to perpetuate a falsehood. It shows what the men could do, be it good or bad, elegant or hideous, civilized or barbaric. The men who built the edifices of Uxmal, Palenque, Copan, and Chichen-Itza, were far removed from the condition of nomadic tribes. Taste and luxury had long been grafted on the mere wants of the natives. They had learned to build, not only for protection against weather, but for permanent residences whose internal arrangements afforded comfort, and whose external embellishment might eratify public taste. Order, symmetry, elegance, beauty of ornament, gracefulness of symbolic imagery, had all combined for the manifestations which are always beheld among people who are not only anxious to gratify others as well as them- selves, but to vie with each other in the exhibition of individual tastes. Here, however, as in Egypt, the remains are chiefly of temples, palaces, and tombs. The worship of God, the safety of the body after death, and obedience to authority, are demonstrated by the temple, tomb, and rock-built palace. ‘The masses who felt or imagined they had no constant abiding place on earth, and that posterity had little interest in them as individuals, did not, in all likelihood, build those numerous and comfortable dwellings, under whose influence modern civilization has so far sur- passed the barren humanism of the valley of the Nile.” 1 Pp. 35, 36, 2d edition, Philadelphia, 1844. ® Mexico; Aztec, Spanish, and Republican, Vol. I. 12 MEXICAN HISTORY AND ARCHAOLOGY. “Tf the far-off past has not always been able to write its name, it has left its mark,” says Robert Cary Long, in his ingenious discourse on the ancient architecture of America, delivered before the New York Historical Society, in 1849." “Its stony autographs loom out largely from the page of time. Egypt has piled hers in Pyramids; India has quaintly carved hers in the Rocks of Ellora; Greece has delicately shaped hers, in a form of ever living beauty, upon the Acropolis; Rome has rounded hers in magnificent proportions in the dome of the Pantheon; and the Middle Ages have ‘illuminated’ their signature with those heaven-reaching coruscations, the Gothic cathedrals.” * * * * “Inthe monuments of the past we have the human deposit of the ages—the truth of the historical past. Architec- ture, in this view, is the geology of humanity. Ceasing its testimony at the present surface of the globe, geology tells nothing of that subsequent history which com- mences with the existence of men. Here, architecture resumes the thread of the narrative, and bears witness of that compound existence to which it owes its origin. * & + That consecutiveness which is dimly descried in documents, in architecture is apparent; that human progress, in which all believe, but which so few show forth distinctly, is beautifully narrated in the monumental series.” In the absence of unquestionable historic and recorded evidence, I have always considered architectural forms, disclosed in the remains of antiquity, as the most valuable hints for detecting the relative stages of the human family in the process of civilization. Craniology and osteologic science may show the relative capacity of races for civilization, but they do not demonstrate the degree attained; while the Druidical stonehenge, the Indian mound, the Egyptian tomb and palace, the Greek temple, and the Roman Coliseum, are types of the progressive intellectual erades of their respective builders. It is true that, where there are intertribal or international communications between people, the arts of the most advanced may be adopted by those who are in the rear; but it is dangerous, and I think unscientific, to start with the theory that resemblances, or even identities, in any of the arts, indicate either international connection or imitation. The basis of all action is the mind, and we know that it originates similar inventions,—according to individual capacity,—throughout the most widely separated conditions of the human family. “ Analogies of this kind,” says Baron Humboldt, in his Voyage Pittoresque, “prove very little in favor of the ancient intereommunication between people, for, under all the zones, men have indulged in a rhythmic repetition of the same forms.” To understand the force of this and its sensible value, let us recur to the simple and natural process in the law of inventive progress. A hunter or shepherd will content himself by leaning the branches of trees against each other to shield him- self from sun or rain in his temporary bivouac, and, hence the first form is that of the tent: : \ . If he is a wanderer, and inhabits, at times, the plains as well as the forest, he will construct a permanent and portable covering of skins and poles, 2 Long’s Ancient Architecture of America, pp. 5 and 6. ae, MEXICAN HISTORY AND ARCH AOLOGY. 13 so as to constitute the Indian lodge, which preserves the same shape as the tent. As he becomes less nomadic, begins to possess property, family, flocks, and herds, and requires more covered space for protection as well as comfort, he discovers that a square affords more commodious room than an angle, and his edifice assumes a new shape by the use of several of his simple architectural elements, instead of two. Accordingly, he plants his stouter timbers upright in the ground, and lays across them a covering of branches and leaves, so as to form a square: lero But this, in the course of time, admits of improvement—especially as the flat covering is not as sure a protection against rain as his original tent; and, accordingly, on the last of his inventions he elevates the first, so as to preserve his space and insure additional comfort: | . Perhaps, instead of forming his tent by simple boughs or poles, lodged against each other, he has contented himself with bending the saplings together, and thus produces the elemental shapes of the Roman and Gothic arches : . As wandering families unite in tribes, and tribes grow into communities, and communities associate in municipalities or nations, their most skilful builders discover that mechanical genius has no more elements for architectural progress in forms than a straight line and a curve; so that all invention is limited, by an irreversible law, to their wise and tasteful combination. Is it hazarding too much, then, to assert that, in early stages of civilization, we must naturally expect to see much of the type of national statws in architectural combinations of the mound and pyramid? Oo coo i a 7 a Again; is it venturing too far to suggest that, when people emerge from early stages of civilization, and rise to vigorous, masculine, and refined nationality, they abandon the propped weakness of leaning pyramidal shapes, and seek the massive, self-sustaining independence of upright, perpendicular forms?? 1 These are general suggestions upon the world’s progress in mechanics and taste, and altogether independent of art as controlled by climatic or geological necessities. A perfectly flat roof in Switzer- land would cave in under accumulated snows, and an unsupported edifice in a volcanic region would be destroyed wherever earthquakes were frequent and violent. CAS PH bve levi: Tux aborigines of our country at the period of the Discovery, or their ancestors, were all more or less engaged in building for defence or worship. The elaborate works of Squier, Davis, Whittlesey, and Lapham, published by the Smithsonian Institution, have described, perhaps everything of value among the Indian remains within our territory.’ These aboriginal relics—chiefly earthworks—may be comprised in two classes: simple Mounds, and Enclosures bounded by parapets and circumvallations or walls. The mounds are asserted to have been places of sepulture, sacrifice, and worship, or sometimes devoted to various mixed uses; while the enclosures were intended either for defence, or for sacred or superstitious purposes. The rude pyramidal mounds were frequently of great and massive dimensions, while the bird and beast shapes of their ground plans, in Wisconsin, as described in the work of Mr. Lapham, are as singular as they are inexplicable.” The mound, or heap-shape—derived, perhaps originally, from the earth that was piled over a body in burial—seems to have been the most common throughout our entire territory as far as the northern shores of the Gulf of Mexico and the Rio Grande. It indicates the early condition of art or the unprogressive character of the builders, who either disappeared from the land, degenerated into the modern Indian, or passed southward to become the progenitors of semi-civilization in more genial regions. In the mounds have been found ornaments, carvings, pipes, skeletons, shells, spear and arrow-heads, hornstone knives, axes, copper chisels and gravers, silver, galena, and various utensils of pottery; but all the forms of these implements, and especially those of the domestic vessels and images, indicate a rude state of art, taste, invention, and wants. No discoveries have yet been made to show that the mound-builders communicated or preserved facts by permanent records or monu- ments; and their nearest approach to printing is a figured stamp, found, some years since, in a mound at Cincinnati, which resembles the stamps I have seen in Mexico, used by the ancient people of that region, either to impress marks upon paper or patterns on their stuffs.* * See Squier’s Paper in the 2d Vol. Trans. Am. Eth. Soc., pp. 136, 137, 138, and his Ancient Mon. Vall. Miss., and of N. York, &c. &c.; Whittlesey’s Descrip. of Ancient Works in Ohio; Lapham’s Antiq. of Wisconsin. ? See Lapham’s Antiquities of Wisconsin in the Smithsonian Contributions. * This stamp, of which I possess a cast, is very accurately represented in Squier and Davis’s Ancient Mon. Val. Mississippi, p. 275. The inscribed stones and rocks that have been found are very apocryphal as to period and purpose ; nor are they numerous enough to indicate an ancient system. MEXICAN HISTORY AND ARCH AOLOGY. 15 Quitting the shores of the Gulf of Mexico, and penetrating the old northern territories of New Spain, we find, for the first time in our southern progress, the remains which have become so generally known in Spanish, as the “CasAS GRANDES,” or Large Houses; all of which are probably ruins of villages and towns occupied by the aboriginal tribes described by Castafeda, in the expedition of Francisco Vasquez de Coronado, in 1541, in search of the rich cities which had been reported to exist in those northern regions. The accounts of Castafieda and of modern travellers, coincide as to the character of architecture, ground-plans, and general purposes of the remains; and it is here that we see perpendicular walls, another evidence of an improved degree of civilization. The houses were not built of stones, but of adobés, or sun-dried bricks; and, as the natives had no lime, they substituted for it a mixture of earth, coals, and ashes. Some of these houses were four stories high, while their interiors were reached by ladders from the outside, so as to render the external, doorless walls, protections against enemies in the wars which seem to have been almost constantly occurring. The village of Acuco, described by the Spanish writers as lying between Cibola and Tiguex, was built on top of a perpen- dicular rock, which could only be ascended by three hundred steep steps cut in the stone, and clambering eighteen feet more by the aid of simple holes or grooves in the precipice. The tribes are spoken of as agricultural and warlike, nor does it seem that they had advanced further in social progress than by constructions for defence and comfort, of a superior character to those of the tribes beyond the waters of the Rio Grande. The fact is established, by Coronado’s expedition, says Mr. Gallatin, that “at the time of the conquest by Cortez, there was, northwardly, at the distance of eight hundred or one thousand miles from the city of Mexico, a collection of Indian tribes in a state of semi-civilization, intermediary between that of the Mexicans and the social state of any other aborigines.”* Moving southward, we enter the present actual territory of the Mexican Repub- lic, and encounter the first remarkable architectural remains of antiquity in the State of Zacatecas, on an eminence called the “Cerro de los Kdificios,” or Hill of the Buildings, situated about twelve leagues southwest from the city of Zacatecas, about one league north of La Quemada, and in the neighborhood of 222° north lati- tude, at an elevation of 7,406 feet above the sea. Clavigero speaks of Chico-mozoc, or Chico-comoe, a sojourning place of the Aztecs in their southward emigration, and inclines to the belief that these remains are the relics of their provisional archi- tecture. A very full account of the ruins is given in Captain Lyons’s travels in Mexico, and another in Nebel’s “ Voyage Pittoresque et Archeologique,” in which the walls, squares, pyramids, terraces, roads, pavements, &c., are described and partially delineated. The site of the remains seems to have been the citadel, fortress, or defensive portion of a settlement which was spread out extensively over the adja- cent plain. The northern side of the hill rises by an easy slope from the plain, and is guarded by a double wall and a kind of bastion; while on the other sides, 1 See Castafieda, Voyage » Cibola, Paris, 1888. Am. Eth. Soc. Trans., Vol. I, p. Ixxxiii of intro- duction. Mr. Gallatin of course means the ‘‘social state of any other’ northern ‘‘aborigines.” See, also, Mr. ‘‘ Bartlett’s Personal Narrative,” in relation to the Worth Mexican remains. 16 MEXICAN HISTORY AND ARCH HOLOGY. the precipitous rocks of the hill itself form natural defences. The whole elevation is covered with fragments; the rock-built walls (many of which are twenty-two feet in thickness) are sometimes joined by mortar of no great tenacity, but are retained in their positions mainly by their massiveness.’ If we leave these loftier regions of the table-lands of Mexico, and descend towards the eastern coast of Mexico, through the State of San Louis Potosi, we find the architectural remains, sculpture, &c., visited by Mr. Norman, in 1844.” The relics discovered by this intelligent traveller were of mounds, pyramids, edifices, tombs, images, fragments of obsidian knives or arrows, and pottery. Hewn blocks of concrete sandstone were, in many instances, the materials used for building ; and, besides the images of clay, he found others rudely cut in stone in bold relief. The most significant of these remains, as well as the most extensive evidences of civic civilization, were placed, by Mr. Norman, at about 22° 9’ of north latitude, and 98° 31’ of west longitude. The State of Vera Cruz, in Mexico, adjoins Tamaulipas on the south, and here, in the vicinity of Panuco, an old town of the Huestecos, Mr. Norman found remains of architecture and sculpture scattered over an area of many miles, the history and traditions of which are altogether unknown among the present indolent inhabi- tants of the region. Three leagues south of Panuco are more ruins, known as those of Chacuaco, represented as covering about three square leagues, all of which seem to have been comprised within the bounds of a large city. Five leagues southwest of these are some remains at San Nicolas; and six leagues, in nearly the same direction, are others, at La Trinidad. More relics of the same character, together with quantities of pottery, vessels, clay images, &c. &., are found in the same district; and it is to be regretted that the character of the inhabitants, as well as the health of the region, do not invite a more thorough scientific examination of the State. Sixteen leagues from the sea, and fifty-two north of the city of Vera Cruz, on the eastern slope of the Cordillera, and two leagues from the Indian hamlet of Pa- pantla, lie, spread over the plain, the massive ruins of an ancient city, which, in its palmy days, was perhaps more than a mile and a half in circuit. The best account we have of this spot is to be found in Nebel’s work, and, if we can rely on the accuracy of his drawing of the Pyramid—called by the neighboring Indians “El Tajin’—it is unquestionably one of the most perfect and symmetrical relics of antiquity within the present limits of the Mexican republic. Time has done its work upon the edifice; but, according to Nebel, the whole form and character of the architecture are still discernible beneath the trees and vines that have sprung up among its loosened joints. The pyramid is represented by this artist as being built of sandstone, nicely squared and united, and covered with a hard stucco, which seems to have been painted. Its base, on all sides, is one hundred and twenty feet; and as it is ascended by a stair, composed of fifty-seven steps, each ‘ See Lyons’s Travels in Mexico; Nebel’s Voyage, &c. &c.; Mexico; Aztec, Spanish, and Republi- can; Clavigero, ‘Storia de Messico.’ * Norman’s Rambles by Land and Water, and Notes of Travel in Cuba and Mexico. ‘ : 4 } MEXICAN HISTORY AND ARCH AZOLOGY. 17 measuring a foot in height, it may be calculated that the summit was at least sixty feet from the ground. It consists of seven stories or bodies, each decreasing in size as it ascends from the base, and all of the form shown by the annexed profile of the lower story :— CTU eee Gan ia A few miles from Papantla, near an Indian rancho, called Mapilca, Mr. Nebel discovered more pyramids, carved stones, and the ruins of an extensive town, but everything was so overgrown with the tropical vegetation, that he found it im- possible to penetrate the district, and examine the relics. The artist has preserved the drawing of only a single sculpured stone, which he describes as twenty-one feet long and of close-grained granite. The figures carved on the fragment differ from the ancient sculptures found east of the main Cordillera, and somewhat resemble those in Oajaca. By excavating in front of the stone, Mr. Nebel dis- covered a road formed of irregular blocks, not unlike the old Roman pavements. About fifteen leagues west of Papantla, and still in the State of Vera Cruz, in a small plain at the foot of the eastern Cordillera, are the remains known as those of Tusapan, which is supposed to have been a settlement of Totonacs. The vestiges of this small aboriginal establishment are nearly obliterated, and the only striking objects at present are a fountain—in human shape,—and a pyramid of four stories or bodies, in which the pyramidal and vertical lines are again united—the second story being reached, at a door, by a flight of steps. This pyramid is built of stones, of unequal sizes, and has a base of thirty feet on each of its four sides. In front of the door stands a pedestal, but the idol it probably supported has been destroyed. Around the pyramid are scattered masses of stone, rudely carved, to represent men and various animals; yet, from the inferior manner in which the work is executed, we may judge that the art of ornamentation was just beginning to be engrafted on the pyramidal and vertical architecture of the builders. The fountain to which I have alluded, is cut from solid rock; is nineteen feet high, and represents a female in an indecent, squatting attitude. The remains of a pipe which conveyed water to the image, is still seen in the back of the head, and the liquid passed through the body of the gigantic work, till it was discharged below the figure into a basin and canal, which carried it to the neighboring town. On the Island of Sacrificios, just south of the present city of Vera Cruz, there are no longer any architectural remains of edifices used for those brutal rites which made the spot so celebrated at the period of the conquest; but the soil has yielded many relics in the shape of vases, images, carvings, sepulchres, and skeletons; and it is said that fragments of pottery and obsidian are still found in considerable quantities. If we go westward from this spot, and penetrate the State of Vera Cruz until we 9 oO 18 MEXICAN HISTORY AND ARCH AOLOGY. strike a ridge of mountains in the district of Misantla, about thirty miles from the well known and beautiful town of Jalapa, we encounter a precipitous elevation, near the Cerro of Estillero, on whose narrow strip of table-land the remains of an extensive town were discovered in 1835. It is described as perfectly isolated. Steep rocks and ravines surround the mountain, and beyond these precipices there is a lofty wall of hills from the summit of which the sea is visible. As the moun- ' tain plain is approached, the traveller discovers a broken wall of massive stones united by a weak cement, which seems to have constituted the boundary or fortifi- cation of a circular area or open space, in whose centre a pyramid, with three stages (but without any mixture of vertical lines in the shape), rises to a height of eighty feet, having a base of forty feet, on two sides, by forty-nine on the two others. Beyond the encircling wall are the remains of the town, extending northward for nearly three miles along the table-land. The stone foundations—large, square, and massive—are still distinguishable, and the lines of the streets may be traced in blocks, about 300 yards from each other. Some of the walls of these edifices are still standing, in broken masses, at a height of three or four feet from the ground. South of the town are the fragments of a low wall, evidently intended for defence in that quarter; while, north of it, there is a tongue of land, jutting out towards the precipitous edge of the mountain, the centre of which is occupied by a mound, supposed by explorers to have been the cemetery of the ancient inhabitants. Twelve tombs, built of stone, and a number of carved figures, vases, and utensils were exhumed; but the images and minor objects were taken to Vera Cruz, and all trace of them has unfortunately been lost.’ In November, 18438, further east of these remains, Don José Maria Hsteva found in a thick forest, about three miles and a half from the Puente Nacional or national bridge, the interesting remains of architecture which had been first visited in 1819 or ’20 by a clergyman named Cabeca de Vaca. The temple or teocalli seems to be an exceedingly steep pyramid of steps, the base of which is shaped as follows: Loma It is elevated on a mount about one hundred and fifty feet above the level of a stream which flows at its feet; and, in consequence of the inequality of the ground, is thirty-three Spanish feet high on some of its sides and forty-two on others. It fronts eastwardly, and the platform of its top is reached by thirty-four + Mosaico Mejicano. MEXICAN HISTORY AND ARCHAOLOGY. 19 steps, so as to be almost perpendicular to the base. This platform is forty-eight Spanish feet broad and seventy long, and the steps rise on all the sides indicated on the above ground-plan by the letter S. The entire structure is of sand, lime, and large stones taken from the bed of the stream; and though very old and of course covered with a thick mantle of tropical plants and trees, its form is declared to be almost perfect. At first it was supposed to be solid, but an entrance was discovered from the west, but so small and clogged that the explorers were not disposed to venture within for fear of venomous insects and serpents with which the interior in all likelihood is swarming.' 1 See Museo Mejicano, II, 465, for plate and description. CoB AR ER. Vi. Fast of the State of Vera Cruz, but separated from it by Tobasco and the southern bend of the Gulf of Mexico, lies the State of Yucatan ; and, southeast of it, the State of Chiapas. ; The physical character of these States demonstrates the prolific and agreeable climate that probably attracted the large population with which the region must have been filled before the Spanish conquest. Since 1840, three important works have been issued by the American press relative to the architectural remains in these States. ‘Two of these are from the pen and pencil of the late Messrs. John L. Stephens and Catherwood, while the third is the result of a visit paid to Yucatan in 1841-2, by Mr. B. M. Norman.’ In the “long, irregular route” pursued by Stephens and Catherwood, “they discovered the remains of fifty-four ancient cities, most of them but a short distance apart, though, from the great change that has taken place in the country and the breaking up of old roads, having no direct communication with each other. With but few exceptions, all were lost, buried, and unknown, never before visited by a stranger, and some of them, perhaps, never looked upon by the eyes of a white man.” In Chiapas, the travellers encountered remarkable architectural remains at Ocozingo and Palenque, between 16° and 18° of N. latitude; and passing thence to Yucatan, they found the more northern peninsular region crowded with monumental ruins at Maxcanu, Uxmal, Sacbey, Xampon, Sanacte, Chun-hu-hu, Labpahk, Iturbide, Mayapan, San Francisco, Ticul, Nochacab, Xoch, Kabah, Sabatsche, Labna, Kenick, Izamal, Saccacal, Tecax, Akil, Mani, Macoba, Becanchen, Peto, Chichen, in the interior of the State; and at Tuloom, Tancar, and on the island of Cozumel, on its eastern coast. All these architectural remnants of the past, lie between the 18° and 213° of N. latitude. Of all this numerous catalogue, the remains at Palenque in Chiapas, and of Uxmal and Chichen in Yucatan, are certainly the most remarkable for their archisectural forms as well as embellishments; but they have been made known so popularly throughout the world by the books of our countrymen, that it is unnecessary to dwell upon their characteristics in this summary sketch. Mr. Stephens believed, after full investi- gation, that most of these cities and towns were occupied by the original builders and their descendants, at the time of the conquest.’ If any reliance is to be placed 4 Rambles in Yucatan, by B. M. Norman, 1 vol. ; Stephens’ Incidents of Travel in Central America, Chiapa, and Yucatan, 2 vols. ; and Stephens’ Incidents of Travels in Yucatan, 2 vols., both of the latter works being illustrated by Mr. Catherwood, who has since published many of his drawings in a sepa- rate folio. 2 See his first work, Vol. II, Chapter XXVI; and his second, Vol. II, p. 444. See, also, Trans. Am. Eth. Soc., Vol. I, and Stephens’ Yucatan, for an account of the calendar and language of the people, and some other ethnographic facts. MEXICAN HISTORY AND ARCH AOLOGY. Q1 on the theory of progressive architectural forms, the drawings of Catherwood show that these tribes or nations of the aborigines had advanced to a very important stage, though their style of “ ornamentation” indicates that they had not entirely abandoned the barbaric for the beautiful. Returning again, northward, from the extreme southern limits of Mexico, we find, in the State of Puebla—which lies directly west of the northern part of the State of Vera Cruz—at about 19° of north latitude, the well known remains of the Pyramid of Cholula. It was originally constructed of adobés, or sun-dried bricks, and may therefore be considered a sort of earthwork. The huge pyramidal mass rises abruptly from tbe plain of Puebla to a height of 204 feet," and was composed of four stages or stories connected by terraces; but the materials of the mound have been so worn by the attrition of time and seasons, that at present it resembles one of those Indian heaps of our own West, with which the reader has been made acquainted in the volumes of Squier and Davis. The most striking and valuable facts In regard to it—as its shape was simply pyramidal—are to be found in the labor and materials which were expended on a work whose base line measures 1,060 feet, and whose present elevation reaches 204. Adjoining the State of Puebla, immediately west of it, and, of course, in the neighborhood of the same latitude, we enter the State of Mexico, the seat and centre of the Aztec population which submitted to Cortez. The Spanish settlement which occupied the site of the ancient capital, very soon obliterated every archi- tectural vestige of the aborigines, so that I am not aware, either from my own personal examinations, or from the reports of travellers, that any remains of temples, palaces, pyramids, or other edifices, are preserved in or very near the city of Mexico. The National Museum, and a few private collections, are full of small relics of various characters, which have been found on the surface or disinterred in the neighborhood. These relics are either of stone, carved with skill or roughly ; or of clay burnt to the requisite hardness for utensils. T’o the images or objects, connected, as is supposed, with the religion and science of the Aztees, various and perhaps arbitrary names have often been affixed by antiquarians, but their descrip- tion belongs to another branch of archeology than that which now engages our attention.” But, if the city of Mexico and its immediate neighborhood are destitute of ancient architecture, the present limits of the State are not without some valuable remains of that character. Across the Lake of Tezcoco, at a distance of about twelve miles from the capital, and in the northwestern part of the modern town of Tezcoco, the 1 According to the accurate scéentific measurements of Lieut. Semmes, of the U. 8. Navy, and Lieut. Beauregard, of the U. S. Engineers, thus differing from Humboldt, whose work states the elevation to be 162 feet. See Mexico, Aztec, Spanish, and Republican, II, 230. 2 The reader will find a full account of these lesser remains in my first and second volumes of “‘ Mexico, Aztec, Spanish, and Republican ;” and, of two or three of the most important, in Gama’s ‘‘ Descripcion de las dos Piedras, &c.” The size and sculpture of some of the larger stones are quite wonderful ; the image called ‘‘ Teoyaomiqui,” is cut from a@ single block of basalt, nine feet high and five and a half broad ; the ‘ Sacrificial stone,” also of basalt, is cylindrical, nine feet in diameter and three high ; while the ‘‘ Calendar stone,” of the same material, is cleven feet eight inche8 in diameter, and about two feet in thickness. 99 MEXICAN HISTORY AND ARCH MOLOGY. explorer will find a shapeless mass of burnt bricks, mortar, and earth, thickly over- grown with shrubbery and aloes, among which there are several slabs of basalt neatly squared, and laid due north and south, forming, in all likelihood, the only fragments of one of those royal residences for which the Tezcocan princes were celebrated by the conquerors. When Mr. Poinsett visited Tezcoco, in 1825, this heap had not been pillaged, for architectural purposes, as much as it has been since; and, among the ruins, he found a regularly arched and well-built passage, sewer, or aqueduct, formed of cut stones of the size of bricks, cemented with the strong mortar used by the aborigines of the Valley in all their works. In the door of a room, he noticed the remains of a very jlat arch, the stones of which were of prodigious bulk. ‘In the southern portion of Tezcoco, are the extensive remains of three pyramidal masses, whose forms were still tolerably perfect in 1842. They adjoin each other in a direct line from north to south; and, according to a rough measurement by myself, are about 400 feet in extent on each front of their bases. These erections were constructed partly of burnt and partly of sun-dried bricks, mixed with frag- ments of pottery and thick coverings of cement, through which small canals had been grooved to carry off the water from the upper terrace. Bernal Diaz del Cas- tillo says that the chief ¢eocalli of Tezcoco was ascended by 117 steps; and, from the quantity of obsidian fragments, vessels, and images, found on the sides of these structures, it may be surmised that, like the teocallis of the capital, they were devoted to the same bloody rites that are described in the writings of the Spanish chroniclers and of Mr. Prescott. About three miles east of Tezcoco, across the gently sloping levels, a sharp, coni- cal mountain rises precipitously from the plain, and though now covered with a thick growth of nopals, agaves, and bushes, seems to have been the site of some Aztec or Tezcocan works of considerable importance. The hill is full of the debris of ancient pottery and obsidian ; and, about fifty feet below the top, facing the north, the mountain rock has been cut into seats surrounding a sort of grotto or recess in a steep wall, which tradition says was once covered with a calendar. The sculptures have been entirely destroyed by modern Indians, who cut them to pieces in search for treasure, as soon as they found the spot became an object of interest to foreigners. Winding downwards by the remains of ancient terraces cut in the hiil, we find the path suddenly terminated by an abrupt wall which plunges down the mountain precipitously for two hundred feet. Here, another recess has been cut in the solid rock, also surrounded by seats, while in the centre of the area is a basin, into which the water was conveyed by a system of ingenious engineering. Hast of this hill, and filling a ravine, are the remains of the stone, masonry, earthwork, and aqueduct pipes, by which the ancients brought the mountain streams to the Hill of Tezco- cingo, from the more eastern and loftier elevations.’ 1 There is an account, in Spanish, of the palace and gardens of Nezahualcoyotl, at Tezcocingo, extracted from Ixtlilxochil’s History of the Chichimecas, in the third volume of Prescott’s History of the Conquest of Mexico, p. 430, The hill referred to by the Indian historian is, probably, the one whose remains I have noticed. FS a ge ee ee ee ene ie ts MEXICAN HISTORY AND ARCH AOLOGY. OS A ride on horseback of three hours will bring a traveller from Tezcoco, north- eastwardly, to the village of San Juan, lying in a plain hemmed in by mountain spurs and ridges on all sides except towards the east, where a depression in the chain leads into the plain of Otumba. In the centre of this valley of San Juan are the two pyramids known as the Tonatiuh-Ytzagual, or House of the Sun, and the Meztli-Ytzagual, or House of the Moon, and generally denominated the Pyra- mids of Teotihuacan. At the distance from which they are first beheld in crossing the hills, the foliage and bushes that cover them are not easily discerned; but as they are approached, the work of nature appears to have encroached on that of art to such a degree, that all the sharp outlines of the pyramid are blurred and broken. In advancing towards these works, the evident traces of an old road, covered for several inches with hard cement, may still be observed ; and, at their feet, smaller mounds and stone heaps extend in long lines from the southern side of the “ House of the Moon.” Earth and perhaps adobes, seem to have been the chief materials used in the erection of these pyramids; but, in many places, the remains of a thick coating of cement with which they were incrusted in the days of their perfection, were still to be found in the year 1842. The base line of the House of the Sun is stated, by Mr. Glennie, to be 682 feet, and its perpendicular height 121. Returning again to the city of Mexico, and going thence southward over the mountain barrier that surrounds the valley of Mexico, we descend into the warmer regions of the valley of Cuernavaca; and, about eighteen miles south of the town of that name, near the latitude north of 183 degrees, but still in the State of Mex- ico, we encounter the Cervo of Xochicalco, or “hill of flowers,’ which, a few years back, was still crested by the remains of a stone pyramid. The base of the hill is reached across a wide plain intersected by ravines, and is surrounded by the remains of a deep wide ditch. The summit is gained by winding along five spiral terraces, supported with stones joined by cement. Along the edge of this winding path are the remains of bulwarks fashioned like the bastions of a fortification. On the top of the hill there is a broad level, the eastern portion of which is occupied by three truncated cones, while on the three other sides of the esplanade there are masses of stones, (which may have formed parts of similar tumuli), all of which were evidently carefully cut and covered with stucco. In the centre of the area are the remains of the first story or body of the pyramid, which, before its destruction by the neighboring planters, who used the carved and squared stones for building, is said to have consisted of five pyramidal masses placed on each other, somewhat in the style of the pyramid of Papantla. The story that has been spared is rectan- L x Ue ear Outline of part of Xochicalco. 24 MEXICAN HISTORY AND ARCHAOLOGY. gular, faces due north and south, and measures sixty-four feet on the northern front above the plinth, and fifty-eight on the western. The distance between the plinth and frieze is about ten feet, the breadth of the frieze three and a half feet, and the height of the cornice one foot five inches. The most perfect portion is the northern front, and here the sculpture in relief on the pyramid is between three and four inches deep and distinctly perfect. ‘The massive stones, some of which are seven feet long and two feet six inches broad, are all laid upon each other without cement, and kept together simply by the weight of the incumbent mass. The dimensions of the fragments of so fine a structure will give the reader an idea of the ingenuity as well as the labor employed in its building; for it must be recollected that the aboriginal skill was not taxed in the shaping or adornment of the stones in a neighboring quarry, but that the weighty materials were drawn from a considerable distance and carried up a hill 300 feet high, without the use of horses. The sculptures on this monument are somewhat rude and grotesque, but they appear to resemble the images delineated in the works of Stephens and Catherwood, as found by them in Yucatan and Chiapas. There seems to be no doubt, from the lines and irregularity of the stones, that the reliefs were cut after the pyramid was erected. Besides the external works of pyramid and terraces, it is said that the interior of the hill was hollowed into chambers. Some years since a party of gentlemen, under orders from the Mexican government, explored the subterranean portions, and, after groping through narrow passages, whose walls were covered with a hard glistening gray cement, they came to three entrances between two huge pillars cut in the mountain rock. Through these portals they entered a chamber, whose roof was a regular cupola built of stones ranged in diminishing circles, while, at the top of the dome was an aperture which probably led to the surface of the earth or to the summit of the pyramid. Nebel, who visited the ruins some years ago, relates, as an Indian tradition, that this aperture was immediately above an altar placed in the centre of the chamber, and that the sun’s rays fell directly on the . centre of the shrine when the luminary was vertical! This idea is perhaps a fair specimen of the traditions and guesses with which ingenious archeologists bewilder themselves and their readers.’ 1 See Revesta Mejicana, I, 539. Mexico; Aztec, Spanish, and Republican, II, 284. Nebel, Voy- age Archexologique et Pittoresque: Plate—Xochicalco. GST IN Te GUO Te dbs Soutn of the State of Vera Cruz, adjoining the State of Chiapas, and on the western slopes of the Cordillera, bounded by the Pacific, lies the State of Oajaca. This region, from the great quantity of architectural and image-remains found throughout it, seems to have been the seat of an advanced civilization, though its history is much less known than that of the central portions of Mexico. The State has been by no means thoroughly explored, either for its resources or antiquities ; but most interesting remains are known to exist at Tachila, where there are tumuli ; at Monte Alban, two leagues S. W. from the town of Oajaca, where there are tumuli and pyramids; at Coyfla; at San Juan de los Cites; at Guengola; at Quiotepec, and at Mitla. Most of the relics present pyramidal shapes, in combination with the vertical; a specimen of which is here copied from Lord Kingsborough’s plates of Dupaix’s expedition. i : (I a ae 7 Ui iy Yi} y] i} Ui Up Mi iy Wp Remains near Tehuantepec, Oajaca. In 1844, an examination was made, by order of the Governor of Oajaca, of the remains near Quiotepec, a village about thirty-two leagues northwardly from the capital of the State. These ruins, originally constructed of cut stone, are found on the Cerro de las Juntas, or Union Hill, so called from its neighborhood to the junction of the Rivers Salado and Quiotepec. The eminence is said to be covered, in every direction, with remains of works of a defensive character, designed, as it appears, to protect the dwellings erected on the hill, and the large temple and palace, whose massive ruins still crown the sum- mit. These fragments of the past are represented to be somewhat similar to those of Chicocomoc or Quemada, in the northern part of Mexico, which I have already described in the notice of architectural antiquities in Zacatecas. The resemblance 4 OGue MEXICAN HISTORY AND ARCH HOLOGY. consists in the style of building, and the mingling of worship and civic defences. There does not appear, however, to be any similarity between these ruins and the remains found in Yucatan and Chiapas, where the designs are much carved and ornamented, denoting, perhaps,'a higher degree of luxury, taste, and civilization. The temples of Quiotepec, and that of Chicocomoe, or Quemada, are both pyra- midal, like most of the Mexican structures; but the architectural style generally, at the former place, is rather more sumptuous than that at Quemada. ees ee Ta | i nl NGA ih Mi Ut | NY iN i \ HANI Hh H eh Ht ¥ {tin ni it ea null tt i \ i NH NLU INH \ ANAT Mi ——— Remains near Tehuantepec, Oajaca. The most interesting, perhaps, of the architectural remains within the present bounds of Mexico, in Oajaca, are those of Mirna ; and, as it was not until the year 1494 that the Aztecs finally subdued the people of Micrna, in the province of Huaxaca,’ it is not likely that the constructive talent or tastes of that region were modified or controlled by the inhabitants of the Valley of Anahuac. The same remark applies to all the other districts, in every quarter outside the valley, where the aborigines became subject to the Aztecs, either by alliance or conquest. It is * See Museo Mejicano, Vol. III, p. 329, for drawings of these monuments. See, also, Vol. I, p. 401, of the same work, and Vol. III, p. 135, for accounts of Zapotec remains; and Vol. I, p. 246, for an imperfect notice of military fortifications, &e. &c., near Guengola, Tehuantepec. * Gama; Gallatin, Eth. Soc. Trans., Vol. I, 137. Mexican Chronology. Clavigero, Lond. ed., Vol. I, p. 185. MEXICAN HISTORY AND ARCH AOLOGY. Q7 very probable that hundreds of the unfortunate Zapotec inhabitants of Mitla and Huaxaca, or Oajaca, who had become prisoners to Aheutzotl, in previous wars, swelled the splendid but brutal sacrifice of human victims, with which the great temple of Mexico was dedicated in 1487." Very soon after the jist success of Cortez in the city of Mexico, the people of Oajaca sent embassies to claim his protection; and, as soon as the country was absolutely conquered, and the victor had learned the value of the region from the reports of Alvarado and the Spaniards who began to settle there, he seems to have selected it as his own particular domain. When the crown raised him to the dignity of “ Marquess of the Valley of Oajaca,” he was endowed with a vast tract of land in the province, and there is no doubt that his twenty large towns, and twenty-three thousand vassals, were to be found mainly within the boundary of his Zapotec territory. These facts are mentioned to show that the acts of Cortez himself indicate the value of the region in which Mitla lies; and, in all likelihood, illustrate the degree of civilization it possessed prior to the Aztec conquest. It is to be regretted that there are so few traces of the ancient Zapotec tribes, and that we are left to grope in the dark, with scarcely a cobweb to guide us through the ruined labyrinth of their history. The great natural features and characteristics of the region remain of course the same; and from its general salubrity, its fertility of soil, the nature of its productions, its geological structure, and beauty of natural scenery, we may fairly suppose that its famous “valley” possessed many attractions similar to those which induced the Aztecs to make their lodgement in the Vale of ‘Anahuac. Zachila, which is a corruption of the word Zaachillatt6d, as written in an ancient MS. seen by Dupaix, is situated in the midst of the great Valley of Oajaca, and, in former times, is said to have been the seat and court of the Zapotec kings. Ten or twelve leagues southeastwardly from the town of Oajaca, engulfed in a deep valley, crested with cerros whose dry, sterile, and poorly watered soil is probably more prolific of snakes and poisonous insects than of anything else, lies the modern village of San Pablo-Mitlan. Its name was derived from Mictlan, or Miquitlan, “a place of sadness,” which it probably received from the Aztecs, while the Zapotec appellation seems to have been Liuba or Leoba, “the tomb.” It is here that we * The cruelty of the Mexican sacrifices of human beings has always been one of the principal argu- ments against the civilization, and in favor of the barbarism of the Aztecs. All religion includes the idea of sacrifice—spiritual or physical—actual or symbolical. The Christian sacrifices his selfish nature ; the Idolater propitiates by victims. The Aztec sacrifice arose, probably, from a blended motive of propitiation and policy. The human sacrifice by that people was, perhaps, founded on the idea that the best way of getting rid of culprits, dangerous people, and prisoners of war taken in immense numbers, and whom it was impossible to support or retain in subjection without converting a large portion of their small kingdom into a jail—was to offer them to their gods. It is true, that savage nations, such as the Africans of Dahomé, &c., admit the purest barbaric notions of human sacrifice ; but can such cruel contradictions be attributed—with their more brutal motives—to the Aztecs, who, in other respects, possessed so many titles to civilization ? Still, it must be admitted, that if we regard the grossness of the Aztec idolatry alone, at the time of the conquest, we could form no idea of that people’s intellectual progress in other respects. Yet their architecture, laws, government, private life, and astronomical knowledge, show that their social condition was much more refined than their faith, so that we must suppose the Valley of Anahuac was full of priestcraft and superstition, and that its cultivated society was in advance of its religion. 98 MEXICAN HISTORY AND ARCH AOLOGY. find the architectural remains which were first made known, partially, by the draw- ings of Don Luis Martin, in 1802, of Dupaix, in 1806, and are now shown in the accompanying pictures, drawn on the spot, in 1837, by Mr. J. G. Sawkins. According to the traditions reported by the earlier explorers, the chief object designed in the erection of these edifices was to preserve the remains of Zapotec princes ; and it is alleged, that at the death of a son or brother, the sovereign retired to this place, and taking up his residence in a portion of the building which was calculated for habitation, performed religious services and gave vent to cere- monious sorrow. Other reports, of the same period, say that these solitary and dreary abodes were inhabited by an association of priests who devoted their lives to expiatory services for the dead. It must be confessed that the site is admirably calculated for any one, or all, of these gloomy purposes; for, according to the accounts of travellers, the silence of the lonely valley, which is reached conve- niently but by one approach, is unbroken even by the songs of birds. Perhaps it was—not only in location, but destination—an aboriginal Escorial, where life, death, and religion mingled their austere but courtly pageants. Plate No. 1 presents a general picture of the ruins; while the following cut, A, taken from a drawing by Martin, in 1802 (and, perhaps, noi strictly accurate, except as to parts of the main edifice), shows a ground-plan or sketch of the whole group, so as to make the scene intelligible to the reader.’ Fig. A. Yeu A large portion of the valley in the neighborhood of the three mountains, seen in Plate 1, is said to be still covered with heaps indicating the sites of ancient architecture ; but, as most of the ground is under cultivation, every relic of the architecture itself is destroyed, and even the ground-plans have become so indistinct * Martin, for instance, seems to indicate five remains, while there are only four; and gives two columns at the entrance of the remaining building, while there are three. MEXICAN HISTORY AND ARCH HOLOGY. 99 as to make all researches useless. But the group which at present interests us, seems, from Mr. Sawkins’s observations, to have consisted originally of four con- nected, or nearly connected, buildings, each one fronting a cardinal point, the whole inclosing a square court. ‘The original erections may, in all likelihood, have resem- bled the following sketch, in their ground plan :— ae cr Of the southernmost of these edifices, Mr. Sawkins found five upright columns still standing—four supporting portions of a wall, while the fifth, which was taller than the rest, stood alone. These fragments are seen in Plate No. 1, immediately in front of the spectator. On the west of the square, there are the remains of crumbling and indistinct walls; on the north, everything seems to be obliterated ; while, on the east of the quadrangle, is the edifice forming the main feature of Plate No. 1, and which is represented, at large, from the rear, in Plate No. 2. Passing over the court-yard, or quadrangle—still floored with a hard cement and slabs of sandstone—we approach the entrance of this building, which consists of four apertures between three low, square columns, or door jambs, through which the interior can only be reached in a crouching posture. These four apertures admit the passage, through each, of but one person at a time. On either side of this portal, as seen in No. 1, there are niches or recesses, on the front, which were pro- bably filled by images. This portion of the exterior wall, or facade, is said by Mr. Sawkins to be, at present, without any.adornments; but whether such was its original state, or whether it has been stripped of its coverings by the neighbor- ing Mexicans, we are not distinctly informed. The large stones forming the cornice over the entrance, were especially remarked by our traveller, as indicating—both by size and neatness of workmanship—the ingenuity and power of the builders.’ Upon entering through one of the low and narrow adits, just described, Mr. Sawkins found himself in an oblong court or apartment, of very considerable size. Its walls were covered with a rich, highly polished, red plaster, so hard as to resist the knife. At the two ends of this court there were niches, as well as one directly in front of the entrance; but the images or utensils they were intended for by the aborigines, had long disappeared. It was in a line along the centre of this 1 Mr. Glennie, a British traveller, states the dimensions of some of the stones above the entrances of these buildings to be: eighteen feet long, four feet ten inches broad, three feet six inches thick ; another is nineteen feet four inches long, four feet ten and a half inches broad, and three feet nine inches thick ; a third is nineteen feet six inches long, four feet ten inches broad, and three feet four inches thick ! 30 MEXICAN HISTORY AND ARCHAOLOGY. apartment that Martin, in 1802, and Dupaix, four years after, found the six eylin- drical stone columns, without bases or capitals and of a single shaft, the position of which is shown in the ground-plan I have given, on another page, from Martin’s drawing! But when Mr. Sawkins visited Mitla, in 1837, the columns had been removed, probably by the present villagers, for their domestic purposes. These columns had evidently been intended to support the roof which formerly covered this portion of the edifice, and are represented by Dupaix to have been one vara in diameter and five and a half varas high; or near three feet in diameter by about fifteen in altitude! The large court, or saloon, just described, communicated at its rear, by a narrow passage (as will be seen in Martin’s plan), with another body of the edifice, which that artist represents to have been a sort of interior court, surrounded by four rooms without windows, each of which was entered by a single door. Don Luis Martin represents it, evidently, as a structure resembling the modern edifices of the Mexi- cans, which are similarly constructed around a patio, or court, without external windows. It is probable that such may have been the state of the ruins in 1802, but when they were seen by Mr. Sawkins, in 1837, he found the whole interior quadrangle an unoccupied area, while three of its walls were covered with nine long recesses on each side, in three tiers, each recess being large enough for the reception of a human body. These vaults were plastered with the same kind of cement that was found in the first apartment, but they were all empty. In the centre of the main court-yard of the whole group, there are said to be subterranean apartments similar to those which have been found elsewhere in this valley, and which have been represented as adorned in the following cuts. i) i i SAGO i ot es — td | ma ie — a = 1 See cut on page 28. i a el er ra ae MEXICAN HISTORY AND ARCH AOLOGY. 31 If we leave the interior of this building, we may now obtain an accurate and excellent idea of its outside from the minute drawings of Mr. Sawkins, in Plate No. 2. It is a monument which cannot fail to strike the student of American architectural archeology as being the first effort of the aborigines that not only abandons the vertical and pyramidal, but absolutely reverses the latter, and, at the same time, indulges in a style of elaborate and regular adornment which far sur- passes many remains of Etruscan art, and may almost be said to resemble the Greek. These exteriors have been constructed with great labor as well as in- genuity. Above the ground, the building,—whose interior wall is formed of adobés, or sun-dried bricks,—is cased, for about five feet, with a pyramidal base of stone slabs about two inches thick; and, from this point, the walls, still of stone, and sharply cut, begin to incline outwards till they reach a height of near twenty-five feet. Hach of the seven exterior walls, as seen in Plate 2, is divided into nine compartments, corresponding with the sepulchral recesses or vaults we noticed on the interior. From the pomt where the walls strike outwards from the perpen- dicular, all the corners and divisions appear to be formed by stouter stones than the slabs which encase the base. The bands, which are the frames, as it were, of each of these sixty-three divisions, are all of solid stone, cleanly and sharply chiselled ; while the ornamental figures contained in the squares are formed by a Mosaic work of small square stones, artistically placed beside each other, in high relief, and imbedded in a mass of adamantine cement, similar to that which covers the inte- rior walls. The spectator who looks at one end of this singular building, with its basket-like outline and beautiful adornments, might almost fancy that he stood in front of a gigantic sarcophagus, designed and sculptured in advanced periods of Grecian and Roman art." About half a mile west of these ruins, Mr. Sawkins found a large, dark red, porphyritic column, which, for the sake of illustration, he has taken the liberty to represent in Plate No. 2, as lying near the edifice. It had probably been carried off from the building by some vandals, and abandoned before they could devote it to their private uses. The artist states that the marks of the chisel or chipping tool are still visible on this column, and remarks that many blocks, from these and other edifices of the valley, were employed in building the church which is seen in Plate No. 1. To the southwest, near the point indicated in the picture by the union of the three hills with the plain, Mr. Sawkins saw the ruins of many other edifices, but all were so dilapidated that nothing could be made out. Wherever he detected the remains of cement or mortar, either on the roads, in the open air, or on walls, he found it still perfectly hard and serviceable, and but little injured either by time or attrition. There seems to have been a great fondness among the Zapotecs for red, and it is alleged that a color, which is so unpicturesque in archi- tecture, seems to have been plentifully distributed over the exterior as well as the interior of the remarkable edifice we have been considering. Plate No. 3 exhibits the characteristics of the image-remains of the Zapotecs. 1 Humboldt says that the walls extend, on a fine, about forty metres, and are five or six high: a metre, in round numbers, is 39. English inches. 39 MEXICAN HISTORY AND ARCH HOLOGY. No. 1 was drawn by me from the original in sandstone, which I found in Mexico in 1842, in the fine collection of the ConpE peL PrNAsco. Archzeologists whu are familiar with the style of images found among Aztec remains, in the Valley of Mexico, as well as with the same class of objects from Yucatan, Tabasco, and else- where in that quarter, will at once observe their difference from the images repre- sented in the plate. Grotesque and hideous as they are, they seem to possess, in the symmetrical arrangement of the designs, and in their originality, many more elements of a7t than are found in the images of the Aztec or Maya tribes. I have introduced them here for the purpose of hinting that, in all the Zapotec remains of architecture and ornament that have come down to us, we find traces of rather more inventive talent and taste than among the other aboriginal tribes with which we are acquainted.’ About a league northeasterly from the ruins of Mitla, Mr. Sawkins visited the remains of the Zapotec fortification which he has represented in Plate No.4. A steep, isolated hill, about three hundred feet high, with a base nearly a league in extent, rises in this spot and commands the whole plain. The broad, oval summit, whose greatest diameter is about six hundred feet, is reached with difficulty from all sides except the southern. By this approach, the entrance or gateway is attained in a wall about six feet thick and eighteen high. The plate shows the character of the works, which contain a second or inner wall, as is seen in the rear of the first behind the gateway; while in the interior, are the remains of three edifices, which were probably intended for the barracks of the defenders. ‘Two of these buildings are on the southern side, overlooking the approach by the gateway, while the remaining one is placed towards the east. It seems from the heaps of piled stones, still to be seen by modern travellers, and from the huge masses of isolated rock found by Mr. Sawkins and represented in his sketch, that these were the principal weapons with which the defenders protected themselves against assailants. How the possessors of this ancient fortress supplied themselves with water, on the top of an abrupt, isolated hill of 300 feet elevation, we are not yet informed by any explorers. It is stated by some travellers that several thousand men might have gathered for protection within these walls; but it may well be doubted whether the structure was ever designed for anything but a temporary refuge in times of extreme danger, when the plain had been invaded and ravaged. I have now completed a catalogue of such architectural remains in Mexico as have become known to us, either by personal observation or the reports of travellers. If we proceed southward, beyond Yucatan and Chiapas, and pass throughout the various states of what is geographically known as “Central America,” we find, in all of them, innumerable images and vessels, and fewer monumental or architectural * The only other ornamental remains possessing nearly equal claims to symmetrical design, are represented in some Peruvian ruins near Truxillo, South America. See Rivero and Von Tschndi. MEXICAN HISTORY AND ARCH AOLOGY. 33 remains of importance than we encountered in Mexico. The taste, too, as well as the design and sculpture, is inferior; nor shall we again meet with traces of evident superiority, until we pass the broad belts of the equatorial forests and rivers, and descend beyond the Amazon to the ancient realm of the Incas in Peru. - I will not close this paper by offering any theory in regard to climatic influ- ences on the degrees of civilization found among the aboriginal races of our continent at the period of the Spanish conquest. Still, I hope it may not be considered improper to remark that, while the hot regions in the neighborhood of the equatorial part of our hemisphere appear nearly destitute of monumental, traditional, or recorded remains of their inhabitants, we find, according to all these sources of knowledge, that the best samples of aboriginal civilization have appa- rently originated and ripened, between 10 and 25 degrees of north latitude, and between 10 and 25 degrees of south latitude. While the equatorial heat degene- rated man into an indolent vegetation, the northern and southern portions of the tropics rendered him progressive and fostered his social instincts. From these points, the marks of civilization seem gradually to fade away towards both poles, till they merge, through the nomadic warrior, into the squalid Esquimaux of the north, and, through the Araucanian, into the barbarous Fuegan of the south. PUBLISHED BY THE SMITHSONIAN INSTITUTION, WASHINGTON, D. C. DECEMBER, 1856. aoe oe o ifs tari Sinclair's lith Phil& T OF THE ARCHITECTURAL REMAINS AT MITLA. \ A GENERAL VIEV Sa Rees) 21d UBT 8, Ite “WILIW GVAN SNINY IWHYNLIALIHOYV LES i192 § ULTMES 7) Pp s s1d HT SSeS. AL ‘VILIW LY GNNOJ S10dI “ll i Got foi n hs Sn nt if ae “WILIW YVAN NOILWOI4ILYO4 LNAIONY Ea SMITHSONIAN CONTRIBUTIONS TO KNOWLEDGE. RESEARCHES ON THE AMMONIA-COBALT BASES. BY WOLCOTT GIBBS AND FREDERICK AUG. GENTH. [ACCEPTED FOR PUBLICATION, JuLy, 1856.] ot Py COMMISSION, 4 4p TO WHICH THIS PAPER HAS BEEN REFERRED, aN Prof. Joun F. FRAZER, : Prof. Joun Torrey. ee ) JOSEPH Hevry, SS % 5 : : Bia Kae ceaay! Secretary S. I. T. K. AND P. G. COLLINS, PRINTERS, 3 Z PHILADELPHIA, ps a AON GASE YoU: CoAGI: ale Nan eXe: PAGE INTRODUCTION . : : : : 9 : ; 1_4 Methods of analysis ernloredl : : 0 : : 6 0 4—T GENERAL ACCOUNT OF THE SALTS OF ROSEOCOBALT . 3 7 Chloride of Roseocobalt, its formation, properties, relyeeet Conenention and rearrtfionns j—11 Chlorplatinate of Roseocobalt, probable constitution : 3 11 Sulphate of Roseocobalt, its formation, constitution, properties, Caecinne Ream and products of decomposition . : 11—14 Anhydrous nitrate of Roseocobalt, its fommton and aRgamEion, caapvaniien, erystal- line form, products of decomposition and constitution : 6 ; ; 14—16 Scaly nitrate derived from 16 Hydrous nitrate of Roseocobalt, oametfiom, oapseiliine foam, properties ond aensie tution é : 6 16—18 Oxalate of Rosescopalt ueniion ceetalline form, ana coneatation) : ; 18 Cobaltideyanide of Roseocobalt, formation, properties, analyses : é 0 nya) Ferridcyanide of Roseocobalt, properties, ee : 5 : : : 19 Oxide of Roseocobalt : : : 20 Magnetic oxide of cobalt, hydrous, Soamuattion, “eonsitinition, ami arrorpanies : : 20, 21 Anhydrous magnetic oxide of cobalt, formation, and constitution : 6 6 21 GENERAL ACCOUNT OF THE SALTS OF PURPUREOCOBALT 6 é 21, 22 Chloride of Purpureocobalt, formation, properties, omiscliine form, cron, pro- ducts of decomposition, reactions . ; : : 22—28 Chlorplatinate of Purpureocobalt, formation, properties comeistinion 2 0 28, 29 Oxalate of Purpureocobalt, formation, constitution, properties . 29 Acid sulphate of Purpureocobalt, modes of preparation, crystalline form, arora, analyses, peculiarity of constitution : : : 30—32 Acid oxalo-sulphate of Purpureocobalt, formation, comatimisien, PrOnenics : d 3238 Neutral oxalo-sulphate of Purpureocobalt, formation, analyses, peculiar constitution . 33, 34 Oxide of Purpureocobalt : 2 ‘ : é : : : 34 GENERAL ACCOUNT OF THE SALTS OF LUTEOCOBALT . 35 Chloride of Luteocobalt, preparation, crystalline fon, anaes, ample) contin tion, and reactions . : 5 : : : 35—37 Chlorplatinate of Luteocobalt, form, aromatics, and cometitnton é . : 37, 38 Chloraurate of Luteocobalt, properties, analyses 5 : : : 6 39 Jodide of Luteocobalt, properties, constitution ¢ 5 5 . 3 39 Bromide of Luteocobalt 3 : é : 6 : : . 39 Cobaltidcyanide of Luteocobalt é : 40 Sulphate of Luteocobalt, modes of rpencition, eroneries oaretciline Foran, isomor- phism with the chloride, analyses, products of decomposition 4 0 : 40—44 lv ANALYTICAL INDEX. Chromate of Luteocobalt c i Nitrate of Luteocobalt, preparation, anenrantiog crane Ravin, anlees and con- stitution . 3 : : Oxalate of Tenceoeouale! constieniion Provence : , : Carbonates of Luteocobalt, neutral and acid, analyses, crystalline form, properties Oxide of Luteocobalt GENERAL ACCOUNT OF THE SALTS OF XANTHOCOBALT Fischer’s salt as a means of separating cobalt 0 6 Chloride of Xanthocobalt, mode of preparation, properties, omelbiass, aw constitution Chloraurate of Xanthocobalt, properties and constitution Chlorplatinate of Xanthocobalt, properties and constitution . Chlorhydrargyrate of Xanthocobalt, properties and constitution Ferrocyanide of Xanthocobalt, properties, constitution, analyses Sulphate of Xanthocobalt, formation, properties, analyses, and constitution ; Nitrate of Xanthocobalt, preparation, properties, crystalline form, constitution, reac- tions, products of decemposition : . : Oxalate of Xanthocobalt, formation, Properties and analyses i ¢ : THEORETICAL CONSIDERATIONS : 4 i Views of Claudet, Weltzien, and Rogojs The Authors’ views Claus’s theory of bases wantintitine ammonia en metallie odiles New theory of the platinum bases Genéralization of results Tabular view of the formule of the eect peered in the anesen memoir Conclusion PAGE Ad 45 46 46, 47 48 48—50 48, 49 50—52 52 52, 53 53 53, 54 54—56 56—58 59 59—67 59—61 61—63 63 63—65 65, 66 66, 67 67 RESEARCHES ON THE AMMONIA-COBALT BASES. PAR Tae facility with which alkaline solutions of many metallic protoxides absorb oxygen from the air, attracted the attention of chemists at an early period. The protosalts of iron, manganese and cobalt, are particularly remarkable in this respect. In the presence of an excess of the fixed caustic alkalies and their carbonates, salts of the protoxides of these metals are more or less rapidly con- verted into basic salts of their higher oxides. A similar effect appears to be pro- duced by all of the more powerful fixed bases, while it is remarkable that neutral or acid solutions of the same salts are oxidized much more slowly, an effect which is perhaps owing to the tendency which per-salts in general exhibit to become basic, and to the influence which an excess of acid exerts in producing neutral or acid compounds. Ammonia acts like potash and soda in causing the oxidation of solutions of iron and manganese. In the case of these two metals either basic salts or hydrates of the peroxides are formed, which contain no ammonia, at least in chemical com- bination. With salts of protoxide of cobalt the result of the oxidation is very different. The sesquioxide of cobalt at the instant of its formation unites with a certain number of equivalents of ammonia so as to produce a conjugate base of which ammonia forms an integral portion. The new base partakes in some mea- sure of the properties of the alkalies, the peculiar character of the salts of cobalt being wanting. It is with this class of bases that we have at present to deal. The earliest observations which we possess upon the oxidation of the salts of cobalt are due to Leopold Gmelin, who, in a memoir, published in 1822," described the changes of color which are produced when ammoniacal solutions of the chlo- ride, sulphate, and nitrate of cobalt are exposed to the air. The solutions under these circumstances absorbed oxygen and became brown, and Gmelin consid- ered it probable that they contained a cobaltic acid. Dingler,’? who subsequently endeavored to determine the amount of oxygen absorbed, inferred that the cobaltic acid consisted of one equivalent of cobalt and two equivalents of oxygen, since the brown solution gave with sulphide of ammonium a black precipitate of bisulphide of cobalt. Winkelblech*® denied the existence of a metallic acid in the solution, but > 1 Neues Journal der Chemie und Physik. Neue Reihe, V, 235. 2 Kastner’s Archiv, XVIII, 249. Annalen der Pharmacie, XIII, 148, 253. 2 RESEARCHES ON THE though his memoir contained many interesting and valuable contributions to our knowledge of the oxides of cobalt, it threw no light upon the true nature of the ammoniacal compounds, except by establishing in them the existence of sesqui- oxide of cobalt. The subject was next investigated by Beetz,’ who analyzed an ammoniacal sulphate and nitrate of sesquioxide of cobalt formed during the direct oxidation of ammoniacal solutions. These analyses led to the formulas Co,0;.880;+3NH,+NH,O, and Co,0;.83NO;+3NH,+NH,0, but as the substances employed were not crystallized, and as the analytical methods were difficult to execute, but little reliance could be placed in the results. Beetz, however, con- sidered the sesquioxide of cobalt in these compounds as playing the part of an acid, the ammonia being present as a salt of ammonium. A The oxidation of ammoniacal solutions of various salts of cobalt was also observed by Rammelsberg,’ and the products of the action in several cases analyzed. None of the formulas obtained, however, appear to belong to well defined and dis- tinct compounds. A memoir published by one of ourselves, in 1851,° contained the first distinct recognition of the existence of perfectly well defined and crystallized salts of am- monia-cobalt bases; in fact we have not been able to trace in any earlier paper even the idea of the existence of such a class of compounds. The results made public in this paper had been obtained by the author, in Marburg, in 1847, had been at that time freely though verbally communicated, and a suite of the salts obtained had been left in the laboratory at Giessen. Want of opportunity pre- vented a complete and systematic investigation, particularly from the analytical point of view. The memoir in question contained, however, besides several analyses, an accurate description of the two bases now to be described under the names of Roseocobalt and Luteocobalt. Though the analyses were from neces- sity not sufficiently complete and extended to fix the constitution of the bases in question, yet the fact is indisputable that this memoir contained, not merely the first announcement of the existence of ammonia-cobalt bases, but also a scarcely less accurate and complete description of two of these bases than any which has since appeared. As its title states, the memoir in question was intended simply as a preliminary notice; circumstances, however, prevented a speedy resumption and continuation of the subject. In a paper published in 1851,* Claudet described with some detail the properties of the chloride of Purpureocobalt, and the mode of obtaining it, as well as a few other ammonia-cobalt salts. With the exception, however, of more complete analyses, the memoir in question contained nothing which is not to be found in the previously published paper above alluded to. In two notices com- municated to the Academy of Sciences’ in the same year, Frémy announced as his —¥ 1 Pogg. Ann., LXI, 494, 480, 490. ? Pogg. Ann., XLVIII, 208. XLIV, 268. * Nordamerikanischer Monatsbericht fiir Natur. und Heilkunde, 1. Januar. 1851. Vorliufige Notiz tiber gepaarte Kobaltverbindungen von Dr. Friedrich August Genth. + Phil. Mag., II, 258, and Ann. de Chimie et de Physique, XXIII, 483. > Comptes Rendus, XXXII, 509, 808. AMMONIA-COBALT BASES. 83 own, the discovery of a class of compounds containing cobalt and ammonia, and produced by the oxidation of ammoniacal solutions of protosalts of cobalt. In the following year his complete memoir appeared.’ In this Frémy describes anew the ammonia-salts of protoxide of cobalt, first obtained by H. Rose, passes then to the description of two new classes of compounds discovered by himself, and named by him Oxy-cobaltiaque and Fusco-cobaltiaque, and finally describes at some length the principal salts of Genth’s two bases, the constitution of which he correctly determines. Frémy appears not to have been aware that these two bases had been described in a manner little less complete than his own two years before the appearance of his memoir. The chloride of Luteocobalt and its platinum salt have also been described and analyzed by Rogojski,* and what we now term the chloride of Purpureocobalt, by Gregory,’ who corrected the analyses of Frémy. The researches of Claus* on the ammonia-iridium and ammonia-rhodium bases established the existence of compounds of these metals exactly analogous to Roseo- cobalt and its salts, and chemists will look with impatience for the publication of his results in detail. Recently Weltzien has published some theoretical views on the constitution of the ammonia-cobalt bases which possess much interest. The salts of Xanthocobalt were discovered in November, 1852, by W. G., and the principal results which are contained in the present memoir were communi- cated to the American Association for the Advancement of Science, at its meeting in Cleveland in August, 1853. The formulas of several of the more remarkable bases are also given in a Report on the recent progress of organic chemistry, read before the same association, at its Providence meeting in August, 1855. The nomenclature of the ammonia-cobalt bases proposed by Frémy is so simple and convenient that we have adopted and extended it to meet every case. We have, however, considered it desirable to drop the terminal syllable “iaque,” employed by Frémy, not merely because it is not’ an English termination, but because by omitting it we obtain shorter and more convenient words. Thus, we say Roseo- cobalt and Luteocobalt, instead of Roseo-cobaltiaque and Luteo-cobaltiaque, or Roseo-cobaltia and lLuteo-cobaltia, which are the English equivalents. The shorter names, as will hereafter appear, also agree better with our own theoretical views, since we consider the compounds in question conjugate metals and not ammonias. With the view of making the description of our salts as complete as possible, we have followed the excellent example of Frémy, and referred the colors of these substances to Chevreul’s chromatic scale. Frémy had the advantage of Chevreul’s own determinations. We have employed, for the purpose, the chromatic scales recently published in Paris by Digeon, and which appear to be reliable; in any event they give some precision to determinations of color. As we have found that “very many of the salts of the ammonia-cobalt bases exhibit a well marked dichro- 1 Ann. de Chimie et de Physique, XXXV, 257. 2 Journal fiir praktische Chemie. 8 Ann. der Chemie und Pharmacie, LXX XVII, 125. * Bulletin de Académie de St. Petersburg, 1855, XIII, 97, quoted in Handwiérterbuch der reinen und angewandten Chemie, VI, 843. 4 RESHARCHES ON THE ism, we have in most cases examined the light reflected from layers of crystals, by Haidinger’s dichroscopic lens, and have given the colors of the ordinary and extra- ordinary images as obtained in this way. As a curious physical result, we may here mention that, in general, the cobalt color predominates in the ordinary image. We are indebted to Prof. Dana for the determination of the systems to which many of our crystals belong, and of their principal forms, as well as for our figures, and embrace this opportunity of expressing our grateful acknowledgment of his valuable assistance. METHODS OF ANALYSIS. The accurate quantitative determination of the different elements which enter into the constitution of the ammonia-cobalt bases and their salts, is attended with great difficulties. We have in general -found it necessary to study out with much labor the methods of analysis proper to be used in each particular case; and it has been only after many trials that we have at length been able to obtain accurate results. Before proceeding to the description of the compounds in question, it may therefore be proper to state the analytical methods employed. CopaLT. The determination of the cobalt in these salts may, in most cases, be very easily and accurately effected by the following process. A weighed portion of the salt is gently heated in a deep platinum crucible, with a quantity of pure and strong sulphuric acid sufficient to moisten the whole mass. Some effervescence is generally produced by the addition of the acid, but there is no danger of loss if the crucible be sufficiently large, and if the heat be applied only after the first action of the acid is over. The mixture is to be gently heated over a spirit lamp, until the excess of the acid, sulphate of ammonia, and other volatile matters have been expelled. During the whole time of heating, the cover of the crucible must be so placed as to prevent the possibility of loss by spattering, and at the same time to permit the escape of volatile matters. When, however, the quantity of acid has not been too great, the whole process goes on very quietly to the end, when the mass becomes dry. The heat is finally to be raised, for an instant, to low red- ness, the cover of the crucible being quickly lifted off and then replaced. The erucible is then to be allowed to cool and weighed, when the quantity of cobalt may easily be calculated from the weight of the dry and pure sulphate. After the weighing, the mass in the crucible must be carefully examined. It should have a fine rose color, and be perfectly soluble in warm water, leaving no black residue. In case this is observed, which happens only when the heat has been too high, a drop of sulphuric acid and a few drops of oxalic acid may be added, and the whole evaporated to dryness, and again ignited. When, however, there is much oxide of cobalt present, it is better to reject the analysis at once. With a little care and practice the operation succeeds almost invariably, and the result, as we shall here- after show, leaves nothing to be desired in point of accuracy. When chlorine is present in the salt to be analyzed, a little free chlorine is sometimes found among the products of the action of the sulphuric acid, and the platinum crucible is slightly acted upon. In such cases we usually add a little oxalate of ammonia to Q AMMONIA-COBALT BASES. 5 the salt before dropping the acid upon it. The quantity of salt to be taken for analysis may vary from three to five decigrammes; when more is used, there is apt to be some loss from effervescence. In consequence of the small quantities of sub- stance employed, the weighings must be as accurate as possible. In calculating the weight of the cobalt from that of the sulphate, we have the advantage of determin- ing one substance from another with an equivalent more than twice as high. - In certain cases, as, for example, when phosphoric acid, chromic acid, &c., are present, the above method cannot be employed. In such compounds we have found it advantageous to separate the cobalt as a hydrate of the sesquioxide, by boiling the salt with a solution of caustic potash, washing the precipitate thoroughly, and estimating the ignited precipitate as Co,O,, or as metallic cobalt after reduction by hydrogen. Frémy justly observes that this ignited oxide usually contains potash ; but an accurate result may always be obtained by washing it well with boiling water after the ignition, and weighing a second time. It is remarkable that Frémy asserts that cobalt may be accurately estimated in the form of sulphate, in conse- quence of the stability of this salt, while the direct application of the method, as we have described it above, appears to have escaped him entirely. Hyprocen. We have in almost all cases determined hydrogen directly by com- bustion with chromate of lead, metallic copper being placed in the anterior part of the tube. In the case of the nitrates, however, an excess of hydrogen in the result is almost unavoidable, because it is impossible, even with freshly reduced copper, to decompose completely the great quantity of oxides of nitrogen formed during the combustion. In other cases this effect is much less marked, and the hydrogen determinations are at least as accurate as in ordinary organic analyses. Cuiorine. The accurate determination of the chlorine in the ammonia-cobalt salts is very difficult. Nitrate of silver, it is true, precipitates chlorine from most of its combinations in these salts, but the precipitation is never complete, because the chloride of silver is somewhat soluble in the ammonia-cobalt chlorides, forming with them peculiar double salts. By long boiling with free nitric acid in the solu- tion, nearly all the chlorine may be determined as chloride of silver, but very accurate results cannot be obtained in this manner. The best method consists in igniting the chloride with lime in a combustion tube, in the manner usually prac- tised with organic bodies. In some cases, however, we have obtained very good results by decomposing the solution of the chloride by sulphurous acid, or by boil- ing the solution of the salt until it is completely decomposed, adding sulphurous or nitrous-nitric acid to reduce the sesquioxide of cobalt, and then precipitating with silver. The process is, however, always troublesome, and requires much time and great care. Carbon. This element is best determined by the usual processes of organic analysis. In consequence, however, of the very large quantity of oxides of nitro- gen, which are always produced during the combustion of these salts, we have found it very advantageous to employ a method first suggested, we believe, by Winkelblech, and which consists in mixing with the oxide of copper a quantity of finely divided metallic copper, in the form in which it is obtained by reducing the oxide by hydrogen. In this manner the formation of the oxides of nitrogen 6 RESEARCHES ON THE may be completely prevented. Great care must, however, be taken when it is wished to determine hydrogen at the same time with carbon, because, copper re- duced from the oxide by hydrogen, always contains water, which it is difficult to separate. Nirrocen. No element has presented such difficulties as nitrogen. We have found it impossible to obtain results within two or three per cent. of the truth by employing the old methods of analysis, that of Dumas for instance. The quantity of nitric oxide formed during the combustion is surprising, and it is absolutely im- possible to get rid of it by means of ignited metallic copper, placed in front of the combustion tube. Will and Varrentrapp’s method with soda lime is inapplicable, because one equivalent of ammonia is always decomposed by the equivalent of oxy- gen set free in the reduction of sesquioxide to protoxide of cobalt. Good results could not be obtained by boiling the salts with caustic alkalies, collecting the ammonia in chlorhydriec acid, and determining it by bichloride of platinum. Hven after the reduction of the sesquioxide of cobalt to protoxide by means of sulphur- ous acid, this method was found unreliable. The improvements made by Simpson in the absolute determination of nitrogen by volume at last furnished us with a reliable process; and nearly all the analyses in this memoir were executed by his method. The improvement introduced by Simpson consists essentially in mix- ing oxide of mercury with the oxide of copper employed to effect the combustion. The vapor of metallic mercury completely decomposes the oxide of nitrogen, and any excess of free oxygen is absorbed by means of metallic copper. By this method we have analyzed most of our compounds without special difficulty, though we have often found it necessary to employ a much larger proportion of oxide of mercury than is recommended by Simpson. One class of ammonia-cobalt bases have, however, been the source of frequent analytical failures, and of great loss of time and material. We refer to the salts of Xanthocobalt, a base containing deut- oxide of nitrogen, and giving off this gas at a gentle heat, below that at which oxide of mereury is decomposed. Simpson’s method has not always been found accurate, since even when a very large amount of oxide of mercury is employed there is frequently much nitric oxide in the nitrogen collected for measurement. In many cases the simple admixture of a large proportion of metallic copper with the oxide, as recommended by Winkelblech, has been found to give most excellent results. It is proper also to state here that, in consequence of difficulties in obtaining proper apparatus with which European chemists do not have to contend, we have, in the majority of cases, measured the volume of nitrogen in the old way, using, however, very accurately graduated tubes for collection, and correcting with great care for temperature and pressure. We have also found it advantageous to operate upon quantities of substance sufficient to yield at least two hundred cubic centimetres of gas, since in this way the error of reading becomes extremely small. SuLPHuRIC Acip. This acid cannot be accurately determined in the ammonia- cobalt salts by direct precipitation with chloride of barium. In almost all cases, a great apparent excess of acid is obtained, and this may amount to five per cent., even when the sulphate of baryta appears to have been completely washed. We have, therefore, in all cases preferred to decompose the salt to be analyzed, by ey =I) en \ GPRS See AMMONIA-COBALT BASES. vit boiling it with a little ammonia. After complete precipitation of the sesquioxide of cobalt, chlorhydric acid is to be added to reduce and dissolve the oxide, when the sulphuric acid may be directly thrown down by chloride of barium. Even with these precautions, our results are not unfrequently two-tenths or three-tenths of one per cent. too high, almost never too low. Oxanic Aci. The ordinary methods for the quantitative estimation of this acid fail entirely with the class of salts under consideration. A solution of ter- chloride of gold is reduced only after very long and tedious boiling, and then incompletely. Even after previous reduction of the cobalt to the form of protoxide, the method is found to be very inconvenient and inaccurate. The conversion of the oxalic into carbonic acid by oxidation, and its determination from the weight — of this last, gave no better results, inasmuch as the oxidation is effected with difficulty. We have therefore in all cases had recourse to the ultimate organic analysis, which alone gives reliable results. The methods employ ed in the determination of other substances will be described, when necessary, in treating of particular compounds. ~ ROSEOCOBALT. The description of the salts of Roseocobalt forms, upon the whole, the most convenient starting point in a statement of the results of our investigation. These salts are in general easily obtained, and the products of their decomposition include several of the other bases, which we shall have occasion to describe. They are almost all well crystallized, and are in general nearly insoluble in cold water, soluble without decomposition in warm water slightly acidulated, but easily decomposed when the neutral solutions are boiled, a hydrated hyper-oxide of cobalt. being thrown down, while free ammonia is given off. The salts of Roseocobalt have a purely saline, not metallic taste; their color varies, being sometimes dull or brick-red, and sometimes cherry-red. They are usually dichrous, though a few of them do not exhibit this property in a marked degree. Heat decomposes the dry salts readily, the final products of the decomposition being usually ammo- nia, a salt of ammonium and a salt of protoxide of cobalt. Intermediate pro- ducts are, however, sometimes formed, as we shall hereafter see. Thus in many cases the salts of Roseocobalt on boiling yield salts of Luteocobalt, which then, by continued boiling, are completely decomposed. The salts of Roseocobalt may almost always be prepared by the direct oxidation of ammoniacal solutions of salts of protoxide of cobalt, but the particular circumstances, which accompany the formation of each one, will be best considered in treating of the separate com- pounds. Roseocobalt is a triacid base. CHLORIDE OF ROSEOCOBALT. An ammoniacal solution of chloride of cobalt absorbs oxygen readily from the air, becomes at first brown and then gradually passes through various shades of color to a deep red. The red solution leaves upon a filter a quantity of hydrate of 8 RESEARCHES ON THE sesquioxide of cobalt, which is sometimes almost inappreciable, sometimes in com- paratively large amount. In one experiment, in which we employed perfectly pure chloride of cobalt and pure ammonia, there was no deposit whatever of oxide. In this case, however, no chloride of Roseocobalt, but only chloride of Purpureo- cobalt was formed. When impure materials are used the precipitate is abundant, and contains many of the impurities of the substances employed, as well as much sesquioxide of cobalt. The rate at which oxygen is absorbed varies much with the degree of concentration of the solution, with the temperature, with the quantity of ammonia present, and with the extent of liquid surface exposed to the air. Fre- quent agitation of the solution materially shortens the time required for complete oxidation, and the same effect is produced by passing a current of oxygen directly through the liquid, which soon becomes brown and subsequently red. As a general rule, the first effect of the oxidizing action is to give the liquid a brown color, the layer next the surface being the first to change its tint. The brown color then passes gradually into a deep red, and the oxidation is complete, when the whole mass of liquid has the color of red Burgundy wine. The presence of chloride of ammonium is not necessary in this process; a large quantity of this salt in the solution often gives a lilac or purple precipitate as the oxidation advances, but this is composed principally of the chloride of Purpureo- cobalt. As will be seen from the above, the chloride of Roseocobalt is not always formed during the oxidation of an ammoniacal solution of chloride of cobalt. On the contrary, it often happens that not a trace of this salt can be obtained from the oxidized solution, which contains only the chloride of Purpureocobalt. We have observed the absence of the chloride of Roseocobalt only in solutions which had been oxidized in a warm room, or during the summer season. This fact, taken in connection with the facility with which heat transforms solutions of Roseocobalt into those of Purpureocobalt, renders it, to say the least, extremely probable, either that a comparatively high temperature prevents the formation of the chlo- ride of Roseocobalt entirely, or else that this salt is converted into chloride of Purpureocobalt as fast as it is formed in the solution. To obtain the chloride of Roseocobalt from the oxidized solution, cold and strong chlorhydric acid is to be added to it, the slightest elevation of temperature being carefully avoided. A brick-red precipitate is thrown down, which is to be washed with strong chlorhydric acid and then with ice-cold water, thrown upon a filter, and dried by pressure, great care being taken to operate at as low a tempera- ture as possible. As the formula of the chloride of Roseocobalt is, 5NH;.Co,C]l,+2HO, its forma- tion by the oxidation of the ammoniacal solution of chloride of cobalt may be explained by the equation 6CoC14+ 1ONH,+30=2(5NH;.Co,Cl;) +Co,03. In those cases in which no sesquioxide of cobalt is precipitated, we may suppose that the sesquioxide unites directly with ammonia, as represented by the equation 6CoC1]+15NH,+30=2(5NH,.Co,Cl,) + 5NH,.Co,03. On adding an excess of chlorhydric acid to such an oxidized solution, 5(5NU;. AMMONIA-COBALT BASES. 9 Co,Cl,) must be formed, which satisfactorily explains the precipitation of the brick- red chloride by the acid. Frémy assigns to the brown substance, which is the first product of the oxidation, the formula 4NH;.Co,0,. We have not yet’ been able to obtain this substance in a condition fit for analysis, and Frémy does not consider the formula, which he pro- poses, as by any means established. It will be seen from the above that, in the formation of the chloride of Roseo- cobalt, the elements of ammonia unite with sesquioxide or sesquichloride of cobalt at the instant that these are formed by the absorption of oxygen from the air. Claus has recently shown that the sesquichloride of rhodium' unites directly with five equivalents of ammonia to form a chloride exactly analogous to the chloride of Roseocobalt, and having the formula 5NH;.Rh.Cl,. We have made various experiments to determine whether sesquioxide of cobalt once formed could unite directly with ammonia. A solution of chloride of ammonium was poured upon freshly prepared sesquioxide of cobalt, strong ammonia-water added, and the whole allowed to stand for some time in a closed bottle and in a rather dark closet. Even after many weeks, however, only traces of chloride of Roseocobalt could be detected. A quantity of sesquioxide of cobalt was dissolved in strong acetic acid, and to the solution chloride of ammonium and ammonia-water added. In this case chloride of Roseocobalt was formed after a few days, but it is doubtful whether its forma- tion was not due to the oxidation of a small quantity of protoxide of cobalt in the sesquioxide employed. In another experiment, strong ammonia was added to freshly prepared sesquioxide of cobalt, and the whole allowed to stand for several weeks, after which time it was boiled with chlorhydric acid, and considerable quan- tities of chloride of Purpureocobalt, Luteocobalt, and Praseocobalt, were obtained. This experiment leaves no doubt that the Ammonia-cobalt bases can be prepared by the direct action of ammonia upon sesquioxide of cobalt, though this mode of preparation is not economical. The chloride of Roseocobalt may also be prepared by adding cold and strong chlorhydric acid to a completely oxidized solution of the ammoniacal nitrate or sulphate of cobalt. A brick-red precipitate is formed in either case, which must be purified by repeated washing with chlorhydric acid. Strong chlorhydric acid also precipitates the chloride from solutions of the sulphate and nitrate of Roseocobalt. In all these cases, however, it is difficult to obtain the chloride in a perfectly pure state. The chloride of Roseocobalt is usually precipitated as a brick-red powder, which, under the microscope, appears to be composed of indistinct granular crystals. It may be purified, though with difficulty, by solution in ice-cold water and sponta- neous evaporation in the cold. The salt is soluble in cold, as well as in hot water, with a dark-red but not violet-red color, the portions still undissolved becoming lilac or purple before dissolving. ‘The most remarkable property of this salt is the facility with which it is converted into chloride of Purpureocobalt. The hot + Since the above was written, Claus has extended his observation to the sesquichloride of iridium, which forms a similar base with five equivalents of ammonia. 2g a 10 RESEARCHES ON THE solution yields, on cooling, small but brilliant erystals of the latter chloride; in fact even solution in warm water converts a portion of chloride of Roseocobalt into chloride of Purpureocobalt, as may easily be observed by the change of color. This transformation is, however, far more striking when a solution of chloride of Roseocobalt is boiled with a little chlorhydric acid: the solution speedily changes its color from a dull-red to a beautiful violet-red, and on cooling deposits an abundant crystallization of chloride of Purpureocobalt. There is in this case a direct conversion of Roseocobalt into Purpureocobalt, an isomeric radical; the reactions of the violet-red solution being entirely different from those of the same solution previous to boiling with acid, except in one or two particulars, to be pointed out hereafter. The dry chloride of Roseocobalt is also slowly converted into chloride of Purpureocobalt by keeping, changing its color to violet-red; in this case, however, the change is not complete, even after a long time, unless heat be applied. The formula of the chloride of Purpureocobalt, as we shall hereafter show, 1s 5NH;.Co,C1;. This differs from that of the chloride of Roseocobalt only by containing no water of crystallization. The change which takes place in the conversion of one chloride into the other does not, however, consist in the mere loss of water. As we shall show, the chloride of Roseocobalt corresponds to a triacid oxide, while that of Pur- pureocobalt yields a biacid oxide. It is to be carefully borne in mind, that the substance which we have called chloride of Roseocobalt is not the chloride of Roseo- cobaltiaque of Frémy, Claudet, and other chemists who have studied the subject. To the chloride described by Frémy under the name of chloride of Roseocobaltiaque we have given the name of chloride of Purpureocobalt. The necessity of this change of name has arisen from the fact that hitherto two different bases have been con- founded, the chloride of Purpureocobalt having been considered as the chloride corresponding to the sulphate and nitrate of Roseocobalt. The chloride of Roseocobalt is dichrous, the ordinary being paler than the extra- ordinary image; both are rose-red, with a faint brownish orange tint. Chloride of Roseocobalt, as already mentioned, has the formula ONH;,.Co,C],+2HO as the following analyses show : 0.7291 grs. gave 0.4235 grs. of sulphate of cobalt = 22.10 per cent. of cobalt. 0.6247 grs. gave 0.3619 gers. i GS CAS) 68 oY 0.9834 grs. gave 0.5742 gers. chloride of silver = 89,54 4 chlorine. 1.8112 grs. gave 2.9095 grs. ef as = 39.71 “ ft 2.2390 grs. gave 1.2829 ers.. water = 637 * hydrogen. 1.4993 grs. gave 0.8784 gers.“ = 6.50 * ss 1.2235 grs. gave 282 c. c. nitrogen at 22.95 C. and 766"".82 (at 23° C.) = 254.91 ¢. e. at 0° and 760™ = 26.16 per cent. The formula requires— Calculated. Found. Cobalt . ; DEG FT, 21.99 22.10 Chlorine . : i . 39.66 BST 39.71 Hydrogen : é be) (B5838} 6 37 6.50 Nitrogen ’ : . 26.08 26.16 a eg AMMONIA-COBALT BASES. 11 With respect to this formula, it must be remarked that it is extremely difficult to obtain this chloride perfectly free from chloride of Purpureocobalt, into which it is so easily converted. The uncertainty, however, will concern only the number of equivalents of water. ‘The chloride of Roseocobalt combines with the chlorides of the electro-negative metals to form well defined salts. The platinum salt, which we have not yet fully examined, appears to have the formula ONH;.Co.Cl;+ 3PtCl,+ 8HO. A neutral solution of the chloride of Roseocobalt is easily decomposed by boiling, with evolution of ammonia, and precipitation of a black powder. This powder is probably a hydrate of the magnetic oxide, Co,0,+ «HO, but we have deferred its examination to the second part of our memoir. The reactions of the chloride of Roseocobalt are as follows : Terchloride of gold gives no precipitate at first, but after standing a lilac or purple precipitate, which is probably merely the chloride of Roseocobalt. Bichloride of platinum gives a pale orange red precipitate. Chloride of mercury gives a pale rose or flesh-colored flocky precipitate. Ferridcyanide of potassium gives beautiful orange-red oblique rhombic crystals. Cobaltidcyanide of potassium gives fine red crystals. Ferrocyanide of potassium gives a cinnamon, passing to a chocolate brown pre- cipitate. Oxalate of ammonia gives a brick-red precipitate of small granular crystals. Neutral chromate of potash gives no precipitate. Bichromate of potash gives a dark brick-red precipitate. The following reactions, which were obtained with a solution of the hydrated nitrate of Roseocobalt may also be introduced in this place. Pyrophosphate of soda gives a dull rose-red precipitate soluble in an excess of the precipitant to a clear red liquid, which in a few minutes solidifies to a mass of fine rose-red needles. Picrate of ammonia gives a fine bright orange-red precipitate soluble in hot water. Todide of potassium gives no precipitate either with the chloride or nitrate. The precipitate with chloride of mercury is readily soluble in chlorhydric acid, and the solution after standing gives beautiful small granular crystals of a brownish red color. The reactions which are peculiar to the sulphate of Roseocobalt will be described when speaking of that salt. SULPHATE OF ROSEOCOBALT. An ammoniacal solution of sulphate of cobalt absorbs oxygen readily from the air, becoming at first brown and then dark red. The time required for complete oxidation varies remarkably. The process is sometimes complete in a few days, but often requires many weeks. From the perfectly oxidized solution, sulphuric acid cautiously added usually throws down the sulphate of Roseocobalt as a bright red crystalline powder, which, after washing with cold water, is readily purified by solution and crystallization, a very small quantity of acid being added to prevent decomposition. 12 RESEARCHES ON THE The sulphate of Roseocobalt is, however, not always the only salt formed under these circumstances. In some cases in which the ammoniacal liquid was allowed to stand several months until there remained only a dry mass of red crystals, warm water dissolved out a red salt in small quantity, much more soluble than the sulphate of Roseocobalt, and giving different and very characteristic reactions. In other cases, and especially when a little chloride of cobalt was originally present, warm water dissolved out another sulphate, crystallizing in octahedra of an orange-red color, the examination of which is not yet complete. We are unable to confirm Frémy’s assertion that sulphuric acid precipitates from oxidized ammoniacal solutions of sulphate of cobalt, an acid sulphate of Roseo- cobalt, having the formula 5NH;.Co0,0;,580;+ 5 HO. The salt precipitated under these circumstances is merely the neutral sulphate, as repeated analyses lave shown, and as the crystalline form at once proves. The formula of the neutral sulphate is SNH;.Co,0;,380;+ 500 as the following analyses show : 0.8160 grs. gave 0.3800 ers. sulphate of cobalt = 17.72 per cent. cobalt. 0.8272 grs. gave 0.3869 grs. @ Bo = yoy®), ay 0.2760 grs. gave 0.2908 grs. sulphate of baryta = 36.11 per cent. sulphuric acid. 0.5781 grs. gave 0.6074 grs. te ff 3 OS OOM tid a he 1.4925 grs. gave 0.8250 grs. water == (6.00455 114 hydrogen. 1.2840 grs. gave 0.7109 ers. ej Gulley @ tf 1.2108 grs. gave 220.5 ¢. c. nitrogen at 189.4 C. and 761™".23 (at 18°.9) = 201.97 c. ¢. at 0° and 760" = 20.95 per cent. nitrogen. ; 1.0404 grs. gave 194.2 c. c. nitrogen at 209.5 C. and 754™".37 (at 209.5) = 174.67 ¢. c. at 0° and 760" = 21.08 per cent. nitrogen. ‘ The formula as above stated requires Eqs. Calculated. Found. Mean. Cobalt. Yee) 59.0 17.71 17.72 17.79 17.75 Sulphuric acid . 8 120.0 36.03 36.11 36.38 36.24 Hydrogen m0) 20.0 6.00 6.14 6.15 6.14 Nitrogen . 5 70.0 21.02 - 20.95 21.08 21.01 Oxygen . Baars) 64.0 19.24 — — 18.86 333.0 100.00 100.00 The sulphate of Roseocobalt has a fine cherry-red color. The light reflected from a layer of the crystals when analyzed by the dichroscopic lens, gives a rose-red ordinary, and an orange-red extraordinary image. The dichroism is very distinct. In this, as in our other observations upon dichroism, the reflected rays examined made an angle of about 60° with the normal, but no material variations of color could be observed by changing the angle of incidence. The exact color of the crystals is, according to Chevreul, the second red 2-10ths. The crystals of sulphate of Roseocobalt belong to the dimetric or square prismatic system, as determined AMMONIA-COBALT BASES. 13 by Prof. Dana. The observed forms are represented in Figs. 1, 2, and 3. The measured angles are as follows: Fic. 3. Fie. 1. 1:1 = 107° 20’ ys 1: a = 126° 20’ w@ : 1d = 137° 21’ | O : 1d = 132° 35’ (cale. 132° 39’) a = 1.0866. 4 Prof. Dana remarks that the angles are very close to those of Cerasine; and also to those of Scheeletine or tungstate of lead, if 17 be 4 and 1 be Ii. The sulphate of Roseocobalt is nearly insoluble in cold water, but is soluble in much boiling water, and crystallizes readily as the solution cools. By slow evapo- ration, it may be obtained in large crystals, which, however, seldom exhibit very perfect faces. Ammonia in dilute solution dissolves the sulphate, giving a fine purple solution, from which the salt crystallizes unchanged. The neutral solution is readily decomposed by boiling, ammonia being evolved, and a dark brown preci- pitate of the hydrated magnetic oxide of cobalt, Co,0,+3HO, thrown down, while sulphate of Luteocobalt remains in solution. The decomposition in this case extends to the sulphate of Luteocobalt also, so that much less than one equivalent of this salt is obtained for two equivalents of the sulphate of Roseocobalt decom- posed. Strong ammonia poured upon dry sulphate of Roseocobalt usually changes its color almost immediately from a red to a buff yellow, while the liquid itself be- comes red. The buff colored substance formed in this case, is the sulphate of Luteo- cobalt; the red solution contains sulphate of Roseocobalt. When dry sulphate of Roseocobalt is carefully heated in a porcelain or platinum crucible, ammonia is evolved, and there remains a lilac-red mass, which contains sulphate of Luteocobalt, sulphate of Purpureocobalt, and a leek-green crystalline substance which we have called provisionally Praseocobalt. We shall speak of all these reactions more fully when treating of the sulphate of Luteocobalt. A current of the red gas which arises from the action of nitric acid upon starch, and which probably consists chiefly of NO, converts an acid, neutral, or ammonia- cal solution of sulphate of Roseocobalt into one of the nitrate of Xanthocobalt. A solution of sulphurous acid gently heated with sulphate of Roseocobalt gives, in a few minutes, an orange precipitate of a substance containing ammonia, sesqui- oxide of cobalt, sulphurous and sulphuric acid, and which we shall describe fully in the second part of our memoir. Strong sulphuric acid digested with sulphate of Roseocobalt yields, under some circumstances, sulphate of ammonia and sulphate of Luteocobalt. In other cases 14 RESEARCHES ON THE it yields the acid sulphate of Purpureocobalt. By double decomposition with salts of barium the sulphate of Roseocobalt yields the other salts of this base. The reactions of the sulphate are somewhat different from those of the chloride, as will be seen from the following statement. Ferridcyanide of potassium gives no precipitate at first, but after two hours very distinct and well defined small augitic crystals. Cobaltidcyanide of potassium behaves in a precisely similar manner, giving red crystals. Neutral chromate of potash gives no precipitate. The bichromate gives none at first, but after two or three hours, groups of reddish brown needles. We shall hereafter state our reasons for believing that in certain cases there is a conversion of the triacid Roseocobalt in the sulphate of this base, into the biacid Purpureocobalt. ANHYDROUS NITRATE OF ROSHOCOBALT. The ammoniacal solution of nitrate of cobalt absorbs oxygen very readily from the air, and the oxidation is usually complete after a few days. As a general rule, a considerable quantity of nitrate of Luteocobalt is formed under these cir- cumstances, and being insoluble in the ammoniacal liquid, forms a bright yellow crystalline precipitate upon the bottom and sides of the vessel. During the process of the oxidation, crystals of the compound -deseribed by Frémy as the nitrate of Oxycobaltiaque are frequently formed in some quantity, but these disap- pear at a later stage of the oxidation, when the liquid takes a deep wine-red color. The crystals of nitrate of Oxycobaltiaque were first observed by Leopold Gmelin. We have not particularly examined or analyzed them, though Frémy’s analyses do not appear to us satisfactory. The dark-red liquid formed under these circumstances contains nitrate of Roseo- cobalt. When nitric acid is added to this solution, a brick-red precipitate is thrown down, which is the hydrated nitrate of Roseocobalt. This nitrate is readily solu- ble in water, and exists unchanged in the solution, but by boiling with nitric acid, the solution yields a fine violet-red crystalline precipitate of the anhydrous nitrate of Roseocobalt. The presence of nitrate of ammonia facilitates the oxidation and formation of nitrate of Roseocobalt, but is not indispensable. The preparation of pure nitrate of Roseocobalt is attended with difficulty, as the precipitated crystalline nitrate almost always contains a little nitrate of Luteocobalt. It is best to dissolve the crude nitrate in water, to which a little ammonia has been added, to filter and allow the solution to evaporate spontaneously. After some days, large and well defined crystals of the nitrate are formed, while the bottom of the evaporating vessel is covered with minute red crystals of the same salt. The difference between the appearance of the large and small crystals is so great that we suspected a difference in their constitution. Analysis and the behavior of the two kinds towards reagents, showed, however, no difference. A marked variation in the color of the large and small crystals of the same substance is very commonly AMMONIA-COBALT BASES. 15 observed in the ammonia-cobalt compounds, and might easily lead to erroneous conclusions. The nitrate of Roseocobalt is readily prepared by decomposing a solution of the chloride with nitrate of silver, but the solubility of the chloride of silver in chloride of Roseocobait renders it somewhat difficult to obtain a pure salt in this manner. Nitrate of copper also gives nitrate of Roseocobalt with chloride of copper, when mixed with an equivalent proportion of chloride of Roseocobalt; but the purification is difficult. Finally, a pure nitrate may be prepared by double decomposition of nitrate of baryta and sulphate of Roseocobalt. The anhydrous nitrate of Roseocobalt, when in large crystals, has a fine red color, which, accord- ing to Chevreul’s determination, as given by Frémy, is the first red =. The crystals are dichrous; the ordinary image is clear rose red, the extraordinary image bright red. According to Prof. Dana, this salt, like the sulphate, crystallizes in forms belonging to the dimetric system. Figs. 4 and 6 represent some of the more usual combinations, Fig. 5 is a very rare form, which was obtained only once. Fic. 4. Fie, 5. Fic. 6. 1: 1 (over the base) = 82° 40’. ES Z Whence 0 : 1 (not observed) = 138° 20’. oe Ammonia dissolves the nitrate with a fine purple red tint, and the salt usually crystallizes unchanged from the solution, though sometimes the hydrous nitrate is obtained. In cold water the nitrate is rather insoluble, though more soluble than the sulphate. Hot water dissolves it rather more easily; but the solution, unless it be acid, is quickly decomposed, and this effect is very speedily produced by boiling. The products of the decomposition in this case are a dark-brown oxide of cobalt, and a solution containing the nitrate of Luteocobalt and nitrate of ammonia. The quantity of Luteocobalt is small in comparison with that of the nitrate of Roseocobalt employed. When heated, the nitrate of Roseocobalt explodes, though not with violence. A black anhydrous oxide remains, which is probably Co,0;. The reaction in this case is easily explained, if we remark that the oxygen in the nitric acid is exactly sufficient to form water with the hydrogen of the ammonia. The simplest equa- tion representing the reaction is SNH;.Co,0;,3 NO;=Co,0;+ 8N +15HO. In point of fact, however, the decomposition is less simple, as red vapors are always evolved. When a current of NO, is passed through a solution of nitrate of Roseocobalt a rapid absorption takes place, and after a short time crystals of nitrate of Xantho- cobalt are deposited. 16 RESEARCHES ON THE A solution of sulphurous acid converts the nitrate of Roseocobalt, at first into an orange-colored compound containing SO,, and afterward reduces this completely to nitrate and sulphate of cobalt and nitrate of ammonia. Nitrate of Roseocobalt has the formula 5NH;.Co,03,3NO; as the following analyses show: 0.2308 ers. gave 0.1081 grs. sulphate of cobalt = 17.82 per cent. cobalt. 0.1272 grs. gave 0.0599 grs. ee OSS yee o 0.1448 grs. gave 0.0681 ers. ‘ CO er MBO e 0.9370 ers. gave 0.3915 gers. water = 4.64 per cent. hydrogen. 0.6632 grs. gave 0.2862 gers. “ = 479 * ue 2.7312 grs. gave 1.1258 gers. “‘ c=) AUDIO mane He 0.5564 ers. gave 168 c. c. nitrogen at 24° C. and 766.31 (at 249.5) = 150.54 ¢. e. at 0° and 760™" = 33.98 per cent. 0.7400 grs. gave 213 c. c. nitrogen at 18°.5 C. and 764"™.28 at (13.98) = 200.55 ¢. c. at 0° and 760" = 34.03 per cent. The formula above mentioned requires Eqs. Calculated. Mean. Found. Cobalt . 6 2 59.0 17.87 17.88 17.82 17.92 17.90 Hydrogen . 15 15.0 4,55 4.60 4.64 4.79 4.57 Nitrogen . 8 112.0 B40 34.01 83.98 34.03 — Oxygen Pls 144.0 43.65 43.51 — — — 330.0 100.00 100.00 When nitrate of Roseocobalt is dissolved in water containing much nitrate of ammonia and a little ammonia, and the solution is allowed to evaporate sponta- neously, beautiful purple-red scaly crystals separate. These crystals cannot be purified by recrystallization, as they are decomposed by solution in water. When boiled with chlorhydric acid there is copious effervescence and a purple-red solu- tion is obtained, which appears to contain the, chloride of Purpureocobalt. The empirical formula of the scaly nitrate appears to be 5NH,.Co,0,,2NO;+ 7HO. From the effervescence with muriatic acid we are disposed to consider it 4NH;. Co,0;,NO,+NH,O,NO,+6HO, but further investigation is required before we can pronounce with certainty on this point. HYDROUS NITRATE OF ROSEOCOBALT. When ammonia is added in excess to a solution of the nitrates of cobalt and of ammonia and the solution is exposed to the air, oxidation takes place with con- siderable rapidity, and as we have already stated when speaking of the anhy- drous nitrate, the solution becomes dark purple-red, while yellow scales of the nitrate of Luteocobalt are more or less abundantly deposited upon the bottom of the vessel. When the red liquid is boiled with nitric acid in excess, a dark crimson precipitate of nitrate of Roseocobalt is formed, while a portion of the same salt remains in solution. It has hitherto been supposed from these facts that AMMONIA-COBALT BASES. 17 the anhydrous nitrate of Roseocobalt is a direct product of the oxidation of the ammoniacal liquid. This, however, is not the case. If the oxidized liquid be filtered from the nitrate of Luteocobalt and allowed to evaporate spontaneously, very fine large oblique rhombic crystals are formed, which are the hydrous nitrate of Roseocobalt. The crystals of this nitrate belong to the monoclinic or oblique rhombic system, according to Prof. Dana’s determination. The observed forms are J li, wi, -li, u, or in other symbols, 0, 1-00, c-0, —l-o, o-%. Hig. 7. The angles are IKE Ya rs if = 1028 li: % = 136° -lé:% = 140° 30’ ian 1d :-1¢ = 96° 30’ and ¥3° 30’ 5 The hydrous nitrate of Roseocobalt is readily soluble even in cold water; the hot neutral solution is very easily decomposed with evolution of ammonia and precipitation of a black powder. The addition of a few drops of nitric acid pre- vents the decomposition. An excess of nitric acid added to a cold solution of the nitrate produces a brick-red precipitate, which is readily soluble in cold water, and which is the unchanged salt. The solution has a dark brick-red color, and exhibits all the reactions of the chloride of Roseocobalt. When boiled with an excess of nitric acid for some time, the brick-red color gradually becomes violet-red, and there remains at last a beautiful violet precipitate, which is the anhydrous nitrate of Roseocobalt. From this it appears that, im some cases at least, and particularly when nitrate of ammonia is present during the oxidation, the hydrous nitrate of Roseocobalt is the first product of the oxidation of an ammoniacal solution of nitrate of cobalt, and that it is the action of nitric acid upon this salt which con-~ verts it into the anhydrous nitrate. The nitrate of Roseocobalt obtained by direct oxidation may be recrystallized by adding to its solution a few drops of nitric acid and allowing it to stand a few days for spontaneous evaporation. In this manner beautiful crystals are obtained, adhering to the bottom of the evaporating vessel, and mixed with a dull-red matter in crystalline crusts, which exhibits the same reactions with the large and clear crystals, and appears to have the same constitu- tion, though upon this point we cannot speak with certainty at present. We consider the formula of the hydrous nitrate of Roseocobalt as most probably 5NH,.Co,0;,3NO;+ 2HO as the following analyses indicate : 0.8265 gers. gave 0.37038 grs. sulphate of cobalt = 17.05 per cent. cobalt. 0.5275 grs. gave 0.2370 gers. . aC = WyoQ) a 0.8012 ers. gave 217.8 c. c. nitrogen at 119.5 C. and 761"™.48 (at 11°.4 C.) = 206.05 c. ¢. at 0° and 760" = 32.30 per cent. 0.7667 grs. gave 207 c. c. of nitrogen at 14° C. and 766"".56 (at 149.2 C.) = 194.91 ¢. c. at 0° and 760" = 31.92 per cent. The formula requires : Eqs. Calculated. Found. Cobalt 2 16.95 17.05 17.09 Nitrogen 8 32.18 52.30 31.92 (Sk) 18 RESEARCHES ON THE It is true that the analyses here agree with the formula as well as can be reasonably expected. We have, however, found in other crystals from the same mass 17.82, 17.86, 17.92, 18.06 per cent. cobalt, numbers which agree much better with the formula of an anhydrous nitrate, having the same formula as the nitrate of Roseocobalt already described, which contains 17.87 per cent. In any event, the doubt appears to be simply with respect to the quantity of water in the salt, the ratio of the equivalents of cobalt and nitrogen being as 1 to 4, or 2 to 8. We shall return to this point at another time. S OXALATE OF ROSHEOCOBALT. The oxalate is precipitated from the chloride almost immediately by the addition of a solution of oxalate of ammonia. From a solution of the nitrate it is deposited much more slowly, often only after some hours, and sometimes in remarkably distinct and well formed crystals. The oxalate as first thrown down may be purified by solution in ammonia-water and recrystallization by spontaneous evaporation. The salt then forms beautiful prismatic crystals, which are nearly insoluble in water, and which have a fine cherry-red color, resembling the crystals of sulphate of Roseocobalt. The crystals are dichrous, the ordinary image being pale violet, while the extraordinary image is dark rose-red. The precipitated oxalate has a dull brick-red color. According to Prof. Dana, the crystals of oxalate of Roseocobalt belong to the right rhombic or trimetric system, the observed forms being a rhombic prism of about 101° 48’, with a brachydome of 108° 54’. The constitution of the oxalate of Roseocobalt is represented by the formula, 5NH;.Co,05,3C,0,+ 6HO as the following analyses show: 0.5504 ers. gave 0.2625 gers. sulphate of cobalt = 18.15 per cent. 0.3325 gers. gave 0.1585 grs. “ Ge tea a eal 1.5381 grs. gave 0.6170 grs. carbonic acid = 32.82 per cent. oxalic acid. The formula requires Eqs. Calculated. Found. Cobalt . i gee! 17.87 18.15 18.14 Oxalic acid . 5 8} 32.73 32.82 — COBALTIDCYANIDE OF ROSHOCOBALT. This beautiful salt is precipitated from a solution of the chloride or hydrous nitrate of Roseocobalt, by a solution of cobaltidcyanide of potassium. It may be prepared with equal facility from a solution of the chloride of Purpureocobalt, which under these circumstances, as we conceive, undergoes a direct change into a salt of the triacid Roseocobalt. The cobaltidcyanide is usually precipitated at once in the form of cherry-red prismatic crystals, which, so far as it is possible to judge from their appearance under the microscope, belong to the oblique rhombic AMMONIA-COBALT BASES. 19 or monoclinic system, much resembling some of the simpler forms of augite. The salt is very insoluble in cold water; hot water readily decomposes it. It forms an extremely characteristic test for the salts of Roseocobalt in general, as well as for the chloride of Purpureocobalt, but, as already remarked, it is precipitated from the sulphate of Roseocobalt only after some hours. The crystals are usually remarkably large when compared with the mass of liquid from which they are thrown down. They are more distinct in form the more slowly the precipitation takes place. The salt has the formula 5NH;.Co,Cy,+ Co,Cy,+ 3HO as the following analyses show : 0.1924 grs. (from chloride of Purpureocobalt) gave 0.1540 grs. sulphate of cobalt = 30.46 per cent. cobalt. 0.7150 grs. (from chloride of Roseocobalt) gave 0.5755 grs. sulphate of cobalt = 30.63 per cent. cobalt. 0.8111 grs. (from chloride of Roseocobalt) gave 272 ¢. ¢. of nitrogen at 10° C. and 761"".99 (at 10° C.) = 259.48 ¢. c. at 0° and 760" = 40.18 per cent. The formula requires Eqs. Calculated. Found. Cobalt . é . 4 80.57 30.63 30.46 Nitrogen : pple: 39.89 40.18 The analyses of the ferrideyanide of Roseocobalt give additional evidence of the correctness of the formula adopted for this salt. FERRIDCYANIDE OF ROSEOCOBALT. The ferridcyanide is formed like the cobaltideyanide by adding a solution of fer- rideyanide of potassium to one of chloride or nitrate of Roseocobalt or chloride of Purpureocobalt. A very beautiful orange-red precipitate is thrown down in dis- tinct and usually extremely well-defined crystals, which under the microscope, exactly resemble those of the corresponding cobalt salt. The crystals exhibit a remarkable dichroism, the ordinary image being of a fine purple rose color, while the extraordinary image is bright orange red. The crystals are insoluble in cold water; hot water easily decomposes them, ammonia being evolved, while a dark- brown precipitate is thrown down. Heat decomposes the dry salt very gradually and uniformly, and leaves a black residue which contains much carbon. We availed ourselves of this fact to determine accurately the sum of the cobalt and iron in the salt, by first decomposing it by heat, then burning off the carbon in a gentle current of oxygen, and finally reducing the mixed oxides of cobalt and iron in a current of hydrogen. The formula of this salt is 5NH,.Co,Cy,+ Fe,Cy,+3HO “as the following analyses show: 0.3618 grs. gave 0.1086 grs. metallic iron and cobalt = 30.05 per cent. 1.5028 grs , burnt with oxide of copper and oxygen, gave 1.0302 grs. carbonic acid = 18.69 per cent. carbon. Co) 0 RESEARCHES ON THE The formula requires Eqs. Calculated. Found. Cobalt andiron . Phe 30.02 30.05 Carbon 5 0 g 18.79 18.69 There can be no reasonable doubt that this salt is isomorphous with the corre- sponding cobalt salt. Like the latter it is an extremely valuable test for the salts of Roseocobalt and for certain salts of Purpureocobalt. OXIDE OF ROSEOCOBALT. The oxide of Roseocobalt exists only in solution. It is obtained either by decomposing the chloride by oxide of silver, or by adding baryta-water to a cold solution of the sulphate; the latter method is the better one, because the chloride of silver is soluble in solutions of the chloride of Roseocobalt. The solution as thus obtained is red, has an alkaline non-metallic taste and reaction, and is very easily decomposed. By standing in the air it absorbs carbonic acid and forms a carbonate. MAGNETIC OXIDE OF COBALT. In connection with the’ salts of Roseocobalt we may perhaps with propriety describe the peculiar oxide of cobalt, which is, in some cases at least, one of the products of their decomposition. The hydrated oxide which is precipitated by boiling the neutral salts of Roseocobalt with an alkaline solution is considered by Frémy as a hydrate of the sesquioxide, and he attributes to it the formula Co,0,,HO. According to the same chemist, all the other ammonia-cobalt bases give this hydrate by boiling with solutions of the alkalies. It does not appear probable that the oxide obtained by boiling the neutral solution should have a different constitution. We have however found that the dark-brown oxide obtained by boiling a solution of sulphate of Roseocobalt, and afterward washing and drying the precipitate in the air, has the formula Co,0, + 3HO as the following analyses show: T. 0.4430 ers. gave 0.6990 grs. sulphate of cobalt = 60.05 per cent. of cobalt. II. 0.9269 grs. gave 0.1672 ers. water (ignited with chromate of lead) = 18.03 per cent. III. 0.7150 grs. ignited in hydrogen gas gave 0.3010 grs. water, which in connection with the 2d analysis gives 21.38 per cent. oxygen in the oxide of cobalt. The formula requires Eqs. Calculated. Found. Cobalt 5 O 88.5 60.00 60.05 Oxygen . 0 . 4 32.0 21.69 21.38 Water 3 27.0 18.30 18.038 147.5 100.00 99.46 Frémy’s formula requires 64 per cent. of cobalt. Claudet gives also the formula Co,0, + 3HO as probable, but without analyses. On the other hand, it is possible AMMONIA-COBALT BASES. Q1 that the different salts, not only of Roseocobalt. but of the other similar bases, may give different oxides by decomposition. We propose to examine this point more fully hereafter. The hydrate above mentioned and analyzed is a very dark-brown powder, which - dries to a black mass with a gummy lustre. The powder is dark brown. Oxalic acid dissolves it to a green solution, without evolution of gas, but this is decom- posed by heating. Chlorhydric acid also dissolves the oxide, with evolution of chlorine and formation of the protochloride. We have already mentioned that the anhydrous magnetic oxide of cobalt is sometimes obtained during the decomposition of the chloride of Roseocobalt by heat. We are, however, not able to state precisely under what circumstances this occurs; either water or the oxygen of the air must take part in the decomposition, since the chloride contains no oxygen. The anhydrous oxide occurs in the form of small steel-gray octahedra, which are very hard, and which can only be dissolved by long heating with sulphuric acid, or by fusion with sulphate of potash. Nitric, chlorhydric, and nitro-muriatic acids have no decided action upon them. 1.6425 ers. of this oxide gave 1.2059 grs. of metallic cobalt = 73.41 per cent. 1.6425 ers. ignited in hydrogen gave 0.4879 grs. water = 25.91 per cent. oxygen. The formula Co,0, requires Eqs. Calculated. Found. Cobalt. c Sue) 88.5 73.44 73.41 Oxygen . . ie 32.0 26.56 25.91 120.5 100.00 99.32 This oxide has recently been described by Schwarzenberg, who obtained it by igniting chloride of cobalt with free access of air, until the chlorine is expelled. It is, therefore, very probable that in the decomposition of chloride of Roseocobalt by heat, the chloride of cobalt is first produced, and then decomposed in the manner observed by Schwarzenberg. With respect to the black sulphide which is thrown down from solutions of the ammonia-cobalt bases by sulphide of ammonium, it can scarcely be doubted that this is the bisulphide, as Claudet’s analyses lead directly to the formula CoS8., corrobo- rating the results obtained by Dingler already alluded to. PURPUREOCOBALT. The salts of Purpureocobalt are often found among the direct products of the oxidation of ammoniacal solutions of cobalt. They are often formed from the salts of Roseocobalt by heating or by boiling with strong acids, the cobalt passing, as we conceive, from one modification to another. The salts of Purpureocobalt are also formed in great abundance by the action of acids upon salts of Xanthocobalt, and we are disposed to think that they may also occur, though rarely, among the pro-. ducts of the decomposition of salts of Luteocobalt. The salts of Purpureocobalt are distinguished by a fine violet-red or purple color, 92 RESEARCHES ON THE which is common to nearly all of them, and which is very different from the com- paratively dull red of the salts of Roseocobalt. They are in general somewhat less soluble than the compounds of Roseocobalt, and crystallize, for the most part, in well defined crystals. When neutral they have a purely saline, non-metallic taste. Heat readily decomposes the salts of this base; the final products of the decom- position are the same as in the case of the salts of Roseocobalt, but intermediate products are often formed. The neutral solutions are readily decomposed by boil- ing, the products of the decomposition being a black or dark-brown oxide of cobalt and a salt of ammonium, free ammonia being given off. In some cases, however, salts of Luteocobalt are intermediate products of this decomposition. All the salts of Purpureocobalt by long boiling with an excess of chlorhydric acid yield the chloride. CHLORIDE OF PURPUREHOCOBALT. The substance which we shall describe under the name of chloride of Purpureo- cobalt is the same as that to which Frémy gave the name of chloride of Roseo- cobaltiaque. In the course of our investigations it at length became clear that, under the name of salts of Roseocobalt, the compounds of two perfectly distinct bases have hitherto been confounded. It became, therefore, necessary to devise a new name. The purple color of the salts which correspond to the chloride now to be de- scribed, led us to adopt the name of Purpureocobalt for the radical of these salts, as more appropriate than Roseocobalt, which we have retained for most of the salts to which it was originally applied. Such a change is to be regretted; it could not, however, have been avoided, without an introduction of two entirely new names. We have already stated that the chloride of Purpureocobalt is often a product of the direct oxidation of an ammoniacal solution of the chloride of cobalt exposed to the air. In these cases it is sometimes mixed with chloride of Roseocobalt, and sometimes forms the entire product of the oxidation. We believe that the tempe- rature at which the process of oxidation goes on is the condition which determines the character and the amount of the chloride which is formed during the oxidation. The chloride of Roseocobalt is, in our view, the first product of the oxidation under all circumstances. At a moderately high temperature, however, the chloride passes as fast as it is formed into chloride of Purpureocobalt, which may thus be the only final product of the oxidation, or may be mixed with variable proportions of the chloride of Roseocobalt. In one experiment made during the summer season, and in which chemically pure chloride of cobalt and ammonia were employed, the process of oxidation went on very slowly, without the precipitation of any trace of sesquioxide of cobalt. The liquid had a dull purple color, and gave with reagents no precipitates or reactions to indicate the presence of chloride or oxide of Purpureocobalt or Roseocobalt. On boiling with chlorhydric acid, however, the chloride of Purpureo- cobalt was thrown down in abundance, and no other substance could be detected in the supernatant liquid. In this case the oxidized liquid gave no precipitate with a ntint AMMONIA-COBALT BASES. TS chlorhydric acid in the cold, but the cold solution, after some hours standing, deposited distinct crystals of chloride of Purpureocobalt. We believe that in this case a combination of the oxide and chloride existed in the solution, so that, as we have already suggested in speaking of the chloride of Roseocobalt, the oxidation itself would be expressed by the equation 6CoC1+ 15NH;+30=5NH,.Co,0;+ 2(5NH;.Co,C];). If we admit that the oxide and chloride of Purpureocobalt as thus formed are actually in combination so as to form a sort of oxychloride, and are not merely mechanically mixed, we may perhaps explain, why no precipitates of salts of Pur- pureocobalt are obtained in the oxidized liquid, since the reagents added might not be able to overcome the affinity between the oxide and chloride. It is easy to see that by boiling with chlorhydric acid, the combination of oxide and chloride will give the chloride alone, since we may have the equation ONH;.Co,0;+.5(5NH3.Co,Cl,) + 3HC1=3(5NH;.Co,Cl;) +3 HO. We have already mentioned that the chloride of Roseocobalt is readily converted into chloride of Purpureocobalt, by boiling with chlorhydric acid, or even by gently heating its solution. This circumstance explains why only the chloride of Purpureocobalt is obtained by boiling a completely oxidized ammoniacal solution of chloride of cobalt, even when this solution contains only Roseocobalt, or a mix- ture of Roseocobalt and Purpureocobalt. It also enables us to understand why all writers upon the ammonia-cobalt bases, up to the period of the present investiga- tion, entirely overlooked the chloride of Roseocobalt, and consequently described the salts of that base, as if they corresponded to, and contained the same radical as chloride of Purpureocobalt. Tt is not necessary to add chloride of ammonium to the ammoniacal solution of chloride of cobalt, in preparing the chloride of Purpureocobalt. It is, however, ad- vantageous to do so, because, the oxide of Purpureocobalt is converted by it as fast as formed into the chloride, and the formation of the oxychloride is prevented. To prepare the chloride of Purpureocobalt in a pure state from the oxidized liquid, it is only necessary to boil this with an excess of chlorhydric acid. A crimson powder is thrown down, while the supernatant liquid becomes nearly colorless, provided, at least, that a pure salt of cobalt was employed, and that the oxidation was complete. The mother liquor is to be poured off and the precipitate dissolved in a large quantity of boiling water, to which enough chlorhydric acid has been added to render the solution distinctly acid. On cooling, the solution gives small but beautiful crystals of the chloride, almost perfectly pure. A second crystalliza- tion usually removes all traces of impurity. It is not, however, necessary to use a pure chloride of cobalt in preparing the chloride of Purpureocobalt. Any com- mercial oxide will answer, even when arsenic, nickel, iron, &., are present. On the other hand, it is easy to prepare a perfectly pure chloride of cobalt, by heating the chloride of Purpureocobalt in a porcelain crucible until vapors of ammonia and chloride of ammonium cease to be given off. The pure chloride of cobalt thus obtained, is remarkable for its beauty of color, the anhydrous chloride forming pale (So) 4 RESHARCHES ON THE blue taleose scales, while the solution and the crystals obtained from this have a very fine violet-red tint. The chloride of Purpureocobalt may be prepared by other methods. One of the most interesting of these is, by the action of strong chlorhydric acid upon a salt of Xanthocobalt. It is almost a matter of indifference which salt of Xantho- cobalt is employed. As, however, the nitrate is, perhaps, most easily obtained in a pure state, it is usually most advantageous to employ this. The nitrate has the formula NO,.5NH;.Co,0,,2NO;+ HO. On boiling with chlorhydric acid, the salt is slowly converted from a brown-yellow to a lilac-purple powder, which is insoluble in the supernatant acid liquid. After boiling strongly for an hour or two, almost all the original salt is decomposed, NO, is given off in abundance during the boiling, while a lilac colored uncrystallized mass remains at the bottom of the fask. The supernatant liquid is to be poured off, and boiling water added to the insoluble portion. A brown-yellow or dark sherry wine colored solution is usually formed, which is again to be poured off, and the washing repeated till the liquid has a clear purple color. The red mass is then to be dissolved in boiling water, to which a little chlorhydric acid has been added, and filtered. On cooling, the chloride of Purpureocobalt crystallizes in small bril- liant crystals, which must be repeatedly recrystallized to separate all traces of impu- rity. The washings, on boiling with chlorhydric acid, yield a fresh portion of the chloride. The reaction which takes place under these circumstances may be expressed by the equation NO,.5NH,.Co,0;,2NO;+3HC1=NO,+2NO,,HO+5NH;.Co,Cl,+ HO. As already remarked, the chloride or sulphate of Xanthocobalt may be employed in a precisely similar manner, and also yield the chloride of Purpureocobalt. When the sulphate is used, however, the resulting chloride is apt to retain sulphuric acid with much obstinacy, and can with difficulty be freed from it. Another method of preparing the chloride of Purpureocobalt, consists in boiling the chloride or nitrate of Roseocobalt with chlorhydric acid. This method is very convenient, and yields a very pure chloride. The chloride of Purpureocobalt may also be prepared by boiling the acid sul- phate of this base with chlorhydric acid. In this case, however, as in all others in which sulphuric acid is present in the solution, the chloride should be boiled with a little chloride of barium, and repeatedly recrystallized, to separate traces of the isomorphous sulphate of Roseocobalt formed at the same time. The chloride of Purpureocobalt has a beautiful violet-red or purple color, and is dichrous, the ordinary ray being colorless, while the extraordinary ray has a rich violet-red tint. Its solution is violet-red. The salt is nearly insoluble in cold water, but is soluble without decomposition in boiling water, to which a few drops of chlorhydric acid have been added. From this solution it separates, on cooling, in very brilliant small crystals, which are simpler in form, the purer the solution from which they have crystallized. The crystals belong to the square prismatic or dimetric system, according to Prof. Dana, and not to the regular system, as stated in previous memoirs. AMMONIA-COBALT BASES. join, IP Beale Coe 12 Coe 1 :1 over the base = 114° 8’; over the top = 65° 52’. 1 :1 over the terminal edge = 107°—107° 20’ (calculated 107° 12’). O :1 (calculated) = 122° 56’. O : 1d (calculated) = 132° 30’. : 1¢ : 1¢ over the base = 95°; over the top = 85°. a = 1.0916. 25 The observed forms are the octahedron and first and second The angles in Dana’s notation are (see Fig 1): The crystals are usually small but extremely well formed; those which are obtained from solutions containing a little chloride of mercury most frequently exhibit the planes of the first and second prism, and are larger than those which separate from pure solutions. - From these measurements, it appears that the chlo- ride of Purpureocobalt is isomorphous with the sulphate of Roseocobalt. This iso- morphism is the more remarkable, inasmuch as a precisely similar case occurs with the chloride and sulphate of Luteocobalt, between which there is a similar differ- ence of constitution. Thus we have 5NH,.Co,Cl;=5 N H3.Co,0;,880;+ 5HO 6NH,.Co,Cl,=6NH;.Co,0;,350;+5HO. From this it appears that in both cases we have the crystallographic equality 3C1=0,,380,+5HO. The density of the crystals of chloride of Purpureocobalt, as taken in alcohol, is 1.802 at 23° C.; the atomic volume of the chloride is consequently 139.0. The chloride of Purpureocobalt has the formula 5NH:;.Co,Cl, as appears from the following analyses: 0.5215 ers. 0.4962 grs. 0.8514 grs. 1.4116 grs. 0.7550 grs. 0.6116 grs. 0.6124 grs. 1.4184 grs. 1.6636 grs. 0.4754 grs. 0.1966 grs. 0.4972 grs. 0.5963 ers. 0.6036 grs. gave 168.16 c. c. nitrogen at 752™".60 and 15° OC, h = 93™".5, t = 15°.6 ©, gave 0.3230 grs. of sulphate of cobalt gave 0.3073 gers. gave 0.5269 grs. gave 0.8732 grs. gave 0.4105 grs. gave 0.3412 ers. gave 0.3365 grs. gave 0.7800 grs. gave 2.8540 gers. gave 0.8200 grs. gave 0.3365 ers. gave 0.8553 ers. 6c “ec a3 “ce water it “ce sé chloride of silver ce “ce = 23.58 per cent. cobalt. = 23.57 Sy uy = IB fs = WEB cs . = 6.04 per cent. hydrogen. == (pill) sf ee = G10 © Ww = lil sf ue = 42.40 per cent. chlorine. = 42.49 fy ae = 42.31 + a =— 9A 8 es G6 gave 143 c. c. nitrogen at 18° C. and 772™™.4 (at 18°.4 C.) = 133.19 c. ¢. at 0° and 760™" = 28.05 per cent. nitrogen. 0.5542 grs. gave 134 ec. c. nitrogen at 19° C. and 766™".56 (at 199.4 C.) = 123.26 ¢. ¢. at 0° and 760™" = 27.93 per cent. nitrogen. I 135.08 ¢. c. at 0° and 760™" = 28.11 per cent. nitrogen. 0.5755 grs. gave 160.39 c. ¢. nitrogen at 771™".39 and 15° C,h = 112™".7, t = 15° ©, 128.86 c. c. at 0° and 760™™ = 28.12 per cent. nitrogen, The nitrogen in these as in all our analyses was moist. 4 296 RESEARCHES ON THE Hence we have Eqs. Theory. Mean. Found. Cobalt 2 59 23.55 23.56 23.58 93.57 23.55 23.55 Chlorine 3 106.5 42.50 42.43 42.49 42.31 42.52 42.40 Hydrogen . 15 15 5.98 6.11 6.04 6.19 6.10 6.11 Nitrogen . 5 70 27.97 28.01 28.05 27.93 28.12 28.11 250.5 100.00 100.11 The agreement of these analyses leaves no reasonable doubt that the true form- ula of the chloride of Purpureocobalt is 5NH;.Co.Cl,, as first correctly determined by Rogojski, and subsequently by Gregory. Frémy gives in addition one equivalent of water, while Claudet makes 16 in place of 15 equivalents of hydrogen. That the salt, however, contains but 15 equivalents is clear, from the fact that free nitrogen and hydrogen are found among the products of its decomposition by heat in an atmosphere of carbonic acid gas, which could not be the case upon Claudet’s view, since we should then have the equation N;H,,Co,Cl,=5NH,+ 2CoCl+ HCl, while the presence of free nitrogen and hydrogen renders it probable that the decomposition is in reality expressed by the equation 5NH3.Co,C];=2CoCl+ NH,C1+3NH,+N+H,. We have more than once endeavored to determine the amount of gas actually given off during this decomposition, with the view of verifying the equation just given. In every case, however, a portion of the chloride of cobalt was reduced, either by the free ammonia or by the hydrogen, so that much metallic cobalt was found mixed with the chloride. A neutral solution of the chloride of Purpureo- cobalt is readily decomposed by boiling, a dark-brown precipitate, probably of the hydrated magnetic oxide, being thrown down, while the solution becomes brown- yellow, and contains chloride of ammonium and chloride of Luteocobalt, ammonia being at the same time given off. The quantity of chloride of Luteocobalt which is thus formed is always very small, being very much less than one equivalent for two equivalents of the chloride of Purpureocobalt. On the other hand, a solution of chloride of Purpureocobalt may be boiled for a very long time with concentrated chlorhydric acid without decomposition, and this stability in the presence of acids is one of the most remarkable peculiarities of the whole class of ammonia-cobalt salts. Chlorhydric acid and the alkaline chlorides precipitate chloride of Purpureo- cobalt from its solutions almost completely, slowly in the cold, but instantly on boiling. Ignited in a current of hydrogen, the salt yields metallic cobalt as a gray spongy mass. Heated in an open crucible, the salt fuses and swells up, giving off abundant vapors of chloride of ammonium and ammonia, while pure chloride of cobalt remains in lavender-blue scales. In some cases, however, this is mixed with metallic cobalt, while in others, in which the ignition takes place with free access of air, brilliant iron-black octahedra are formed, which are the anhydrous magnetic oxide of cobalt, Co,0O,. The red gas arising from the action of nitric acid upon AMMONIA-COBALT BASES. 07 starch or sawdust exerts a very remarkable influence upon the chloride of Pur- pureocobalt, converting it into the nitrate of a base, which will be described further on under the name of Xanthocobalt. Sulphurous acid solution throws down from solutions of the chloride a dull orange- brown precipitate, which appears to be a sulphite. By boiling with an excess of the acid this is reduced, and there remains a solution of a protosalt of cobalt. Sulphuric acid, under certain conditions, converts chloride of Purpureocobalt into the acid sulphate of the same base. Zine may be boiled a long time with an acid solution of the chloride without producing decomposition or reduction. Formic and oxalic acids have no reducing action. Protochloride of tin simply unites with the chloride of Purpureocobalt so as to form a chloro-salt. The chloride of Purpureocobalt exhibits a remarkable tendency to unite with metallic chlorides to form chloro-salts. Such compounds are formed with the chlorides of Platinum, Palladium, Mercury, Tin, Zinc, and various other metals. The chloride of Purpureocobalt even dissolves chloride of silver in large quantity, doubtless forming with it a double chloride. It is for this reason, that it is not generally advantageous to prepare the salts of Purpureocobalt by double decompo- sition between the chloride and salts of silver. The reactions of a pure solution of the chloride of Purpureocobalt are as follows: Ferrocyanide of potassium gives a yellowish precipitate which quickly becomes chocolate-brown. Ferridcyanide of potassium gives a beautiful bright orange-red crystalline preci- pitate. Cobaltideyanide of potassium gives a fine red crystalline precipitate. Oxalate of ammonia gives a beautiful purple-red precipitate of fine needles. Pyrophosphate of soda gives a lilac precipitate easily soluble in an excess of the precipitant. Neutral chromate of potash gives a brick-red precipitate. Bichromate of potash gives orange-yellow scales. Picrate of ammonia gives a beautiful yellow precipitate. Terchloride of gold precipitates the chloride unchanged. Bichloride of platinum gives a fine cinnamon-brown precipitate of crystalline scales. Sulphide of ammonium gives a black precipitate. Chloride of mercury gives fine rose-red needles, easily decomposed. Bichloride of tin gives pale peachblossom-red silky needles. Molybdate of ammonia gives a pale peachblossom-red precipitate. Alkalies and their carbonates give no precipitate. Iodide and bromide of potassium give no precipitate. Chlorhydrie acid and the alkaline chlorides throw down the chloride of Pur- pureocobalt from its solutions as a violet-red powder. The reactions of the chloride of Purpureocobalt with the ferrideyanide and cobaltideyanide of potassium and with oxalate of ammonia are not sufficient to distinguish it from the chloride of Roseocobalt, which, when pure and freshly pre- 28 RESEARCHES ON THE pared, gives also precipitates with these reagents. The character of the precipi- tates with oxalate of ammonia, bichloride of platinum, and bichromate of potash enable us, however, readily to distinguish the chloride of Purpureocobalt from chloride of Roseocobalt, with which, however, it is not likely to be confounded. CHLORPLATINATE OF PURPUREOCOBALT. When a solution of bichloride of platinum is added to one of the chloride of Purpureocobalt, a brown-red precipitate is thrown down, which is a combination of the two chlorides. When dried it has a fine rich brown-red color and high lustre. The crystals seen under the microscope are usually aggregations of flat pale reddish- brown needles. They are very distinctly dichrous, the ordinary image being pale _violet-rose, while the extraordinary image is rich orange-red. The chlorplatinate is nearly insoluble in cold, and with great difficulty soluble in hot water. It resists the action of reducing agents much more powerfully than the chlorplatinates of the alkaline metals. Thus it must be boiled for a very long time with zine and chlorhydric acid before a complete reduction of the platinum is effected. If the process be interrupted before the reduction is complete, brilliant yellow granular crystals are often formed in the liquid. We have not determined the constitution of these crystals, but they are not chlorplatinate of ammonium. Sulphurous acid reduces this double chloride readily, and yields a red solution containing the protochlorides of platinum and of cobalt. We may here remark, that so far as our observation has hitherto extended, the action of a reducing agent upon any constituent of a compound containing an ammonia-cobalt base extends invariably to the ammonia-cobalt base itself. The chlorplatinate of Purpureocobalt has the formula ONH;.Co,C];+2PtCl, as the following analyses show: 0.6765 ers. (reduced by boiling with SO, and the platinum precipitated as sulphide by NaO.S,O, after adding HCl) gave 0.2267 ers. of platinum = 33.51 per cent. 0.9521 ers. gave 0.3169 grs. of platinum and 0.2483 grs. sulphate of cobalt = 9.93 per cent. cobalt. grs. gave grs. of chloride of silver = 41.80 per cent. chlorine. The formula requires Eqs. Calculated. Found. Cobalt . ; ate 10.10 9.93 Platinum 6 ae 33.50 33.51 Chlorine... Bie 42.01 41.80 This salt is identical with the chlorplatinate described and analyzed by Claudet, and for which that chemist found the same formula, with the exception of the hydrogen, which he makes 16 in place of 15 equivalents. We have also obtained it from a chloride which gave the reactions of chloride of Roseo- cobalt, but we must leave it for the present undecided whether in this case there was a conversion of Roseocobalt into the isomeric Purpureocobalt, by the AMMONIA-COBALT BASES. 29 action of the chloride of platinum, or whether the chloride of Roseocobalt had already undergone the change. We consider it certain that the salt in question is a salt of Purpureocobalt, because it contains two in place of three equivalents of bichloride of platinum. We shall show further on, that the oxygen salts of this base contain either fo or four equivalents of acid, and it is well known that in the chlorplatinates there is—we believe invariably—but one equivalent of bichlo- ride of platinum for each equivalent of chlorine in the chloride with which it is united. Since there are three equivalents of chlorine in this chloride of Purpureo- cobalt, we infer that two of them are differently combined from the other two, so that the rational formula of the chlorplatinate is 5NH,.Co,C1.Cl,+ 2PtCl,. We shall develop this view more fully when speaking of the oxygen salts of Purpureocobalt. ; OXALATE OF PURPUREOCOBALT. This most beautiful salt is readily prepared by adding a solution of oxalate of ammonia to one of chloride of Purpureocobalt. After a short time violet-red needles are thrown down, which may be washed with cold water. As thus pre- pared, the salt is almost chemically pure. The color of the oxalate of Purpureo- cobalt is the violet 5%; of the first circle of Chevreul’s scale; the crystals are not sensibly dichrous. We have not, as yet, obtained measurable crystals of this salt. Under the microscope four- and six-sided acicular prisms are distinguishable, but without characterizing terminal planes. The oxalate of Purpureocobalt has the formula 5NH;.Co,0;,20,0;+ 3H0 as the following analyses show: 0.2723 gers. gave 0.1574 gers. sulphate of cobalt = 22.00 per cent. of cobalt. 0.3545 grs. gave 0.2045 grs. ge ae = 21.95 : ss 0.8970 grs. burnt with oxide of copper gave 0.2973 grs. carbonic acid = 27.11 per cent. of oxalic acid. The formula requires Eqs. Calculated. Found. Cobalt . , Eo) 22.09 22.00 21.95. Oxalic acid . Be 26.96 27.11 — The oxalate is nearly insoluble in cold water, and not very soluble in boiling water, even after addition of free oxalic acid. The salt does not crystallize well from its solutions, and we have always obtained it in the most beautiful form by direct precipitation from the chloride. The salt is neutral to test paper, and is the only neutral oxysalt of Purpureocobalt which we have yet obtained. It will appear from what follows, extremely probable that there is an acid oxalate of Pur- pureocobalt containing four equivalents of oxalic acid. We have not obtained such a salt, however, in one or two experiments made for the purpose. 30 RESEARCHES ON THE ACID SULPHATE OF PURPUREOCOBALT. Our efforts to obtain a neutral sulphate of Purpureocobalt containing two equiva- lents only of sulphuric acid have hitherto been fruitless. When a solution of chloride of Purpureocobalt is treated with sulphate of silver, chloride of silver is formed, and the red supernatant liquid yields, on evaporation, crystals of sulphate of Roseocobalt. Precisely the same result is obtained with the chloride and nitrate of silver; the red solution yielding crystals of nitrate of Roseocobalt. We con- sider it probable that in these cases the sulphate and nitrate of Purpureocobalt, 5NH;.Co,0,,2S0;, and 5NH;.Co,0;,2NO,;, are really formed by double decomposi- tion, but that during evaporation the equivalent of free sulphuric or nitric acid formed at the same time with the sulphate or nitrate, reacts upon this so as to con- vert it into a salt of Roseocobalt with three equivalents of acid. In equations we should have for the sulphate 5NH,.Co,Cl,+-3A¢0,SO,+ HO=5NH;.Co,0;,280, + HO,SO;+ 3AgCl. 5NH,.Co.0;,280,+ HO,SO;=5NH;.Co,0,,350,+ HO. When oil of vitriol is poured upon chloride of Purpureocobalt in quantity suffi- cient to make a thick paste, the mass assumes a fine purple color, and swells up very much at first, so that a large vessel is necessary. If the solution, after the evolu- tion of chlorhydric acid has ceased, be diluted with about twice its volume of water, and allowed to stand for a few hours, a large mass of beautiful violet-red needles is deposited. The mother liquor, after standing for a longer time, deposits more crys- tals. These crystals are to be quickly washed with a little cold water, drained and dried by pressure between folds of bibulous paper. They are usually free from chlorine, and are very nearly pure acid sulphate of Purpureocobalt. The mother liquor contains more of the acid sulphate together with small quantities of another sulphate which we shall describe more fully hereafter, and frequently a little unde- composed chloride. By boiling this mixture with chlorhydric acid chloride of Purpureocobalt is formed, which may be employed in preparing a fresh portion of the acid sulphate. The acid sulphate of Purpureocobalt may also be prepared by the action of strong sulphuric acid upon the sulphate of Roseocobalt. For this purpose oil of vitriol is to be poured upon the sulphate in quantity sufficient to produce an oily liquid on heating in a water bath. The digestion is to be continued for one or two hours, according to the quantity of salt employed, care being taken that no oxygen is evolved. The dark purple liquid is to be suffered to cool, diluted with an equal bulk of water, and allowed to crystallize. The acid sulphate as thus obtained is difficult to purify. By dissolving it in a small quantity of hot water, and evaporating it quickly, fine crystals may some- times be obtained. When, however, the solution is evaporated slowly in the air, crystals of sulphate of Roseocobalt are formed in abundance, while the mother liquor contains free sulphuric acid. When a solution of the acid sulphate is neutralized AMMONIA-COBALT BASES. : 31 with ammonia, and allowed to crystallize by slow evaporation, the sulphate of Roseocobalt is also obtained, but by rapid evaporation dark-red, prismatic crystals are sometimes formed, which we have not yet obtained in sufficient quantity for a complete analysis. They may prove to be the neutral sulphate of Purpureo- cobalt. The acid sulphate of Purpureocobalt crystallizes in fine, red, prismatic crystals, which, according to Prof. Dana, belong to the trimetric system, and are hemihedral. The observed forms are I, w, 37, 17, 7 (?) or in other symbols », o-oo, 1-0 ,12 oo-2 (2): ? Fia. 8. I: I = 106°. I: i = 127° (126° 50’—127° 10’) 4a: i= 129° 49’. 13} 6 19} == aye Gy Gebee— ier 6 ike Weyl Fig. 8 represents an end view of a crystal of this salt; 12 is hemihedral and i2 usually so: the symbol 72 is probably correct, though the observed angle varies much. The acid sulphate is very soluble in water, and has a distinct though not strongly acid taste. It reddens litmus, and expels carbonic acid from the carbonates. The formula of this salt is 5NH;.Co,0;,450,+ 5HO as the following analyses show : 0.620 grs. gave 0.2577 grs. sulphate of cobalt = 15.82 per cent. cobalt. 1.1402 grs. gave 0.4756 grs. HY “= 15.86 “ ey 1.5317 grs. gave 1.9270 grs. sulphate of baryta = 43.19 ss sulphuric acid. 1.5843 grs. gave 0.7570 grs. water = 5.31 per cent. hydrogen. 1.1869 grs. gave 189.5 c. c. of nitrogen at 15° C. and 775™".2 (at 15°.3 C.) = 179.6 ¢. c. at 0° and 760™" = 19.00 per cent. nitrogen. The formula requires Eqs. Calculated. Found. Cobalt 2 15.81 15.82 15.86 Sulphuric acid . 2 42.89 43.19 Hydrogen . . 20 5.36 5.31 Nitrogen. st 15 18.76 19.00 The acid sulphate gives no precipitate with 5KCy,Co,Cy,, but only a fine red liquid, which, on evaporation, yields a red mass. Boiled with chlorhydric acid the sulphate yields the chloride of Purpureocobalt, easily recognized by oxalate of ammonia, with which, however, the acid sulphate itself gives no precipitate. When precipitated with nitrate of baryta the acid sulphate yields a red liquid which probably contains a nitrate of Purpureocobalt, but which on evaporation gives crystals of nitrate of Roseocobalt. It is well worthy of notice, that this red liquid contains a large quantity of sulphate of baryta in solution, which it deposits during evaporation. The products of the decomposition of the acid sulphate are similar to those of 32 _ RESEARCHES ON THE the other salts of Purpureocobalt. A rapid current of NO, passed into the solu- tion gives, after a short time, an abundant precipitate of the nitrate of Xantho- cobalt. The constitution of the acid sulphate might be represented by either of the following formule, besides that already given: 5NH,.Co,0;,390,+HO,S0,+4HO 5NH,,.Co,0,,2S0,+2H0,80,-+ 3HO. We reject the first of these formulz because Purpureocobalt is a biacid and not a triacid base. The second formula appears to us less probable than that which we have adopted, in the first place, because a salt so constituted ought to be strongly acid, and in the second place, because we shall presently show that there exists an oxalo-sulphate of Purpureocobalt, in which ¢wvo equivalents of sulphuric are replaced by two of oxalic acid, and another and neutral oxalo-sulphate in which one equivalent of oxalic acid replaces one equivalent of sulphuric acid. ACID OXALO-SULPHATE OF PURPUREOCOBALT. When sulphate of Roseocobalt is boiled for several hours with an excess of a solution of oxalic acid, a clear red solution is formed, which on evaporation deposits an abundance of crystals of a bright brick-red color, and indistinct acicular form. These crystals are soluble in hot water without decomposition, and may be purified, though with difficulty, by recrystallization. Their constitution is represented by the formula 5NH;,.Co,0,,280,,2C,0;-+ 3 HO as appears from the following analyses: 0.7438 grs. gave 0.3315 grs. sulphate of cobalt = 16.97 per cent. cobalt. 1.3912 ers. gave 0.9535 gers. sulphate of baryta = 23.50 Ss sulphuric acid. 1.6895 grs. gave 1.1564 grs. ae = 23.49 oe sulphuric acid. 2.7702 ers. gave 0.7070 grs. carbonic acid = 20.88 se oxalic acid. 2.0198 grs. gave 340 c. ec. of nitrogen at 149.5 C. and 763™".01 (at 15° C.) = 318.1 ¢.c¢. at 0° and 760™™ = 19.78 per cent. nitrogen. The formula requires Eqs. Calculated. Found. Cobalt . 2 17.00 16.97 Sulphuric acid 2 23.05 23.49 23.50 Oxalie acid 2 20.74 20.88 Nitrogen oS) 20.17 19.78 The reactions of this remarkable salt resemble closely those of the acid sulphate. It has an acid taste and reaction, gives no precipitate with oxalate of ammonia, or cobaltidcyanide of potassium, and yields chloride of Purpureocobalt by boiling with an excess of chlorhydric acid. The formula of this salt may be written in various ways. In the first place, we may consider it as a double salt represented by the formula 5NH,.Co,0,,4S0,+ 5NH,.Co,0,,4C0,0,+ 6HO. AMMONIA-COBALT BASES. 33 The advantage of simplicity is evidently in favor of the formula we have adopted. We may also consider it as represented by 5NH;.Co,0,,280,+2C,0,,HO+HO. In this case the salt should have a strongly acid taste which it has not. On the whole the formula 280, 26,0, * 3HO 5NH,.Co,0; \ appears to deserve the preference. NEUTRAL OXALO-SULPHATE OF PURPUREOCOBALT. When ammonia is added to a solution of the acid oxalo-sulphate just described, a fine violet-red color is produced, and if no more ammonia be added than is suffi- cient to completely neutralize the acid reaction, the liquid yields, on evaporation, beautiful red prismatic crystals of a neutral salt. The neutral oxalo-sulphate is much less soluble in water than the acid salt, and has a purely saline taste: it is easily decomposed by boiling. The formation of this salt is represented by the equation _ONH;.Co,0;,280,,20,0,+ 2NH,O=5N H;.Co,0,,80;,C,0;+ NH,0,SO,+ NH,0,C,0;. The fact that the ammonia unites with both sulphuric and oxalic acid, and not simply with two equivalents of oxalic acid, throws much light on the constitution of the acid oxalo-sulphate, and shows, we think, clearly that the formula of this salt cannot be 5NH;.Co,0,,2S0,+ 2C,0,, 10+ HO. The constitution of the neutral oxalo-sulphate is represented by the formula 5NH,.Co,0,, ' Ag F THO 23 as appears from the following analyses: 0.6367 grs. gave 0.3217 gers. sulphate of cobalt = 19.23 per cent. cobalt. 0.6721 grsi gave 0.2569 grs. sulphate of baryta = 13.12 per cent. sulphuric acid. 0.9760 grs. gave 191 c. c. nitrogen at 179.25 C. and 7677".58 (at 17°.8) = 177.43 ¢c. c. at 0° and 760™" = 22.88 per cent. The formula requires Eqs. Calculated. Found. Cobalt . j Tee? 19.21 19.23 Sulphuric acid ere a 13.02 13.12 Oxalic acid . Sth 11.72 Nitrogen : 5°68 22.80 22.83 We may further remark that the character of the action of ammonia upon the acid oxalo-sulphate leads us to hope that the neutral sulphate of Purpureocobalt may be obtained by the action of this agent upon the acid sulphate, and that in fact, this is the salt already mentioned as so obtained, but not yet analyzed. The two oxalo-sulphates described constitute, we believe, the types of an entirely new 5 34 RESHARCHES ON THE class of salts, and lead to the idea that sulphuric and oxalic acids may possibly be capable of replacing each other in other combinations. OXIDE OF PURPUREOCOBALT. The oxide of Purpureocobalt, like that of Roseocobalt, appears to exist only in solution. It may be prepared, either by decomposing the acid sulphate by baryta water, or by digesting a solution of the chloride with oxide of silver in the cold. The solution is not pure in either case, containing either sulphate of baryta or chloride of silver in solution. The oxide, as thus prepared in solution, forms a violet-red liquid, which absorbs carbonic acid readily from the air, and which is decomposed by concentration. The constitution of the oxygen salts of Purpureocobalt, which we have described, as well as that of the chlorplatinate of this radical, appears to us to leave no reasonable doubt that the oxide is essentially biacid. According to the rule that the number of equivalents of acid in a salt is equal to the number of equivalents of oxygen in the base, the rational constitution of the oxide of Purpureocobalt will be expressed by the formula 5NH;.Co,0.0,. We shall develop this view more fully when occupied with the purely theoretical portion of the subject, and in the second part of our memoir we shall endeavor, by the analysis and description of other salts of Purpureocobalt, to throw more light upon the nature of this remarkable radical. The chromates, pyrophosphate, and picrate of Purpureocobalt have, in particular, occupied our attention. We have mentioned, in speaking of the reactions of chloride of Purpureocobalt, that both the cobaltideyanide and the ferridcyanide of potassium give precipitates ~ in its solution. The constitution, crystalline form and physical appearance of these two precipitates exactly agree with those of the cobaltidcyanide and ferrid- cyanide of Roseocobalt, and we have, therefore, not hesitated to identify them with these last. We believe that in this case there is a conversion of Purpureocobalt into Roseocobalt, since in the salts in question there are three equivalents of cyanogen in the electropositive for three in the electronegative cyanide, the form- ulze being as mentioned above SNH;.Co,Cy,; + Co,Cy,;+3HO, and 5NH;.Co,Cy,+ Fe,Cy,+3HO. As Purpureocobalt is certainly biacid, its cobaltideyanide and ferridcyanide should have the formule 3(5NH;.Co,Cy,) +2Co,Cys, and 3(5NH,.Co,Cy;) +2FeCys, although the frequent occurrence of basic double cyanides may render this point less clear than the others which also involve the biacid character of the radical. AMMONIA-COBALT BASES. 35 “LUTEOCOBALT. The salts of Luteocobalt have a yellow or brown-yellow color, and are almost always well crystallized. They are in general more soluble in water than the corresponding salts of Roseocobalt; the solutions have a brown-yellow color. The salts of Luteocobalt are very stable in the presence of acids in general, but are decomposed by long heating with sulphuric acid. The neutral and alkaline solu- tions are readily decomposed by boiling, like the salts of the other cobalt bases. Nearly all of them have a purely saline taste. When hydrated, these salts gene- rally effloresce in dry air or in vacuo, and become opaque, with a peculiar porce- lain-like lustre and reddish-buff color. The salts of Luteocobalt may be formed, like those of the other bases described, by direct oxidation: it is well worthy of notice, however, that they are often found among the products of the decomposition of the salts of Roseocobalt and Purpureocobalt. This is especially remarkable, because the constitution of Roseocobalt is simpler than that of Luteocobalt, the former base being 5NH,.Co,0;, while the latter is 6NH;.Co,0;. We have here a singular inversion of the usual law, that the products of the decomposition of a complex molecule are more simple in constitution than the body decomposed. Luteocobalt, like Roseocobalt, is a triacid base. CHLORIDE OF LUTEOCOBALT. When an ammoniacal solution of chloride of cobalt, to which a large quantity of coarsely powdered chloride of ammonium has been added, is exposed to the air for some days, it often happens that no traces of chloride of Roseocobalt or Purpureocobalt are found, but the bottom of the vessel becomes covered with orange-yellow crys- tals, which are the chloride of Luteocobalt. Chlorhydric acid precipitates an addi- tional quantity of the salt from the supernatant liquid. The raw chloride, as thus obtained, is easily purified by solution in hot water, filtration, and repeated crys- tallization. This method of preparing the salt is by no means always successful, and very frequently results only in the formation of chloride of Roseocobalt and Purpureccobalt, with scarcely a trace of the chloride of Luteocobalt. We have, however, almost invariably succeeded in preparing, by this process, a mixture of the sulphate and chloride of Luteocobalt, by employing a solution containing both the chloride and sulphate of cobalt. The sulphato-chloride resulting, by boiling with chlorhydriec acid and chloride of barium, yields a solution from which the pure chloride may be obtained by repeated crystallization. The chloride of Luteocobalt crystallizes by slow evaporation, in remarkably beautiful brownish-orange colored crystals, which belong to the trimetric or right rhombic system, and which are isomorphous with the sulphate of Luteocobalt. According to Prof. Dana, the usual 5 5 OYA 5 : 3 ~~ ~ ~~ forms are, in his modification of Naumann’s notation, O, », 2,0-3, 1- &, s- @, ome 36 RESEARCHES ON THE with the angle I: I = 113°. 16’. Fic. 9 represents a erystal of this salt with Dana’s notation for the faces: IG Bl =e TNO) IG! 8%: 8% = 52° 26’ (over O) O : 1% = 145° 55’ 3% : 8¢ = 127° 34’ (adjacent) ON 3t = T16O 13" O:2 = 118° 35’ (by observation) 1%: 1% = 112° 2’ (over O) Frémy states that this salt crystallizes in regular octahedrons; in this case it must be dimorphous, but we have never observed any forms belonging to the regular system. The chloride of Luteocobalt is readily soluble in boiling water, and crystallizes in a great measure from the solution on cooling. Chlorhydric acid and alkaline chlorides precipitate it unchanged. When boiled with sulphuric acid, the salt gives off abundance of chlorhydric acid gas, but it is difficult to drive off all the acid without decomposing a portion of the resulting sulphate. The salt is slowly decom- posed by boiling ammonia, chloride of ammonium, and a dark brown oxide of cobalt being the only products of the decomposition which we have been able to detect. Reducing agents in general act upon this salt as upon chloride of Roseocobalt and Purpureocobalt. We have not yet, however, been able to obtain with the chloride of Luteocobalt compounds analogous to those which are produced by the action of sulphurous acid and deutoxide of nitrogen upon the chlorides of Roseo- cobalt and Purpureocobalt, although we have repeatedly made the attempt. The chloride of Luteocobalt is dichrous. In the dichroscopic lens the ordinary image is pale violet, while the extraordinary image is orange-violet. The color of the salt, in coarse powder, approaches the orange-yellow of the first circle, but the color of the mass of crystals could not be defined by the chromatic scale, which we employed. Chloride of Luteocobalt exhibits a remarkable tendency to form chloro-salts with metallic chlorides. These salts are formed with great ease, by the direct union of the two chlorides, and are worthy of notice for their stability and capacity of crystallization. Of these salts, which are very numerous, we have examined only the compounds with gold and platinum. The analyses of chloride of Luteocobalt lead to the formula 6NH,.Co,Cl., 0.2036 grs. gave 0.1180 ers. sulphate of cobalt = 22.05 per cent. cobalt. 0.3350 grs. gave 0.1938 gers. a i = BLO a a 0.5110 grs. gave 0.2970 grs. He 216 se € 0.3335 grs. gave 0.1980 ers. is ORE} ss tt 0.2942 grs. gave 0.4723 ers. chloride of silver = 39.67 ‘¢ chlorine. 0.4886 gers, gave 0.7846 ers. o = BOSS + a 0.3902 gers. gave 0.2346 ers. water = 6.68 «« hydrogen. 0,4617 grs, gave 0.2800 ers. i = 6.73 i oH AMMONIA-COBALT BASES. 37 0.7305 grs. gave 200.5 ¢. ¢. of nitrogen at 21°.5 C. and 765™".80 (t = 22°.2 C.) = 182.3¢. ¢. at 0° and 760™" = 31.34 per cent. nitrogen. 0.7778 grs. gave 212 c. c. of nitrogen at 18° C. and 762.75 (t = 18°.6 C.) = 194.94 ¢. ¢. at 0° and 760" = 31.49 per cent. nitrogen. Comparing these with the calculated results, we have Eqs. Theory. Mean. Found. Cobalt . 0 2 59.0 22.06 2205 22.05 22.01 22.11 22.02 Chlorine ° 3 106.5 39.79 39.73 39.68 39.78 _— — Hydrogen . 18 18.0 6.73 6.70 6.68 6.73 — — Nitrogen 0 6 84.0 31.42 31.41 31.49 31.34 — — 267.5 100.00 99.89 The formula 6NH;.Co,Cl,; is given, by both Frémy and Rogojski, and no reasonable doubt can be entertained of its accuracy. The density of the chloride of Luteocobalt, as taken in alcohol, is 1.7016 at 20° C., its atomic volume is con- sequently 157.2. The reactions of the chloride of Luteocobalt are as follows: Todide of potassium gives a bright yellow precipitate. Bromide of potassium gives a less brilliant yellow precipitate. Ferrocyanide of potassium gives a chamois colored precipitate, which becomes black on boiling. Ferridcyanide of potassium gives beautiful yellow needles, which are nearly insoluble. Cobaltidcyanide of potassium gives a pale fawn colored precipitate of fine needles. Terchloride of gold gives bright yellow granular crystals of the chloraurate. Bichloride of platinum gives yellow or orange-yellow needles of the chlor- platinate. Chromate of potash gives a bright yellow precipitate of the chromate. Oxalate of ammonia gives a buff yellow precipitate, soluble in oxalic acid. Tribasic phosphate of soda gives, after a short time, a yellow precipitate. Pyrophosphate of soda gives a pale buff colored precipitate. Picrate of ammonia gives a beautiful yellow precipitate of very fine silky needles. Alkalies and their carbonates produce no precipitate in the cold. Sulphide of ammonium gives a black precipitate. CHLORPLATINATE OF LUTEOCOBALT. Chloride of platinum produces, immediately, in a solution of the chloride of Luteocobalt, a beautiful orange or yellow precipitate of the chlorplatinate. When the solutions employed are concentrated, the precipitate is orange colored; when the solutions are dilute, yellow needles are thrown down. The difference is here only in the quantity of water of crystallization, and the orange granular crystals may be converted into the pale yellow needles by solution in a large quantity of hot water and recrystallization. 38 RESEARCHES ON THE According to Prof. Dana’s measurements, the acicular crystals belong to the monoclinic system, so far as it is possible to determine. The crystals are usually hollow and much striated longitudinally. The observed forms are I, i and O, and the angles Fie. 10. 1g lS NOKe tO! I: a = 148° 50’ O : a = 114° 15’ Twin crystals are frequent, the composition being parallel to the plane O. The salt is very slightly soluble in cold water, but dissolves in much boiling water, from which it separates on cooling. When gently heated in a porcelain crucible it gives off ammonia and chloride of ammonium, and becomes green. The green mass, on solution in water, gives globular aggregations of minute crystals of a buff color, which may be a new salt, but which we have not specially examined. Zine decomposes the chlorplatinate of Luteocobalt only by very long boiling in an acid solution, metallic platinum being separated as a black powder, while chlorides of cobalt and ammonium are formed. The formula of the orange salt is 6NH;.Co,Cl;, +3 PtCl,+6HO as the following analyses show : 1.220 ers. gave 0.4321 gers. metallic platinum = 35.41 per cent. 1.220 ers. gave 0.2261 grs. sulphate of cobalt = 7.05 per cent. cobalt. Eys. Calculated. Found. Cobalt . : oy et 7.10 7.05 Platinum : wee 35.64 35.41 The formula of the yellow salt is 6NH;.Co,C1,+3PtCl,+21HO as appears from the analyses: 0.2688 ers. gave 0.0822 grs. metallic platinum = 31.16 per cent. 0.4449 ers. gave 0.6087 grs. chloride of silver = 33.54 per cent. chlorine. Eqs. Calculated. Found. Platinum ; ei) 30.99 31.16 Chlorine . 6 > & 83.42 33.54 Rogojski found in-this salt but one and a half equivalents of water, but his analyses are not very satisfactory, giving a large excess of platinum, hydrogen, and cobalt. AMMONIA-COBALT BASES. 39 CHLORAURATE OF LUTEOCOBALT. A solution of terchloride of gold produces immediately in solutions of the chloride of Luteocobalt a beautiful yellow precipitate of small granular crystals. These crystals are very insoluble in cold water, but more readily soluble in boiling water acidulated with chlorhydric acid. Reducing agents separate gold with full metallic lustre. The formula of this salt is 6NH;.Co,C1,+ AuCl, as the analyses satisfactorily show : \ 0.7308 gers. gave 0.1025 ers. Co,0, 10.53 per cent. cobalt. 0.7308 grs. gave 0.2530 gers. gold 34.62 per cent. 0.6457 grs. gave 0.9714 ers. chloride of silver = 37.36 per cent of chlorine. Eqs. Calculated. Found. Cobalt 2 10.33 10.53 Gold 1 34.50 34.62 Chlorine . 6 37.30 37.36 IODIDE OF LUTEOCOBALT. Iodide of potassium produces immediately in solutions of the chloride, sulphate, or nitrate of Luteocobalt, a remarkably beautiful bright yellow precipitate of the iodide of Luteocobalt. This precipitate is rather insoluble in cold water, but readily soluble in hot water. The solution yields by spontaneous evaporation brown-yellow crystals, which appear to have the same form as the chloride. 0.2224 ors. of this salt gave 0.06308 ers. sulphate of cobalt, corresponding to 10.79 per cent. cobalt. The formula 6NH;.Co,1; requires 10.88 per cent. cobalt. The color of the precipitated and dried iodide is very fine, and its brilliancy led us to hope that it might be advantageously employed as a pigment. On trial, however, the color was found wanting in body; the yellow, moreover, changes to a brown-yellow when the powder is ground in oil or water. BROMIDE OF LUTEOCOBALT. Bromide of potassium gives a rather dull yellow precipitate in solutions of Luteocobalt. The precipitate, re-dissolved in hot water, gives, on slow evapora- tion, wine-yellow crystals of the bromide. These crystals have the same form as those of the chloride, and their formula is therefore 6NH,.Co,Br;. 40 RESEARCHES ON THE COBALTIDCYANIDE OF LUTEOCOBALT. -Cobaltideyanide of potassium produces in solutions of Luteocobalt a pale yellowish flesh-colored precipitate of the double cyanide of cobalt and Luteocobalt. The salt is insoluble in cold water, and easily decomposed by boiling water. It cannot, therefore, be re-crystallized for analysis. Under the microscope the crystals are seen to belong to the oblique rhombic system; they are too small to admit of accu- rate measurement. The formula of this salt is 6NH;.Co,Cy;+ Co,Cy;+ HO. 0.4835 grs. gave 0.3923 grs. sulphate of cobalt = 30.88 per cent. cobalt. 0.7652 gers. gave 0.38580 grs. water = 5.19 per cent. hydrogen. 2.1845 grs. gave 0.6800 grs. carbonic acid = 18.82 per cent. carbon. Eqs. Calculated. Found. Cobalt . C . 4 80.57 30.88 Carbon . 0 eel? 18.70 18.82 Hydrogen. . 19 4.93 5.19 A solution of ferrideyanide of potassium produces a most beautiful precipitate of orange-yellow needles in solutions of Luteocobalt. These, under the microscope, have the same form as the corresponding cobalt salt, and their formula is therefore 6NH,.Co,Cy;+ Fe,Cy;+ HO. SULPHATE OF LUTEOCOBALT. The sulphate of Luteocobalt is easily procured mixed with the chloride, when solutions of both chloride and sulphate of cobalt are rendered ammoniacal and exposed to the air after the addition of coarsely powdered chloride of ammonium in large excess. The mass of yellow crystals formed upon the bottom of the vessel, after a few days, is a mixture of the two salts. To obtaim the sulphate from this mass, the solution in hot water is to be filtered and digested with sulphate of silver, after addition of a few drops of sulphuric acid. In this manner the whole of the chloride may be decomposed, and the filtered solution on evaporation will yield fine crystals of the sulphate. We have frequently prepared large quantities of the sulphate by this method. Another mode of preparing the sulphate of Luteocobalt, which is often very convenient, consists in pouring ammonia upon the sulphate of Roseocobalt, thrown down by cautious addition of sulphuric acid to perfectly oxidized solutions of the ammoniacal sulphate of cobalt. When this sulphate is powdered, and strong ammonia poured upon it, its color frequently changes from red to a dull buff, while the supernatant liquid takes a fine red color. The buff powder on solution in hot water and evaporation yields crystals of sulphate of Luteocobalt. The red liquid is merely a solution of sulphate of AMMONIA-COBALT BASES. 41 Roseocobalt in ammonia. The reaction which takes place in this case may be represented by the equation 5NH,.C,0,,380,-+ NH,=6NH,;.Co,0;,380,, the sulphate of Roseocobalt simply absorbing one equivalent of ammonia. The quantity of sulphate of Roseocobalt dissolved in the ammonia is very variable, being sometimes extremely small. In other cases, however, no sulphate of Luteo- cobalt is formed, but only a solution of sulphate of Roseocobalt in ammonia, from which, by evaporation, the sulphate crystallizes unchanged in large dark-red crystals, frequently of the form represented in Fig. 3. We are unable to assign a satisfactory reason for the capriciousness of the behavior of the red sulphate towards ammonia. Frémy asserts that sulphuric acid, continuously added to a completely oxidized ammoniacal solution of sulphate of cobalt, throws down an acid sulphate of Roseo- cobalt to which he assigns the formula 5NH;.Co,0;,5S0;+5HO. When this acid sulphate is boiled for a few minutes with ammonia, a yellow precipitate of sulphate of Luteocobalt is thrown down. The author does not attempt to explain the reac- tion which takes place in this case, but states that the red mother liquor from which the sulphate of Luteocobalt has~separated, yields on evaporation crystals of the neutral sulphate of Roseocobalt. We have never succeeded in preparing an acid sulphate of Roseocobalt by the process above mentioned, nor by any other. On the contrary, we have uniformly found that sulphuric acid precipitates from the oxidized solution only the neutral sulphate of Roseocobalt in small bright-red crystals, easily recognized by their form. Frémy’s salt must have contained free sulphuric acid, in consequence of imperfect washing. When a pure solution of the sulphate of Roseocobalt is boiled, ammonia is evolved, while sulphate of ammonia and sulphate of Luteocobalt remain in solu- tion, and a dark-colored oxide of cobalt is precipitated. From the solution the sulphate of Luteocobalt may be obtained by evaporation and crystallization. This method yields but little, and is not to be recommended. Sulphate of Luteocobalt is also sometimes obtained, with other products, by digesting sulphate of Roseocobalt with sulphuric acid, before the period of complete decomposition sets in. A very simple and easy method of preparing the sulphate of Luteocobalt consists in decomposing the dry sulphate of Roseocobalt by heat. When the latter salt is gently heated in a porcelain crucible over a spirit lamp, or better still, in a glass flask in a bath of rosin oil to about the temperature of melting lead, ammonia is given off in abundance, and the mass, which should be constantly stirred, assumes a fine purple-lilac hue. The heat, when the lamp alone is used, must never rise to low redness, and no vapors of sulphate of ammonia should be given off. The resulting mass is then to be dissolved in hot water, which gives a fine purple red solution, and chlorhydric acid added in excess. An orange precipitate of sulphato- chloride of Luteocobalt is immediately thrown down, which is easily purified, as above, by sulphate of silver and recrystallization. The acid mother liquor sometimes deposits more sulphate on cooling. The supernatant liquid contains 6 49 RESEARCHES ON THE chloride of Luteocobalt, chloride of Purpureocobalt, and a leek-green crystalline body, which we have called provisionally Praseocobalt, but which we have not yet carefully studied. The sulphate of Luteocobalt, like the chloride, has a fine wine-yellow color, and crystallizes readily. The crystals belong to the right rhombic or trimetric system; they are hemihedral and isomorphous with the chloride of Luteocobalt. According to Prof. Dana’s determinations, the more usual forms are represented in Figs. 11, 12, 13,14. In Figs. 13 and 14 the sulphate is mixed with the chloride. I:I = 113° 38’ O:3 = 137° 19! 13:13 = 88° 44’ and 91° 16’ O : 1% = 146° 4’ O:3 = 118° 38’ li: 1% (over O) = 88° 22’ li: 14 = 112° 8’ (over O) O : 8% = 107° 57’ 3%: 8% = 127° 18’ (adjacent) O: 17 = 134° 11’ These forms in other symbols are O, 0, 3-«, 2, t 1- ©, (Fig. 11). O,0, z, cs 1-%, 8-% (Fig. 12). 1-&, 0-3,3- 6, (Fig.13). 1-%, 0-3, 3-0, 1-~ (Fig. 14). a:6:¢c =1,039 : 1: 1,539. boltoleo Fia. 11. Fie. 12. Figs. 15, 16, 17, are different in habit from the preceding, and do not agree precisely in angles. The forms as lettered are referred to a different fundamental form. Adopting the same fundamental form as in the above figures, the lettering would be as follows: Lettering on figures, O © 12 4 142 I wt v New lettering, O I 8 3% 8% ¢ dw 3% 39 tooo bole Angles obtained and calculated for Fig. 15 (putting the lettering on the figure in brackets) : 1: 1 (2: %2) = 64° 28’ and 115° 32’ 32 : 32, (2 : 4) = 124° 8’ (adjacent). O: 3 (0: 12) = 120° 36’ O : 31(0: 1%) = 119°. Zn — cy = O: 32 (0: 3) = 180° 59’ 72: 2 = 108° 10’ (by calculation). Angles obtained and calculated for Figs. 14, 15: 2% : 3 (I: I) = 108° 30’ 0:29 (0: 3) = 150° 16’. 0:2 (0:12) =120°9 40’ O: 223 (0: %) =120° 16’. O : $1 (O: 31) = 138° 6’. Fig. 18 has still a different habit. The occurring vertical prism, lettered I, gave the angle (approximately) 101° 30’, and the dome 17 has the angle 109° 36’, giving O: 14 = 144° 48, near the angle in Figs. 11, 12. AMMONIA-COBALT BASES. 43 Fic. 15. The sulphate is rather insoluble in cold but is freely soluble in hot water; the dilute solution is yellow, the concentrated solution dark sherry wine colored. By double decomposition with salts of barium it yields the other salts of Luteocobalt. The sulphate like the chloride is dichrous, the ordinary image being pale rose-red while the extraordinary image is bright orange. The color of the salt in coarse powder approaches the orange No. 5 of the first circle. Sulphuric acid does not precipitate this salt from its solution, but chlorhydric and nitric acids throw down in the cold mixtures of the chloride with the sul- phate and nitrate. The salt is decomposed with very great difficulty by long boiling, even after the addition of a little ammonia. No new base is formed during the decomposition. When, however, the dry salt is gently heated in a porcelain crucible, ammonia is evolved, and if the heat be regulated so that no sulphate of ammonia is given off, while the mass is constantly stirred, there remains after a few minutes a red mass, which on solution in water gives a fine red liquid contain- ing a sulphate of a red base, which is probably Purpureocobalt. The reaction is, however, a very uncertain one, and has succeeded in our hands but once. We have in most cases obtained by the process described only a mixture of sulphate of Luteocobalt, sulphate of cobalt, and sulphate of ammonia. We shall consider this subject more fully hereafter. Sulphuric acid, if not too dilute, readily decom- poses the sulphate of Luteocobalt when the solution is heated. It appears pro- bable that there exists an acid sulphate of this base, as there is an acid carbonate, but we have not been able to obtain it as yet. Sulphate of Luteocobalt has the formula 6NH,,.Co,0,,380,+5HO as the following analyses satisfactorily show. The salt analyzed was dried by pressure between folds of bibulous paper only. 0.3618 grs. gave 0.1600 grs. Bulphate of cobalt = 16.83 per cent. cobalt. - 0.4993 grs. “ 0.2205 grs. “ =16.80 * ie 0.4790 grs. “ ‘0.2122 grs. HY GS 1G. ty 1.2023 grs. “ 1.2020 gers. sulphate of berg = 34.32 per cent. sulphuric acid. 0.8203 grs. “ 0.8250 grs. = 34.52 “ i io 0.9355 grs. “ 0.5650 grs. water = 6.71 per cent. hydrogen: 1.1194 grs. “ 0.6722 gers.“ = 6.67 “ 1.0005 grs. gave 205 ¢. c. nitrogen at 12°.5 O. and 753™".61 (at 12°.7) = 191.16 ¢. c. at 0° os and 760™" = 24.00 per cent. nitrogen. 0.9018 grs. gave 185.5 c. c. nitrogen at 19° C. and 763"".36 (at 199.5) = 171. 26 c. c. at 0° and 760" = 23.85 per cent. nitrogen. 44 RESEARCHES ON THE Our formula requires Eqs. Calculated. Mean. Found. Cobalt . ai 59.0 16.85 16.83 16.80 16.85 16.83 Sulph. acid . 3 120.0 34.28 34,42 84.52 34.32 Hydrogen . 23 23.0 6.57 6.69 6.71 6.67 Nitrogen 6 @: 84.0 24.00 23.97 24.00 23.85 Oxygen. 8 64.0 18.28 18.09 — —_ 350.0 100.00 According to Frémy, the sulphate contains but four equivalents of water of crystallization. In vacuo or in dry air the sulphate of Luteocobalt effloresces, becomes opaque and reddish buff colored, and loses 4 eqs. or 10.13 per cent. of water. Rogojski did not succeed in obtaining the sulphate of Luteocobalt by decomposing the chloride with sulphate of silver. According to this chemist, there is produced under these circumstances a sulphato-chloride which has the formula 6NH;.Co,0;,3S0;+ 6NH;.Co,C];. We have already mentioned, however, that the chloride and sulphate of Luteo- cobalt are isomorphous, and we have accordingly found, as might be expected, that these two salts are capable of crystallizing together in all proportions, and cannot be separated by crystallization alone. To show the variation in the constitution of the mixed chloride and sulphate, it will be sufficient to give a few cobalt deter- minations made with the salt as prepared at different times. 0.1510 grs. gave 0.0673 grs. sulphate of cobalt = 16.96 per cent. cobalt. 0.7075 grs. ‘* 0.3210 ers. ue Cee Sa Gue ie i 0.1205 grs. ‘“ 0.0680 grs. oT Se AAT ove ie The parallel which Rogojski draws between the salt which he analyzed and the sulphate of Gros’s base, which Gerhardt considers as a sulphato-chloride of Dipla- tinamin, must therefore be considered as illusory. CHROMATE OF LUTEOCOBALT. A solution of the neutral chromate of potash gives a fine yellow precipitate in solutions of the chloride, nitrate, and sulphate of Luteocobalt. The precipitate is soluble in hot water, and crystallizes readily from the solution in brown-yellow crystals, which resemble those of the sulphate. We have not analyzed this salt, but it is almost certain that its true formula is 6NH,.Co,0,,3Cr0,+5HO, since it forms with chloride of Luteocobalt crystallizable mixtures in various pro- portions, which exhibit in the greatest beauty and distinctness the characteristic forms of the crystals of the sulphato-chlorides above alluded to. The pure chromate can only be obtained by precipitating the nitrate of Luteocobalt by chromate of potash, as the precipitate from the chloride always contains chlorine, and that from the sulphate, sulphuric acid. @ AMMONIA-COBALT BASES. 45 NITRATE OF LUTEOCOBALT. This beautiful salt is almost invariably obtained during the oxidation of an ammoniacal solution of nitrate of cobalt, and is deposited upon the bottom of the vessel in bright orange crystalline scales. The supernatant liquid is usually red, and contains nitrate of Roseocobalt. The orange-yellow salt is easily purified by re-crystallization. The salt may also be easily prepared from the chloride or sul- phate by double decomposition with nitrate of silver or of baryta. The nitrate of Luteocobalt crystallizes readily in forms which belong to the square prismatic or dimetric system. According to Professor Dana, the dimensions and angles of the crystals are as follows: Fig. 19. 1: 1 (over the base) = 110° 20’ O:1 = 124° 50! on . 0:3 = 103° 4’ = 3 : 3 (over the base) = 153° 52’ Sees a = 1.0161 i eno O :2% (ot observed) = 134° 33’ The crystals are usually small and often very brilliant. The salt is readily soluble in hot water, and separates in small crystals on cooling. Chlorhydric acid throws it down from its solution as a yellow crystalline powder; nitric acid also precipitates it, but sulphuric acid converts it into sulphate with more or less complete decomposition. The nitrate of Luteocobalt is anhydrous, and has the formula 6NH;,.Co,0;,3NO; as the following analyses show: 0.1972 gers. gave 0.0880 grs. sulphate of cobalt = 16.98 per cent. cobalt. 0.2090 grs. “ 0.0928 grs. we SP = VOLS, ott “ 1.0859 gers. “ 0.5151 grs. water 5.27 per cent. hydrogen. 0.9126 grs. “ 0.4337 grs. “ 52 Bice be 0.6242 grs. gave 188 c. c. at 119.5 C. and 772"".40 at 119.94 = 180.56 c. c- at 0° and 760™" = 36.33 per cent. nitrogen. 0.7394 grs. gave 226 ¢c. c. at 138°.5 C. and 766™™.05 at 14° = 213.29 c. c. at 0° and 760™ = 36.23 per cent. nitrogen. The formula requires Eqs. Calculated. Mean. Found. Cobalt 5 dl pales 17.00 16.93 16.98 16.89 Hydrogen . Ses 5.18 5.27 5.27 5.28 Nitrogen . 5 Y 36.31 37.28 36.23 36.33 Frémy and Rogojski deduce the same formula from very imperfect analyses. Heat decomposes the dry nitrate of Luteocobalt with a slight explosion, a black powder of an oxide of cobalt remaining. It may be remarked that the oxygen and hydrogen in this salt are exactly in the ratio to form water. 46 RESEARCHES ON THE OXALATE OF LUTEOCOBALT. When a solution of oxalate of ammonia is added to one of a soluble salt of Luteocobalt, a buff colored precipitate of fine needles is thrown down, which is insoluble both in hot and cold water, but which readily dissolves in a solution of oxalic acid. From this solution the neutral oxalate crystallizes in beautiful prismatic crystals, having the color of the sulphate and chloride. In dry air the crystals lose water like those of the other hydrated salts of Luteocobalt. The oxalate has the formula 6NH,.Co,03,30,0,+4HO as the following analyses show : 0.4330 grs. gave 0.2040 grs. sulphate of cobalt = 17.99 per cent. cobalt. 0.4228 grs. gave 0.2000 grs. as sf 18.00 “ ms 0.5345 grs. gave 0.2529 grs. “ g LSFOL a 2.0805 grs. gave 0.8380 grs. carbonic acid 32.95 per cent. oxalic acid. The formula requires Eqs. Calculated. Found. Cobalt . sete TAOS: 17.99 18.00 18.01 Oxalic Acid . 38 32.82 82.95 — — It would a priori appear probable that there exists an acid oxalate of Luteocobalt corresponding to the acid carbonate, but we have not yet been able to obtain such a salt. The oxalic acid in this compound cannot be easily reduced by a solution of terchloride of gold, nor can it be completely separated from the base by means of a solution of chloride of calcium. CARBONATES OF LUTEOCOBALT. The neutral carbonate of Luteocobalt is readily formed by decomposing a solu- tion of chloride of Luteocobalt by carbonate of silver. The yellow solution, by evaporation, yields sherry-wine colored crystals of the carbonate. The salt closely resembles the other soluble salts of Luteocobalt; is easily soluble in hot water, and crystallizes well by slow evaporation. During evaporation, however, the solution absorbs carbonic acid from the air, and crystals of the acid carbonate are found mixed with those of the neutral salt. According to Prof. Dana’s measurement, the crystals of the neutral carbonate belong to the trimetric system, and approach Aragonite in form. Fig. 20 represents a crystal of this salt: fF Fig. 20. I :I = 116° 50’ RA I :i% = 121° 35’ li: 1% (top) = 114° 16’ 1%: 17 over 77 = 65° 44’ a@:b:¢ = 1.0509: 1: 1.6265 AMMONIA-COBALT BASES. 47 The constitution of the neutral carbonate appears to be represented by the formula 6NH;.Co,0;,3C0,+ 7HO. - 0 2495 grs. gave 0.1220 grs. sulphate of cobalt = 18.61 per cent. cobalt. 0.3518 grs. gave 0.0786 grs. carbonic acid = 22.34 per cent. The formula requires Eqs. Found. Cobalt . 0 por] 18.79 18.61 Carbonic acid . + 8 21.01 22.34 The excess of carbonic acid and the deficiency in cobalt, are doubtless due to the presence of a portion of the acid carbonate. The neutral carbonate loses its water of crystallization in dry air, and becomes opaque, with the lustre of porcelain, like many other hydrated salts of this base. The acid carbonate of Luteocobalt is most readily prepared by passing a current of carbonic acid gas into a solution of the neutral salt. The acid carbonate usually separates, after a very short time, in the form of large brown-red or sherry-wine colored crystals, which are less soluble than those of the neutral carbonate. Accord- ing to Prof. Dana, the crystals of this salt belong to the monoclinic system, and closely approach Barytocalcite in form. Fig. 21 represents a crystal of this salt. Fic. 21. O : % = 108° 16’ Ns O: I = 77° 40’ and 102° 20’ IL 3 Ib BHO HY ' a:b6:¢ = 0.7219: 1 : 0.8398 y O: 1 = 139° 50’ © = 71° 44’. I: 1 = 142° 30/ O : -2i = 1119 46’ Ca In Barytocalcite the angle corresponding to O: «7 =106° 54’ and that corres- ponding to 1: I = 84° 52’. The acid carbonate of Luteocobalt retains its water of crystallization in the air, but loses it under the air-pump. The salt is particularly interesting as being the only acid salt of Luteocobalt which we have as yet been able to obtain. The formula of this salt is 6NH;.Co,0;,3Co,+ HO,CO,+5HO as the following analyses show : 0.4715 grs. gave 0.2246 grs. sulphate of cobalt = 18.12 per cent. cobalt. 1.0506 grs. gave 0.2830 ers. carbonic acid = 26.93 per cent. The formula requires Eqs. Found. Cobalt . : an ae 18.04 —~ 18.12 Carbonic acid . o @ 26.91 * 26.93 The very distinctly marked triacid character of Luteocobalt, considered as a base, renders it, to say the least, improbable that the formula of this salt should be written 6NH;.Co,0;.4C0,+ 6HO. 48 ie RESEARCHES ON THE OXIDE OF LUTEOCOBALT. The oxide of Luteocobalt may be obtained by decomposing a solution of the sulphate with baryta water. The solution is brown-yellow, and has an alkaline taste and reaction. It cannot be evaporated without decomposition, ammonia being evolved and a black powder separated. The solution absorbs carbonic acid from the air, and on evaporation, yields crystals of the carbonates; with acids it yields the salts of the base. The oxide of Luteocobalt appears to form compounds with salts of copper, which may be analogous to the ammonia-salts of that metal, or which again may be only double salts of copper and Luteocobalt. |G 26.19 26.05 FERROCYANIDE OF XANTHOCOBALT. This salt is precipitated almost immediately when a solution of ferrocyanide of potassium is added to one of the nitrate of Xanthocobalt. We have not been able to obtain it, however, either from the chloride or the sulphate, with which the ferrocyanide of potassium gives only turbid solutions. The salt is precipitated in prismatic crystals which appear to belong to the oblique rhombic system. Its color is a very beautiful bright orange-red, corresponding nearly with the red-orange No. 5, of the 2d circle of Chevreul’s scale. When freshly prepared, it is one of the most beautiful salts which chemistry can exhibit, but it loses some of its brilliancy of tint by keeping, and becomes a little duller and darker, probably from a slight decomposition upon the surface. The crystals exhibit a fine dichroism by reflection, the ordinary image being pale reddish orange, while the extraordinary image is bright orange. The ferrocyanide of Xanthocobalt is almost insoluble in cold, and is immediately decomposed by hot or even by warm water. The crystals lose water and are partially decomposed in vacuo, or even in pleno over sulphuric acid. They can, therefore, only be dried by pressure between folds of bibulous paper. The impossibility of purifying this salt by recrystallization, and the facility with which it is decomposed, render it difficult to obtain it in a perfectly pure state. - 54 RESEARCHES ON THE The formula of the ferrocyanide appears to be NO,.5NH;.Co0,0,Cy.+ FeCy + 7H0 as the following analyses show: 0.6288 grs. gave 0.1557 grs. metallic cobalt and iron = 24.76 per cent. 0.9047 grs. gave 0.2239 grs. He on OO Poe Rg Ws 0.5896 grs. gave 0.0690 grs. sesquioxide of iron eS yl) 1 iron. 0.6006 grs. gave 0.1811 ers. Co,0,+4C00 = 1688). cobalt. 1.0820 ers. gave 0.4163 gers. carbonic acid = 1049 * carbon. 1.1645 grs. gave 0.6439 grs. water = 6.14 per cent. hydrogen. 0.8718 grs. gave 271 c. c. nitrogen at 20°.8 C. and 765™".04 (at 21°.3 C.) = 246.51 ¢. ¢. at 0° and 760™" = 35.51 per cent. 0.9471 gers. gave 292 c. ec. nitrogen at 179.7 C. and 763"".01 (at 18° C.) = 268.96 ¢. ¢. at 0° and 760" = 35.66 per cent. The formula requires Eqs. Calculated. Found. 1 2 3 Cobalt 2 16.80 24.4747 16.39 24.76 24.74 Tron 1 oOe 8.19 Carbon . 6 10.25 10.49 Hydrogen 5 DY 6.26 6.14 Nitrogen 9 85.89 35.66 35.51 These analyses agree with the formula as well as can be reasonably expected, when the difficulty of obtaining a perfectly pure salt is taken into consideration. It is interesting to remark that in this salt, in which there is but one equivalent of basic cyanide, there are still two equivalents of cyanogen in the basic for one in the acid or electronegative cyanide. SULPHATE OF XANTHOCOBALT. When pure sulphate of cobalt is dissolved in water, an excess of ammonia added, and a current of NO, passed through the liquid, an absorption takes place, and copious fumes of carbonate of ammonia are given off. The liquid gradually assumes a dark brown-yellow color, and frequently deposits an abundance of crys- tals during the passage of the current of gas. Ammonia must be added from time to time, so as to keep the solution strongly alkaline, and prevent the appearance of red vapors at the surface of the liquid. It is not necessary to apply heat, as the temperature rises from the absorption of the gas. When the operation is over, which is indicated by the color of the liquid, the solution may be filtered and allowed to evaporate spontaneously, when a mass of brown-yellow crystals is obtained. ‘These may be purified by re-solution in hot water with addition of a few drops of acetic acid and re-crystallization. This method of preparing the salt is a convenient one, and large quantities may be prepared in a few hours. ‘The time required for the completion of the oxidation depends upon the quantity of sulphate of cobalt employed, and may last from one to twelve hours. It is best to employ a rapid current of the gas. The formation AMMONIA-COBALT BASES. 55 of the sulphate of Xanthocobalt, under these circumstances, may be represented by the equation 2C00,S0;+5NH;+ NO,= NO,.5N H;.Co,0;,280; if we suppose the oxidizing agent to be NO;. If, however, we consider the active agent to be NO,, we may represent the action by the equation 2C00,S0;+6NH;+ 2NO,+ HO=NO,.5NH;.Co,0;,2S0;+ NH,O,NO;. A large quantity of free nitrite of ammonia is always formed during the pro- cess, as we believe, by the direct action of NO, upon ammonia and water. The addition of an acid to the mother liquor from which the sulphate has crystallized, produces an active effervescence arising from the decomposition of the nitrite of ammonia. The process which we have indicated has generally proved perfectly satisfactory in preparing the sulphate. It is proper to state, however, that in some experi- ments, made for the purpose of revision, we obtained by the process above given no sulphate of Xanthocobalt, but only the nitrate. The cause of this we are at present unable to assign, and further experiments are wanting to explain so unex- pected a result. The sulphate of Xanthocobalt crystallizes in thin plates, the form of which we have not been able to determine; they appear to belong to the right rhombic system. ‘The crystals have a fine brown-yellow color, which, however, we cannot define by means of the chromatic scale. The salt is rather soluble in hot, but much less soluble in cold water. Heat readily decomposes the neutral solution, a black powder being thrown down, while ammonia is given off. The dry salt is decomposed like the chloride. Strong sulphuric acid dissolves the sulphate to a red oily liquid, but little deut- oxide of nitrogen being given off. The addition of water to this solution causes a violent effervescence from the escape of deutoxide of nitrogen, and probably nitrous acid. There remains a red liquid consisting chiefly of the double sulphate of cobalt and ammonia, but almost always containing a little acid sulphate of Purpureocobalt. Even very dilute sulphuric acid readily decomposes sulphate of Xanthocobalt by boiling. Long boiling with chlorhydric acid also decomposes this salt, the products of the decomposition being, as already stated, chloride of Pur- pureocobalt, free sulphuric acid, and deutoxide of nitrogen. Sulphate of Xanthocobalt has the formula NO,.5NH;.Co,03,250;+ HO as the following analyses show : 0.5776 grs. gave 0.3142 ers. sulphate of cobalt = 20.69 per cent. cobalt. 0.5630 grs. gave 0.3060 ers. a oS —=)2,0568 a ss 1.2370 grs. gave 1.0150 grs. sulphate of baryta = 28.16 sf sulphuric acid. 1.1472 grs. gave 0.9242 gers. a <= 27.65 “ a 0.7718 grs. gave 0.3868 grs. water = 5.56 i hydrogen. 0.4468 grs. gave 0.2285 grs. = 5.68 BY hy 0.6020 grs. gave 169.48 ¢. c. nitrogen at 14° C., and 769™".61 (h = 91™) = 140.87 ©. ¢., at 0° and 760°" = 29.37 per cent. 1.2624 ers. gave 300 c. ce. nitrogen, at 5° C., and 775™".20 (at 5°.3 C.) = 296.68 c. c., at 0° and 760" == 29.51 per cent. 56 RESEARCHES ON THE The formula requires Eqs. Calculated. Mean. Found. Cobalt 5 Be tee 59 20.55 20.68 20.69 20.68 Sulphuric acid . 2 80 27.94 27.90 27.65 28.16 Hydrogen . 5) NG 16 5.57 5.62 5.56 5.68 Nitrogen . : 6 84 29.26 29.44 29.37 29.51 Oxygen. 4 1) 96 16.68 16.30 — — 835 100.00 A solution of sulphurous acid dissolves sulphate of Xanthocobalt without decom- position. On boiling, however, a complete decomposition takes place, bubbles of gas are given off, and there remains a red solution of the double sulphate of cobalt and ammonia. The gas which is evolved produces no red vapors on contact with the air, and is probably protoxide of nitrogen. The sulphate of Xanthocobalt is also decomposed by boiling with urea, an abundance of a colorless gas without odor being given off. The reactions of the sulphate are similar to those of the chloride. NITRATE OF XANTHOCOBALT. The nitrate of Xanthocobalt may be prepared like the sulphate, by passing a current of NO, into an ammoniacal solution of nitrate of cobalt. The formation of the nitrate goes on very rapidly, and crystals are usually deposited in abun- dance long before the oxidation is complete. It is best in this case, as in the prepa- ration. of the sulphate, to employ a pure salt of cobalt and pure ammonia, as the subsequent purification of the nitrate of Xanthocobalt becomes much more easy. The equations representing the formation of the nitrate are similar to those which we have given for the sulphate. The nitrate of Xanthocobalt may also be easily prepared by the action of NO, upon neutral, acid, or alkaline solutions of the chlorides, sulphates and nitrates of Roseocobalt and Purpureocobalt. We have alluded to the formation of the nitrate of Xanthocobalt by this process already, and will here enter more into detail. It is almost a matter of indifference which salt is selected, as the nitrate is prepared with nearly equal facility from all. The salt is to be dissolved in water, and, to hasten the process, ammonia added; a large excess of ammonia is not necessary, but the process always goes on more rapidly in an ammoniacal than in an acid or neutral solution. The current of gas resulting from the action of nitric acid upon starch or sawdust is then to be passed into the liquid, which speedily becomes hot and gradually changes its color from violet to orange-red, and at last to orange, while orange-yellow crystals of the nitrate of Xanthocobalt are pre- cipitated. The liquid on cooling gives more crystals; the process should not be continued after the whole mass has assumed a clear orange-yellow color. The mother-liquor from which the crystals of the nitrate of Xanthocobalt have sepa- rated contains only salts of ammonia, with a little nitrate in solution. The whole process is very easy to execute, and yields a very pure nitrate. The reac- tions which occur in this process are remarkably beautiful, and may be expressed, AMMONIA-COBALT BASES. 57 in the case of the action of the gas upon the chloride and sulphate of Roseocobalt, by the equations 5NH;.Co,Cl, + 3NO,+ 3HO=NO,.5NH;.Co,0;,2N0,+ 3HCl, 5NH;,.Co,0,,380;+3NO0,+ 3HO=NO,.5NH;.Co,0;,2NO;+3HO,SOs. Tt will be seen from these equations that when neutral solutions of the salts of Roseocobalt or Purpureocobalt are employed, chlorhydric and sulphuric acids are set free. The influence of an excess of ammonia in facilitating the process is thus easily understood. The nitrate of Xanthocobalt, being much less soluble in cold water than the ammonia salts, is easily purified by re-crystallization. In treating of the sulphate and chloride of Xanthocobalt, we have mentioned that the nitrate of Xanthocobalt is often formed while preparing these salts directly. As a mode of preparation, this method is not to be recommended, but it possesses much theoretical interest. The equation which represents the action when the nitrate of Xanthocobalt is formed directly by the action of NO, upon an ammo- niacal solution of the sulphate of cobalt, is possibly the following 2Co0,SO,+ 7NH;+ NO,+3NO0,+ 2HO=NO,.5NH;.Co,0;,2NO;+2NH,0,SO;+ NO,. When the chloride of cobalt is employed instead of the sulphate, other products are always formed simultaneously with the nitrate of Xanthocobalt, and the reaction becomes therefore more complicated. The nitrate of Xanthocobalt crystallizes in small brilliant crystals, which, accord- ing to Prof. Dana’s measurement, belong to the dimetric system. The only form observed as yet is an octahedron, the angle at the base being 100° 45’—101° 15’. The salt is dichrous, the ordinary image being pale orange, while the extraordi- nary is bright orange-yellow. The salt has a clear brown-yellow color, and the mass of crystals is usually very brilliant. It is quite soluble in hot, but rather insoluble in cold water; the solu- tion is readily decomposed by boiling, with evolution of ammonia and precipitation of a heavy black powder. The dry salt is readily decomposed by heating, abun- dance of red vapors being given off, while a black oxide remains. The nitrate is completely decomposed by boiling with chlorhydric acid, red vapors mixed with chlorine being given off, while there remains a solution of chloride of Purpureo- cobalt, from which crystals of this salt are deposited on cooling. When boiled with nitric acid, a similar decomposition is produced, and crystals of nitrate of Roseocobalt are obtained in small quantity. It is probable that nitrate of Pur- pureocobalt is the first product of this reaction, and that this by boiling with excess of acid, passes into the nitrate of Roseocobalt. As a general rule, the quantity of nitrate of Roseocobalt produced is small, and the decomposition results in the conversion of the nitrate of Xanthocobalt into the nitrates of cobalt and ammonia. Nitric acid precipitates nitrate of Xanthocobalt from its solution without sensi- ble decomposition in the cold. By long boiling acetic acid completely reduces nitrate of Xanthocobalt, and a solution of cobalt is obtained which is free from ammonia-cobalt bases. Oxalic acid also reduces the nitrate by boiling, oxalate of cobalt being thrown down. 8 58 Nitrate of Xanthocobalt has the formula 0.3917 grs. 0.6960 grs. 0.5935 grs. 0.5585 ers. 0.4958 grs. 0.9483 ers. RESHARCHES ON THE NO,.5NH;.Co,0;,2NO0;+ HO as the following analyses appear to show: gave 0.1927 gers gave 0.2535 ers gave 0.2330 gers. gave 0.4270 grs. . sulphate of cobalt = 18.72 per cent. cobalt. gave 0.3405 ers. gave 0.2925 ers. . water 3 ce ce ce ce bc = 18.76 = 18.75 = 5.04 = 5.21 = 5.09 oe ce cc 4 “ hydrogen. “ce iG 0.6145 grs. gave 187.45 c. ¢. nitrogen at 69.5 C., and 769"".5 (at 7° C.), (h = 35"".0) = 174.55 c. c. at 0° and 760"" = 35.73 per cent. 0.6024 grs. gave 183.30 c. c. of nitrogen at 5° C., and 759"™.0 (at 6° C.), (h =37"".0) = 169.20 c. c. at OCand 760™ = 35.27 per cent. 0.5912 gers. gave 184.66 c. c. nitrogen at 119.5 C., and 761™".0 (at 12° C.), (a= 32"".5) = 167.13 c. c. at 0° and 760™" = 35.50 per cent. Hence we have Eqs. Calculated. Mean. Found. Cobalt. 2 59.0 18.73 18.74 18.76 18.72 18.75 Hydrogen 16 16.0 5.08 5.11 5.04 5.21 5.09 Nitrogen . 8, 112.0 35.55 85.50 35.73 35.50 35.27 s Oxygen . 16 128.0 40.64 40.65 — — S&S 315.0 100.00 100.00 As the nitrate of Xanthocobalt is, of all the salts of this base, that which is most easily prepared in a state of purity, and as its reactions are most charac- teristic of the base, we shall give them in this place. Chlorhydric acid in excess gives a buff-yellow precipitate. Alkaline carbonates give no precipitate. Ferrocyanide of potassium precipitates beautiful orange-red crystals. Ferridcyanide of potassium gives no precipitate. Cobaltidcyanide of potassium gives no precipitate. Chromate of potash gives a fine clear yellow precipitate. Bichromate of potash gives beautiful orange-red needles. Oxalate of ammonia gives a voluminous precipitate of pale yellow needles. Picrate of ammonia gives beautiful clear yellow needles. Phosphate of soda gives no precipitate. Pyrophosphate of soda gives no precipitate. Chloride of mercury gives a buff-colored scaly precipitate. Protochloride of tin gives, after a short time, granular yellow crystals. Bichloride of platinum gives an orange-yellow precipitate. Terchloride of gold gives, after addition of chlorhydric acid and standing, yel- low needles. lodide and bromide of potassium give no precipitates. | | AMMONIA-COBALT BASES. 59 OXALATE OF XANTHOCOBALT. The oxalate of Xanthocobalt is precipitated when a solution of oxalate of ammonia is added to one of the chloride, nitrate or sulphate of the base. After a very short time yellow acicular crystals make their appearance, the separation being greatly facilitated by strongly agitating the solution. ‘The precipitate is to be thrown on a filter, well washed with cold water and dried, first by pressure and afterwards in pleno over sulphuric acid. As thus prepared, the salt has a pale yellow color, and consists of fine needles, the form of which cannot be determined, even under the microscope. It is nearly insoluble in cold and but very slightly soluble in hot water. The solution is readily decomposed by boiling. ‘The insolu- bility of this oxalate and its characteristic appearance render it of great value in detecting the presence of salts of Xanthocobalt. Oxalate of Xanthocobalt has the formula NO,.5NH;.Co,0,,2C,0,+ 5HO as appears from the following analyses: 0.3191 grs. gave 0.1762 grs. sulphate of cobalt = 21.01 per cent. cobalt. 0.2980 grs. gave 0.1650 grs. se — 10) Oe o 2.2520 grs. gave 0.7075 grs. carbonic acid = 2H10 oxalic acid. 2.2850 gers. gave 0.7260 ers. =“ us = 20.99 “ ss a The calculated results are 3 Eqs. Theory. Found. Cobalt 2 21.14 21.01 21.06 Oxalic acid 2 25.81 25.70 25.99 THEORETICAL CONSIDERATIONS. The empirical constitution of the ammonia-cobalt bases being, as we believe, established, it remains to offer an exposition of our views of their theoretical structure. Claudet' and Weltzien? have endeavored to reduce the salts of Roseo- cobalt and Luteccobalt to the type of ammonium, while Frémy has abstained from adopting any particular theory, and gives, without comment, the results of his analyses in the shape of empirical formule. Claudet’s view is necessarily errone- ous, from the fact that his formula for what we term the chloride of Purpureo- cobalt is incorrect, inasmuch as he assigns to it 16 in place of 15 equivalents of hydrogen. Our own numerous analyses, as well as those of Rogojski and Gregory, have clearly shown that the number of equivalents of hydrogen is fifteen. For an exposition of Weltzien’s views we must refer to his paper; they appear to us wanting in simplicity, since they require us to admit, not merely an equiva- 4 Phil. Mac. (4) II, 258. ? Annalen der Chemie und Pharmacie, XCVII, 19. w 60 RESHARCHES ON THE lent replacement of hydrogen by ammonium and cobalt, but even that the com- pound ammonium thus formed may replace cobalt in its sesqui-combinations. Thus, according to Weltzien, the formula of nitrate of Luteocobalt is N H | aed cs 4) which is obviously reducible to the type R,O;+3NO,. By adopting Gerhardt’s view of the constitution of the sesquioxides, Rogojski reduces the formula of chloride of Luteocobalt, 6NH,.Co,Cl,, to the form 2NH,.coCl in which co represents cobalt with = of its usually received equivalent. ‘To this body he gives the name Dicobaltinamin, and considers it analogous to the chlorides of Diplatosamin and Palladiamin 2NH,.PtCl and 2NH,.PdCl. This view applies very well to several other salts of Luteocobalt, as for example, the bromide, iodide, nitrate, and chlorplatinate, the formulee of which become 0,+3NO,, 2NH;.coBr or N.H,co,HBr 2NH.,.col or N.H;co,HI 2NH,.coO,NO; or N,H,co,HO,NO, 2NH;.coCl1+ PtCl,+2HO or N,H,co,HCl+ PtCl],+ 2HO. We have remarked already that the compound 6NH;.Co,Cl,;+ 6NH;.Co,0;,3803, which Rogojski describes, and to which he attributes the formula 2NH,.coCl+2NH,.co0,80,, or N,H,co,HCl+ S0,H.,2N.H,co. has no real existence, but is merely a mixture of the chloride and sulphate which are isomorphous salts. Rogojski’s parallel between this and the sulphate of Gros’s base, which according to Gerhardt’s view has the formula N.H,pt.,2HCl+ N,H,pt.,SO,H, is consequently illusory. On the other hand, moreover, it must be remembered that Rogojski’s view applies only to the compounds of Luteocobalt, and fails entirely to reduce the formulee of the other cobalt bases to more simple expressions, since it requires us, in these cases, to admit fractions of equivalents. Thus the formula of the chloride of Pur- pureocobalt becomes on this view N;H,coCl, while that of its chlorplatinate must be written 3N;H,coCl+2PiCl.. Even in the case of those compounds of Luteocobalt which contain water, Rogo- jski’s view ceases to give simple expressions, since in the majority of these the number of equivalents of water is not divisible by three. The difficulty becomes AMMONIA-COBALT BASES. 61 still greater in the case of the compounds of Xanthocobalt. We have, therefore, no hesitation in rejecting Rogojski’s theory as too limited in its application. We consider the ammonia-cobalt bases as conjugate compounds of sesquioxide, sesquichloride, &c., of cobalt, the five or six equivalents of ammonia, or of ammonia and deutoxide of nitrogen, forming the conjunct, and serving to give to the sesqui- compound of cobalt the degree of stability which it possesses in this class of bodies. Accordingly we should prefer to write the formula of chloride of Luteocobalt 6NH,.Co..Cl, employing the connecting circumflex, as Kolbe has suggested, as a symbol of conju- gation. Adopting this view, we have the following conjugate radicals, which we assume as existing in the ammonia-cobalt bases precisely in the same sense in which we assume Co, as existing in the sesquichloride and sesquioxide of cobalt. Roseocobalt : 3 : 5 ‘ 5NH,.Co, Purpureocobalt . ; : : , 5NH,.Co, Luteocobalt ‘ : ; ; : 6N H,.Co, Xanthocovaltiy sspears er NO,.5NH,.Co,. We may, however, remark that while this view offers a satisfactory explanation of the fact that two of the ammonia-cobalt bases are triacid, forming in all cases neutral compounds with three equivalents of acid, two are biacid bases, and of these latter, one, namely Purpureocobalt, forms acid compounds with four equiva- lents of acid. Tn these cases we meet with the same difficulty which occurs with the ordinary salts of sesquioxides; thus sesquioxide of iron may unite with one, two, or three equivalents of acid, though there appear to be three in the neutral salts. While some chemists assume that salts of sesquioxide of iron containing one or two equivalents of acid are basic, others consider the different equivalents of oxygen as united in different modes, so that the oxide may he, according to circumstances, Fe,0, Fe,0,.0 Fe,0.0,. Peligot’s theory of the constitution of sesquioxide of uranium is another case in point; as this oxide unites with but a single equivalent of acid, it may be con- sidered, as Peligot has shown, as the oxide of a radical, U,O,.0, so that in this case also, the rule that a base unites with as many equivalents of acid as the base itself contains equivalents of oxygen is satisfied. ; _ To explain the biacid character of two of the ammonia-cobalt bases, we may therefore assume in them the existence of secondary radicals containing oxygen. Thus in Purpureocobalt and Xanthocobalt the primary radicals are 5NH,.Co, NO,.5NH,.Co.; 62 RESEARCHES ON THE while the secondary radicals are 5NH,.Co,0 NO,.5NH,.Co,0. The oxides on this view are 5NH,.Co,0.0, NO, 5NH,,.Co,0.0, and are consequently of the form RO,, so that their biacid character is explained. The doctrine of polyacid bases is by no means new; it is in fact contained in the empirical law above referred to, that there are in neutral salts as many equivalents of acid as there are of oxygen in the base, bearing in mind, however, that the oxygen in the base must be outside of the radical. The ammonia-cobalt bases like the conjugate metals produced by the union of ethyl, methyl, &., with anti- mony, arsenic, and bismuth, serve, however, to place the doctrine of polyacid bases upon the same footing as that of the polybasic acids, so that the two theories are in this way complementary to each other. From this point of view it is interest- ing to remark, that the chlorplatinates and double cyanides of the ammonia-cobalt bases follow the same law as the oxygen salts, thus we have GNH;-Co,Cl,+3PtCl, | - 5NH,.Co,Cl.Cl,+ 2 PtCl, NO,.5NH,.Co,0.Cl,+2PtCl, 6NH;.Co,Cy;+Co,Cy; NO,.5NH;.Co,0.Cy.+ FeCy. In point of fact, the presence of but two equivalents of bichloride of platinum in the chlorplatinate of Purpureocobalt first led us to suspect that the true oxygen salts of this base would be found to contain but two equivalents of acid. Two other points require special notice in this connection. We have already shown that the oxide of Purpureocobalt, in at least two cases, is capable of uniting with jour equivalents of acid so as to form feebly acid salts. We consider these salts the true bi-salts of the base, and not as double salts of Purpureocobalt and water. In other words, we hold that they bear the same relation to the neutral salts of the base which bichromate of potash does to the neutral chromate. If this view be correct, we may perhaps expect to find salts of Roseocobalt or Luteo- cobalt containing siz equivalents of acid. The only acid salt of Luteocobalt hitherto discovered is the carbonate, but this in reality, in our view, is a double salt of Luteocobalt and water, and has the formula 6NH;.Co,0,,300, + HO,CO,. The fact, that both the acid and neutral oxalo-sulphate of Purpureocobalt con- tain two distinct acids, is also a very instructive one, since it completes the analogy between the polyacid bases and the polybasic acids. A polybasic acid, as, for example, tartaric acid, may unite with two different bases at once, and we now AMMONIA-COBALT BASES. 63 learn that a polyacid base may in like manner unite with two different acids. Thus we have CHO» | 0 5NH,.Co,0, aa. = 5NH,.Co,0, 1 5,06 The other point to which we refer, is the peculiarity in the constitution of Xanthocobalt, in which one equivalent of oxygen in the secondary radical is not capable of replacement by chlorine, so that we have for the chloride of this base the formula NO,.5NH,.Co,0.Cl, while for the chloride of Purpureocobalt, we have 5NH,.Co,C1.Cl, and not, as we might expect from the analogy of Xanthocobalt, 5NH,.Co,0.C1,. The appearance of deutoxide of nitrogen as a conjunct (Paarling) is in itself well worthy of attention, and Xanthocobalt forms, we believe, the only known instance in which this occurs. It seems @ priori probable, that iridium and rhodium bases corresponding to Xanthocobalt may be prepared by passing a current of NO, into ammoniacal solutions of protosalts of those metals, or into solutions of Claus’ bases, and we have already instituted experiments with these metals, the results of which we hope hereafter to communicate. The theory which we have proposed for the ammonia-cobalt bases has also been brought forward by Claus, and applied to his rhodium and iridium compounds. Claus has extended the view in question to the ammonia compounds of metallic protoxides, and we conceive with advantage, in the case of those bases which con- tain more than one equivalent of ammonia, as for instance, the platinum, palla- dium, and iridium bases, having the formulee 2NH;.PtO 2NH;,.Pd0 2NH,. 10. The discovery of the biacid character of Purpureocobalt and Xanthocobalt, in connection with the views which we have expressed with respect to the molecular structure of these bases, has led us to extend the theory of conjugation to the ammonia-platinum compounds. We consider these also as conjugate bases, and are of opinion that their constitution may be more simply expressed upon this than upon any other view yet proposed. The ammonia-platinum bases at present known are eight in number, of which two were discovered by Reiset, one by Gros, two by Raewsky, and three by Gerhardt. The empirical formule of these bases are as follows: Reiset’s first base = N,H,PtoO uniacid “ second base = NH,PtO aS Gros’s base = N.H,PtClo @ Gerhardt’s first base = NH,Pt0O, a ss second base = N.H,PtO, aS ss thirds) << = NEERtl® 5 Raewsky’s first base = N,H,,Pt,ClO; biacid is seconds: 9) = NEP te ClO; « 64 RESEARCHES ON THE If we apply to these bases the results which we have obtained in the case of the ammonia-cobalt compounds, we may consider them as conjugates of platinum, chloride of platinum, and oxide of platinum, with one or two equivalents of ammonia, excepting Raewsky’s bases, which may be regarded as containing a deutoxide of chlorine with four equivalents of ammonia. The formule of these bases become on this view Reiset’s second base = N H,.Pt.0 uniacid Gerhardt’sfirss “ = NH,.Pt0.0 a Go - Mmnl Oo. NH,.PtC1.0 « Reiset’s first base = 2NH,, Pt.0 « Gerhardt’s second base = 2NH,.PtO.0 a Gros’s second base = 2NH,.PtCl.O eG Raewsky’s first “ = C10,.4NH,.Pt,0.0, _ biacid “ secondbase = Cl0,.4NH,.PtCl.0, “ In comparing the formule of these bases with those of the ammonia-cobalt compounds, we remark several points of analogy. These are most striking in the case of Raewsky’s two bases, which we consider analogous to Xanthocobalt. Thus we have Oxide of Xanthocobalt ‘ ‘ : NO,.5NH,.Co,0.0, Oxide of Raewsky’s first base . . O10,.4NH,.Pt,0.0,. Raewsky’s second base contains chlorine in the radical in place of oxygen. We consider it, to say the least, very probable that there exists an analogous cobalt base having the formula NO,.5NH;.Co,C1.0; like ‘ 10,.4NH,.Pt.Cl.0, and we may here remark that the compound which we have mentioned as one of the products of the action of a current of NO. upon an ammoniacal solution of chloride of cobalt appears to contain chlorine in the radical, since we have found this element in the dark brown-yellow oxalate which is thrown down by oxalate of ammonia from the solution. The constitution of Gros’s base becomes perfectly intelligible upon this view, as does that of the analogous base containing but one equivalent of ammonia. It can scarcely fail to escape notice that the theory of conjugates brings all the platinum bases under one point of view, and exhibits the analogy in their con- stitution in a very striking manner, by arranging them at once in three groups, of which the first two are exactly parallel. Thus we have for the radicals of the first six bases mentioned the formule NH,.Pt 2NH,.Pt NH,.Pto 2NH,.PtO NH,.PtCl 2NH,.Ptcl, AMMONIA-COBALT BASES. 65 each uniting with a single equivalent of oxygen to form a uniacid base. The occurrence of a deutoxide of chlorine as a couplet is not more remarkable or more improbable than that of deutoxide of nitrogen; but experimental evidence is still wanting to support the view which we have taken of the constitution of Raewsky’s bases which have as yet been very imperfectly examined. Claus’ has also applied the theory of conjugates to several of the ammonia-platinum bases, but has not considered the subject from precisely the poimt of view which we have taken, though his ideas, in the main, are the same. It is in the explanation of the differ- ence in the saturating capacity of the various bases that Claus’ view appears to us less satisiactory than that which we have proposed. It is scarcely necessary to remark that our theory applies to all bases containing ammonia and a metallic oxide. We may, however, observe that it also harmonizes perfectly with the ammonium theory if we consider ammonium as a conjugate hydrogen, or as represented by the formula NH,.H. We will here remark that our view of the theoretical constitution of the ammonia-cobalt bases was distinctly enunciated in the paper already referred to, as published by one of ourselves, in 1851. A glance at the formule of the ammonia-cobalt bases, suggests the possibility of generalizing the results which we have obtained, by two distinct methods. In the first place, it is evidently possible, theoretically at least, to replace one or more equivalents of ammonia in these compounds by an equal number of equivalents of a compound ammonia, as for example, by methylamin, ethylamin, &c. Thus there may be, for example, a species of Roseocobalt, having the formula 5N(C,H,)3.Co,, which would represent the base which we have described under that name, in which methylamin replaces ammonia. We have not yet been able to investigate this point with any degree of thoroughness, and will here only mention, that an experiment made by adding a solution of piperidin to one of chloride of cobalt and allowing the solution to stand for some time in a half-filled flask, with frequent agitation, led to no decisive result. We selected piperidin for this experiment, because this alkaloid is comparatively easy to prepare, and does not itself oxidize by exposure to the air. In the next place, the results of our investigation may be generalized by replacing cobalt by other metals. This, as we have already remarked, has been done by Claus, who obtained ammonia-rhodium and ammonia-iridium bases corresponding to Roseocobalt, and like this, triacid bases. To judge, however, from the imperfect notices of Claus’ papers which have hitherto reached us, his compounds are not isomorphous with those of Roseocobalt. We have ourselves made many experiments in this direction, though as yet without interesting results. Iron and manganese promised to afford similar classes of compounds, yet in their behavior toward ammonia and oxygen the proto-salts Chemisch-Pharmaceutisches Central Blatt No. 25, p. 189, Oct. 1854. 9 66 RESEARCHES ON THE of these metals exhibit no analogy to those of cobalt. With chromium the case may be different, but we cannot as yet pronounce with certainty on this point. Experiments with nickel failed entirely, and yielded only ammonia-salts of the protoxide. The behavior of ammoniacal solutions of proto-salts of iron and manganese toward the mixture of gases which we have denoted by the formula NO, is worthy of notice. When tartaric acid is added to a solution of proto-chloride of iron or manganese, and after the addition of a large excess of ammonia, a rapid current of NO, is passed through the solution, the liquid soon becomes dark colored, and after a time the whole of the iron or manganese is precipitated as a dark brown or nearly black flocky substance. The filtrate is free from the metal employed. No ammonia- iron or ammonia-manganese base is, however, formed under these circumstances. In order to afford a general view of the results of our investigation, we will here give a table of the formule of the bodies which we have analyzed, or whose constitution has been inferred from analogy of crystalline form. Roseocobalt. Chloride Chlorplatinate Sulphate Nitrate Hydrous nitrate 5NH,.Co,.Cl;-+2HO. 5NH,.Co,.Cl, + 3PtCl,+ SHO. (?) 5NH,.Co,.03,380,+5HO. 5NH,.Co,.0,,3NO;. 5NH,.Co,.0;,3NO,+2HO. Oxalate 5NH,.Co,.0,,3C,0,-+ 610. Ferridcyanide 5NH,.Co,.Cy,+ Fe,Cy;+ 3HO. Cobaltideyanide Chloride Chlorplatinate Acid sulphate Oxalate Acid oxalo-sulphate Neutral oxalo-sulphate 5NH,.Co,.Cy,+ Co,Cy,+ 3HO. Purpureocobalt. 5NH,.Co,Cl.Cl,. 5NH,.Co,Cl.Cl,+ 2PtCl,. 5NH,.Co,0.0,,4S0-+5HO. 5NH,.Co,0.0,,2C,0,+ 3110. 5NH,.Co,0.0,,2C,0;,280,+ 310. 5NH,.Co,0.0,,C,0;,80,;+ 7HO. Luteocobalt. Chloride 6NH,.Co..C],. Todide . 6NH,.Co..I,. Bromide 6NH,.Co,.Br,. Chlorplatinate 6NH,.Co,.Cl,+ 3PtCl,+ 2110. 6¢ Co ence AE GET O! AMMONTIA-COBALT BASES. 67 Chloraurate 6NH,.Co,.Cl, + AuCl,. Cobaltideyanide 6NH,.Co, Cy; +Co,Cy,+ HO. Sulphate 6NH,.Co,.05,3S0,+5HO. Nitrate 6NH,.Co,.0,,3NO;. Oxalate 6NH,Co,.0;,30,0,+4H0. Carbonate 6NH,.Co,.0,,3C0,+7HO. Acid carbonate 6NH;.Co.0;,3C0,+ H0,00,+5H0. Chromate 6NH,.Co,.0;,30r0,+ 5HO. Xanthocobalt. Chloride NO,.5NH,.Co,0.C1,. Chlorplatinate NO,.5NH,.Co,0.Cl,+2PtCl,+ 2HO. Chloraurate NO,.5NH,.Co,0.Cl,+ AuCl,+2HO. Chlorhydrargyrate NO,.5NH,.Co,0.Cl,+4HeC1+2HO. Ferrocyanide . NO,.5NH,.Co,0.Cy,+ FeCy + 7HO. Sulphate NO,.5NH;.Co,0.0,,280,+ HO. Nitrate NO,.5NH,.Co,0.0,,2NO,+ HO. Oxalate NO,.5NH,.Co,0.0;,20,0;4 5HO. In concluding’ for the present an investigation to which we have devoted our leisure for several years, and which has been one of extraordinary difficulty, we desire to state our conviction that the subject is by no means exhausted, but that on the contrary there is scarcely a single point which will not amply repay a more extended study. The number of bases which the sesquioxide of cobalt is capable of forming with ammonia is perhaps very large, and a careful study of the products of the decomposition of the salts of each base promises to yield an abundant har- vest of interesting combinations. It is our hope to be able to return to the subject hereafter, and in a second part of our memoir to clear up some points which we have not as yet had time and opportunity fully to consider. In the mean time, we invite the attention of chemists to a class of salts which for beauty of form and color, and for abstract theoretical interest, are almost unequalled either among organic or inorganic compounds. 1 T should do no justice to my own feelings if I did not in this place gratefully acknowledge the: assistance which I have received in the analytical part of the labor from my friend and pupil, Mr. James R. Brant, whose zeal and skill have alone rendered it possible for me, amid the duties of a laborious professorship, to bring my own share of the work to a conclusion. W. G. New York And PHILADELPHIA, July, 1856. af x an 3 t i ; 5 ; N INSTITUTION, Ned ia ‘PUBLISHED BY THE SMITHSONIA “WASHINGTON, D. 0. } ‘DECEM Ber, 1856. SMITHSONIAN CONTRIBUTIONS TO KNOWLEDGE. NEW TABLES FOR DETERMINING THE VALUES OF THE COEFFICIENTS, IN THE PERTURBATIVE FUNCTION OF PLANETARY MOTION, WHICH DEPEND UPON THE RATIO OF THE MEAN DISTANCES. BY JOHN D. RUNKLE, ASSISTANT IN THE OFFICE OF THE AMERICAN EPHEMERIS AND NAUTICAL ALMANAC, ACCEPTED FOR PUBLICATION BY THE SMITHSONIAN INSTITUTION, NOVEMBER, 1855. psa La 4 Pavia C ny RED. 4 ABC AW MISC ECO SE ANISUIUIS) LVN en] Dah HAS BEEN REFER e us j Re tee ty IBENTAMIN| PEIRCE; 9) 5 Cuartes H. Davis. Joseph Henry, — Secretary. CAMBRIDGE: METCALF AND COMPANY, STEREOTYPERS AND PRINTERS. \ INTRODUCTION. § 1. Tue first important step, in the reduction of the planetary perturbations to numbers, is the determination of those coefficients in the perturbative function which depend upon the ratios of the mean distances. This work has been done by different astronomers, but lastly and most completely by Leverrier, whose results were published in Liowville’s Journal for 1841. Since that time Neptune and thirty-eight Asteroids have been added to the catalogue of planets. If, through the ordinary forms of development, we wish to determine the secular and periodic inequalities of the elements of the orbits of the fifty planets, it will be necessary to find the coefficients which correspond to three hundred and sixty- four values of the ratio of the mean distances. This estimate is upon the supposition that the mutual action of the Asteroids is neglected. 2. At Professor Peirce’s suggestion, and with the approval of Commander Davis, the Superintendent of the American Ephemeris and Nautical Almanac, I have undertaken this work, as a part of the systematic labor of a thorough revision of most of the planetary theories, now being carried on, under the superintendence of Commander Davis, as fast as can be done consistently with the demands which the regular issues of the Almanac make upon the annual appropriations made by Congress for its support. 3. The following notation and forms are found in any work upon the theory of the planetary perturbations. (1 —2acos! + a’)~* = 3 6 + bY cos1 4- 6? cos 21+ 69 cos314-+--+ 6 cost. ee In these formulas a denotes the ratio, taken less than unity, of the mean dis- tances of two planets; and s = 4, 3, 3, &c. The series for computing the values of bY), b'P, b}, &c., bY, bP, bP, &e., UP, bP, bP, &c., or as many of them as are needed, are teadily obtained from ( 1) by qubsataiene the proper values of s and 7. The values of a D, 6®, a? D* 6, a? D? b®, &c., are also needed; and the series for computing them are found by taking the successive derivatives of (1) and multi- plying them by a, a’, a, &c. 1V INTRODUCTION. 4, We see from this, that all values of b9 and its derivatives, any one of which may be denoted by f(a), will depend upon a series of the form (2) f(a) = Apa + Ayait? + Ayait4t Ayait® + Ayait®p ++, in which A,, A,, A,, &c. are known functions of s and 7; and to obtain the values of 6 and its derivatives in the mutual action of any two planets, it is only necessary to substitute the proper value of a, and sum the series to as many terms as will give them with the requisite degree of approximation. 5. It is obvious, that not only must these series converge, which they all do, though in very different degrees, but the facility with which they can be used must depend very much upon the degree of convergency. Now it is found, that, although all the values of a fall between 0 and 0.75, these series, with but few exceptions, converge so slowly that they are nearly useless in their present form; and the great problem has been to transform them into others converging more rapidly. This problem Leverrier has treated with ability and success, in the paper to which reference has been made. The coefficients in his transformed series have received the name of the Leverrier Coefficients. 6. At the request of the Superintendent of the American Ephemeris and Nauti- cal Almanac, the values of the Leverrier Coefficients were computed by the late Sears C. Walker, assisted by Mr. Pourtalés, and are published in an Appendix to that work-for 1857. This carefully prepared paper has been of great aid to me, especially the manuscript sheets containing the numerical values of the coefficients carried to a high degree of accuracy, which were better adapted to the changes demanded by the form of the following Tables. 7. Upon undertaking this work, the first question which presented itself was, How do the series giving the values of b®, a D, b®, a? D? b®, &c., vary with a? Now, for special values of s and 7, these coefficients are simply functions of a; and, if their variation with reference to a is slow, terminating in low orders of differ- ences, we may not only make this circumstance a check upon the accuracy of the work, if we compute them for equidistant values of a, but we may tabulate them with reference to a as an argument, and afterwards enter these tables with the special values of a for the system, and take out their corresponding values. If these Tables were extended from a—0O to a=0.75, we should include all the three hundred and sixty-four values of a; and, if the argument intervals were sufficiently small, all the coefficients could be taken from them with trifling labor. Besides, they would undoubtedly include all the planets hereafter to be discovered. It was soon found, however, that these variations, instead of being slow, were in most cases so rapid as to make them entirely useless, with any reasonable amount of labor, for the purposes indicated. 8. But, resuming the equation Ff (2) — Ay ai + A, ait? + Anat? + Azait® + Ayat§+- see 5 may we not find Ff (a) = f' (a) (a transformed series), : me / . 5 6 . ate in which f(a) is an exact. function of a, involving nearly the whole variation of 3 INTRODUCTION. Vv Ff (a), while the transformed series shall vary so slowly with reference to a, as to be perfectly adapted to the ends already specified ? We should then tabulate 5, and, having taken a value of it from the Tables for some value of a, it would only be necessary to multiply this tabular value by the corresponding value of f” (a) to obtain the required value of f(a). And if we could tabulate the logarithmic, instead of the numerical, values of ao we should find log f(a) at once, which is always needed. On these considerations the following Tables are based; and, fortunately, only slight and quite obvious changes in Leverrier’s series were needed, thus, with corre- sponding modifications, making the valuable labor of Mr. Walker entirely available. 9. Since we wish to tabulate the logarithmic values of FS, it must be finite ore @ == (0), But equation (2) fulfils this condition at once if we give it the form (8) FO = Apt Ard + Ana A, Pf Ae po; for when « — 0, £(@ — 4 0° a f 2 is changing relatively to a, at any point between Now, the rate at which log the limits of a = 0 and a = 0.75, is readily determined ; and, if it be sufficiently slow for practical use, then the series (3) needs no further change. oY a Such was found to be the case with log —', which is tabulated on pages 1 to 7. 10. When, however, as in most cases, the variation of the series (3) is too rapid to be practical, it may be transformed in the following manner. If we both multi- ply and divide it by 1 — a? we shall obtain LO _ 1 Sat (A— A) e+(A—A) $A) po hs and by putting a2, AA = dA, A— A= 94, A,— Ap = 34 &e., it becomes (4) Pg = Ao oA @+3Aa+bA,o+dA,d+:+:+, be. The whole variation of (3) from a = 0 to a = 0.75 is 2) A, (2) + 42 i+ AO the whole variation of (4) between the same limits is (2) 8 Ay (2)? + 8A; (2)! + 8-Ay (2/8 F< * 75 the difference of these variations is (¢) Ay (2)? + Ar (2) + 42 (2) Fo The coefficients in (3) are positive for all admissible values of s and7z; and if vi INTRODUCTION. they are all increasing, (6) will be positive, and (4) will vary more slowly than (3); but if they are all decreasing, (b) will be negative, and (4) will vary more slowly than (3) only when (6) is numerically less than (a). Otherwise (3) will be pref- erable to (4). But the reverse may, at the same time, be true with respect to the convergency of these series. 11. By a similar transformation of (4), putting * 8A,— A, = 8A, 64, —8A,=8A,, 5A,—8A,=8'A,, &c., we obtain (5) fg = Ay + PA, 4 RA a +A pees. Continuing the same transformations and notation, we find H@) ee 3 2 3 4 3 6 ae ees (6) aize gs — fo Aya’ | OA, ol + A, ob 5 Jie) 4 2 4 4 4 PMN oda (7) gine ga 40 b 8 Ay at + 8A, a! + 8° Ay a? 5 HO) 2 5 4 5 6 eee. (8) gow gn = A+ FA P+ PA + PAH, &c., &c. When we have a series corresponding to special values of s and 7, that is, when the coefficients in our series have been reduced to numbers, the number of such transformations needed to obtain the series most desirable, both with respect to con- vergency and the amount of variation relatively to a, will be a practical question which can, in most cases, be settled by simple inspection. It has been found practicable to tabulate the following functions, b? a D, bY a” De bY) a® D? oD a DR GS log me og ai=2 ge” log a4 pi’ log ai—6 Bo ” og a8 BB” a BY a® D, b a? D2 UD a? UD log G3 av’ log 5 as” Hes eras? log S=5 ge for all values of 7 generally needed in the perturbative theories of the planets. These tabular values have been limited to i= 9; since, for values of 7 larger than 9, only few values of these, or any other functions, are needed. 12. The following special case will show the effect of the above transformations. In order to take the differences more readily, the series may be written vertically, with the corresponding function at the top of the column. a D, 500) 08 D, 40) a8 D, po) a D, y) a D, p20 a8 D, p00) ae a0 ga aa Gh a Be at BS a? pi : a + 567.35451 + 567.35451 + 567.35451 -+576.35451 +576.35451 -+576.35451 a + 1934.16309 + 1366.80858 ++ 799.45407 +232.09956 —335.25495 —902.60946 at + 4442.53086 + 2508.36777 +1141.55919 +342.10512 +110.00556 +445.26051 a® + 8494.50955 + 4051.97869 +1543.61092 +-402.05173 + 59.94661 — 50.05895 a + 14547.79565 + 6053.28610 +2001.30741 +457.69649 + 55.64476 — 4.30185 a0 + 23114.83086 + 8567.03521 +2513.74911 -1512.44170 + 54.74521 — 0.89955 al2 + 34762.53860 +11647.70774 -+3080.67253 -++-566.92342 + 54.48172 — 0.26349 al4 + 50112.23098 +-15349.69238 +3701.98464 +621.31211 ++ 54.38869 — 0.09303 alé + 69839.57190 +19727.34092 +4377.64854 +675.66390 + 54.35179 — 0.05690 al8 + 94674.56137 -+24834.98947 +5107.64855 -+-730.00001 + 54.33611 — 0.01568 a20 +-125401.52839 -+-30726.96702 +-5891.97755 -+-784.32900 + 54.32899 — 0.00712 az -+-162859.12777 +37457.59938 +6730.63236 +838.65481 + 54,32581 — 0.00318 INTRODUCTION. Vii hg iy all : : : 2p. pom Now it is evident that the series which gives the value of a more rapidly than any of the preceding ones; and a little examination will show that it also converges more rapidly than the one which will result from taking the next order of differences. It is therefore the one best adapted to finding special : 3 400) . values of a? D, b&; but the function es is much the best one of the set to a converges tabulate, since its whole variation, between the limits of a = 0 and a — 0.75, is only about half of that of the two functions which immediately precede and follow it. 13. The series for computing those coefficients of which but few values can ever be needed, are given on pages 42, 43, and 44. The coefficients corresponding to such high values of i are mostly needed in the long-period terms in the theory of Venus and the Earth. The few values of a* D? b) needed in the theory of Jupiter and Saturn, were computed from the series given by Mr. Walker. 14. Resume (4), and write it (9) f (2) = Ad e4+ @ (3A, a' + 8A, ait? + 3A, at#+t $A, ai tS 1 ++. -), Now, since the series in this parenthesis has precisely the same form as (2), it may, by putting 5 3A, —8A, = 8A, 34,—84,— 8A, 84,—84A,= 8A, &c., be written 8A, a? e+ B? (S° Ay a + SA, ait? + & A, at! + SA, ait + eee oss and, by substituting this form in (9), it becomes (10) F@ — Ay a—* B? 6A, ai? pt + gt (8° Ay a + & A, at? + § A, a eee o)\, By a similar transformation (11) Ff (2) — Ay aa? Be + 6A, a2 Bt + & A, mins. + 6° (8° Ay a + SA, ait? + & A, ait4 + eee NR and, continuing this process indefinitely, we finally get (12) f (a) = ai? 6 (Ay + 8.Ay B+ 8Ay BY + 8° Ay B+ 8! Ay BP +++ "Ay A”). In practice, the value of f(a) is obtained from the most convergent of these transformed series, which may usually be determined by simple inspection. These are the forms adopted by Leverrier; but we have derived them by a much simpler process. 15. Professor Peirce has also suggested transformations, which, as far as conyver- gency is concerned, leave nothing to be desired; but, as most of his series are func- tions of differences of the required quantities, tables constructed upon this basis would not have been so practical as those we have given. Besides, it was very desirable to make the whole subject rest upon a numerical basis prepared with such great care as Mr. Walker's paper. The coefficients Ao, 8 Ay, 8? Ay, 8° Ay, &c., are the Leverrier Coefficients computed by Mr. Walker. It will be seen that these coefficients are readily converted into those necessary to compute the functions we have tabulated. For this reason, we have adopted the series involving the same order of differences as those adopted by Leverrier; al- vill INTRODUCTION. though in some cases the series expressed in terms of the order preceding or fol- lowing vary less rapidly relatively to a. In constructing the following Tables, each term was computed for every .03 of a between the necessary limits, and the accuracy of the computations for all the larger terms was tested by differences. The series were then summed to as many terms as were necessary to give the last figure in the tabular logarithms accurate, and the numerical values of the function checked by differences. Logarithms of these values were then taken and checked in the same way. Next, these logarithms were interpolated to every .01 of a, and those functions of which but few values are ever needed are printed in this form ; the remaining ones interpolated to every .005, are practically without third differences, and in this form they are printed. Nearly all the functions given to every .005 of a are accompanied by the logarithms of their variations for every .001 of a. These variations correspond to the value of the argument opposite to which they are written, and their differences are so small that the second differences of the functions may be taken into account with- out any difficulty. Since f(a) is usually a small fraction, f(a) will always be found with a high degree of accuracy. 16. In printing these Tables, the proof was read by copy, and then the page was stereotyped. Plate-proofs were then tested by taking a new set of differences, and all the errors thus found were corrected in the plates. Proofs from the corrected plates were used in preparing the Supplement. As fast as the pages of the Sup- plement were stereotyped, they were tested by a duplicate computation entirely independent of the first. The series printed on pages 42, 43, 44, were also com- puted in duplicate. In conclusion, I must express my obligations to my friend and colleague, Mr. Isaac Bradford, for the valuable aid he has rendered me in preparing the Tables for the press, and in computing a duplicate of the Supplement. TABLES FOR DETERMINING THE VALUES OF i) AND ITS DERIVATIVES. 1 LOGARITHMIC VALUES OF (0) log var. for yh) log var. for § pi?) log var. for } a?) log var. for us log Uy oor ofe. | = | oovote. | ES | co1ofa. | 1s = O01 of a. .000 | 0.3010300 —c | 0.0000000 —O 9.8750613 —c@ | 9.7958800 — a 005 .38010328 1.0414 # .0000040 1.2068 -8750655 1.2480 } .7958847 1.2765 -010 -3010410 -3385 | .0000161 5106 .8750790 -5587 f .7958989 .5786 015 .3010546 -5145 | .0000364. 6884 .8751017 -7364 | — .7959226 -7559 020 .3010737 -6395 } .0000650 8143 .8751335 -8603 f .7959559 .8814 -025 0.3010982 1.7356 | 0.0001017 1.9112 9.8751744 1.9571 || 9.7959987 1.9782 -030 .3011281 .8142 || .0001466 1.9903 8752243 2.0366 | .7960511 2.0573 .035 -3011634 .6814 | -0001996 2.0577 .8752832 .1031 -7961129 1245 -040 .3012042 .9395 -0002608 1155 -8753511 -1614 } .7961843 1824 -045 .3012504 1.9903 | .0003301 1667 -8754281 .2125 | .7962652 2338 -050 0.3013020 2.0362 }} 0.0004076 2.2127 9.8755142 2.2586 || 9.7963556 2.2797 055 .3013591 .0777 | .0004933 .2543 -8756094 .3002 § .7964556 0214 -060 -3014217 -1159 } .0005872 -2922 .8757138 .3381 9 .7965652 3595 -065 .3014897 .1508 | .0006893 .3274 .8758273 731 - 7966844 3945 .070 -3015632 .1833 § .0007997 .3598 .8759499 -4055 -7968132 4267 075 0.3016422 2.2138 || 0.0009183 2.3901 9.8760817 2.4358 | 9.7969516 2.4570 080 -3017269 £2422 | 0010452 -4183 .8762227 4642 9 .7970996 -4853 -085 .8018170 .2688 4 .0011804 4450 .8763729 -4908 -7972573 .5120 -090 .3019127 .2940 } .0013239 4702 .8765324 5161 | .7974247 5371 095 3020139 .3178 .0014.757 .4940 .8767011 .5398 | .7976018 5611 -100 0.3021205 2.3405 0.0016358 2.5166 9.8768790 2.5625 9.7977887 2.5839 -105 .3022328 .3621 | .0018042 5382 .8770662 .5841 -7979854 -6054 .110 .3023507 .3827 f .0019811 5588 .8772628 6049 # .7981918 6258 115 .3024742 4024 -0021664 .5785 .8774687 .6245 | .7984080 6458 120 .3026033 .4214 | .0023601 5974 .8776841 6434 9 .7986342 6649 125 0.3027380 2.4396 | 0.0025622 2.6156 9.8779088 2.6616 | 9.7988703 2.6831 .130 .3028785 4572 .0027728 6331 .8781429 -6791 § .7991162 -7005 BIS, 3030246 A741 4 ~=.0029919 6501 .8783865 6961 } .7993721 -7176 -140 -3031763 4904 | .0032196 .6665 .8786395 -7125 f = .7996382 -7339 145 .3033338 5062 | .0034559 6822 .8789021 -7283 | .7999142 -7497 -150 0.3034971 2.5215 # 0.0037008 2.6975 9.8791744 2.7436 # 9.8002002 2.7648 155 .3036662 .5364 | .0039543 7124 .8794563 -7585 |} .8004962 -7797 .160 .3038410 5508 9¥ .0042165 7268 .8797478 .7729 4 .8008024 .7941 .165 -3040216 5648 | .0044874 7408 -8500490 .7868 — .8011187 .8081 .170 .3042081 -5784 4 .0047671 7545 .8803599 -8004 | .8014452 .8217 175 0.3044005 2.5917 # 0.0050556 2.7678 9.8806806 2.8137 f 9.8017520 2.8350 .180 .3045986 6047 } .0053529 7807 .8810111 8266 § .5021291 .8479 185 .3048028 .6173 | .0056591 7933 .8813515 .8393 1 .8024866 .8606 .190 -38050129 .6296 .0059742 .8056 .8817018 .8516 -8028546 873 sigs .3052290 .6416 -0062982 .8176 .8820621 .8637 |} .8032331 .8851 .200 0.3054510 2.6533 # 0.0066313 2.8294 9.8824325 2.8755 9.8036223 2.8969 .205 -3056790 6648 | .0069734 .8409 .8828129 .8871 } .8040220 9085 .210 -3059131 6761 .0073246 8522 8852035 .8984 ff .8044325 .9199 -215 -3061533 -6872 .0076849 8633 .8836043 9095 | .8048536 .9510 .220 .38063997 6981 .0080545 .8741 .8840153 .9204 | .8052856 .9419 225 0.3066523 2.7087 0.0084333 2.8847 9.8844366 2.9310 } 9.8057285 2.9526 -230 -3069110 aHLON .0088214 .8952 .8848652 .9414 }# .8061822 9631 .235 .3071760 27294 .0092189 9055 .8853104 9517 } .8066470 .9734 .240 .3074473 .7395 4 .0096258 .9156 .8857629 .9618 .8071227 .9835 245 .3077249 -7494 .0100422 .9255 .8862262 .9718 .8076096 2.9935 .250 0.3080089 | 2.7592 } 0.0104682 2.9353 9.8867001 2.9817 | 9.8081078 3.0035 | 2 LOGARITHMIC VALUES OF 3 a 30) TABLES FOR DETERMINING THE VALUES OF a) AND ITS DERIVATIVES. 0 log var. for | vo) log var. for pi?) log var. for } 23) log var. for o og) | Roe. | 1S — | corefu. | HE | oo1cre | 1 || 01 of. 250 | 0.3080089 2.7592 | 0.0104682 | 2.93533 f 9.8867001 | 2.98162 } 9.8081078 | 3.00328 2255 3082993 -7689 | .0109038 94493 .8871848 | 2.99131 | .8086172 .01292 260 3085962 .7784 | .0113491 95440 .8876803 | 3.00084 } .8091380 02243 265 3088996 .7877 |} .0118041 .96374 || .8881867 01022 | .8096702 .03181 -270 3092095 .7969 || .0122689 .97296 }| .8887042 .01945 || .8102141 .04107 275 | 0.3095260 2.8060 | 0.0127437 | 2.98206 } 9.8892326 | 3.02853 } 9.8107695 | 3.05022 .280 3098492 £8150 # .0132284 .99104 | .8897721 .03749 8113367 05925 | 285 .3101791 .8238 || .0137232 | 2.99991 8903228 04634. .8119157 .06816 | -290 .3105157 .8325 } .0142282 | 3.00866 | .8908847 05509 8125066 .07696 2295 3108591 8412 .0147434 .01729 } .8914580 .06375 } .8131095 08565 .300 | 0.3112093 2.8498 | 0.0152688 | 3.02581 } 9.8920428 | 3.07231 | 9.8137246 | 3.09424 305 3115665 .8582 } .0158046 .03423 9 .8926392 .08077 .8143519 10278 .310 .3119307 .8665 | .0163508 04255 8932472 .08915. } .8149914 11113 315 .3123019 .8748 | .0169075 .05079 .8938670 .09745 8156434 11945 320 3126801 .8830 .0174748 05895 |} .8944989 10567 .8163079 12768 -3825 | 0.3130655 2.8910 | 0.0180528 | 3.06703 # 9.8951427 | 3.11381 ] 9.8169851 3.13583 -330 3134581 .8990 | .0186417 07505 }} .8957986 .12187 } .8176751 14390 335 .3138580 9070 .0192415 .08300 | .8964667 .12985 # .8183780 15190 340 3142653 9149 | .0198523 .09088 | .8971471 .13776 } .8190938 15983 345 3146800 .9227 | .0204743 .09870 || .8978400 14562 8198228 .16770 .350 | 0.3151022 2.9304 | 0.0211075 | 3.10645 | 9.8985454 | 3.15341 } 9.8205651 3.17550 355 3155320 .9381 | .0217521 11414 8992636 .16113 } .8213208 18324 360 3159694 9458 } .0224081 .12177 | .8999946 [16879 | .8220901 19092 365 3164145 .9533 9 .0230757 .12934 | .9007386 .17639 | 8228730 19855 370 .3168675 .9608 |} .0237550 .13686 # .9014957 .18393 } .8236697 20613 .875 | 0.3173284 2.9683 | 0.0244461 | 3.14432 | 9.9022660 | 3.19142 }| 9.8244804 | 3.21366 380 .3177972 .9767 0251492 15174 |} = .9030496 .19886 } .8253051 22115 385 .3182741 9831 0258644 .15911 | .9038467 20626 # .8261442 22861 .390 .3187591 9904 4 .0265918 .16643 | .9046574 21361 } .8269978 .23603 395 3192523 2.9977 0273315 17371 9054820 22092 .8278662 24340 .400 | 0.3197539 3.0050 | 0.0280836 | 3.18095 | 9.9063205 | 3.22818 | 9.8287493 | 3.25073 405 .3202639 .0122 | .0288484 .18816 | .9071731 23543 | 8296475 25804 410 .3207824 0194 0296259 19533 |} .9080401 24265 # .8305608 26530 415 8213095 0265 0304163 20246 | .9089216 24985 # .8314895 27252 420 .8218454 .0336 .0312199 20957 .9098177 £25703 | .8324336 .27970 .425 | 0.3223901 3.0407 | 0.0320366 | 3.21665 || 9.9107288 | 3.26418 | 9.8333935. | 3.28684 430 3229438 .0478 || .0328667 22371 | .9116551 27130 | .8343693 29395 435 3235065 .0548 ff .0337104 .23075 | .9125966 .27839 | .8353612 30104. 440 .3240783 .0619 0345680 24776 |} .9135537 628545 |} .8363693 30810 445 18246595 .0689 0354394 124475 f .9145263 £29248 | .8373940 .B1515 450 | 0.38252500 3.0759 | 0.0363250 | 3.25172 || 9.9155148 | 3.29948 }| 9.8384353 | 3.32219 455 3258502 .0828 || .0372248 25866 |} .9165192 30645 8394938 32921 .460 3264600 .0897 .0381391 £26559 | .9175398 31341 8405695 33623 465 .3270796 .0966 | .0390681 27252 |} .9185770 .32037 ] .8416628 34325 470 38277091 .1035 |} .0400120 .27943 }} .9196308 827382 | .8427738 35025 475 | 0.3283488 3.1104 | 0.0409710 | 3.28632 4 9.9207017 | 3.33425 | 9.8439029 | 3.35724 480 .3289986 .1173 0419454 .29320 } .9217898 .34117 | .8450504 36422 A485 3296589 .1242 | .0429354 30007 9228954 .34809 | .8462164 .37118 -490 3303297 .1311 ] .0439411 .30693 | .9240187 35501 .8474011 .37814 A95 .3310112 .1379 | .0449628 .31377 | .9251600 36192 }} .8486050 38509 .500 | 0.3317034 3.1447 | 0.0460006 | 3.32061 } 9.9263197 | 3.36883 } 9.8498283 | 3.39205 —————— TABLES FOR DETERMINING THE VALUES OF 0) AND ITS DERIVATIVES. 3 pt) | LOGARITHMIC VALUES OF —% | o 79) log var. for | oo) log var. for p?) log var. for } p(3) log var. for a log b $ Gi of a. } Tog) nan Ol of w. F log + tay of a. | log + 001 of «. 500 | 0.3317034 | 3.14472 } 0.0460006 | 3.32061 || 9.9263197 | 3.36883 } 9.8498283 | 3.39205 505 .3324067 15159 0470550 .32746 .9274980 37574 8510714 39900 510 3331213 15846 0481260 33431 9286951 38265 | .8523345 40595 515 .3338472 16533 0492141 .34116 9299114 38955 || .8536180 41290 520 3345847 17221 0503196 34801 9311472 39645 f} .8549229 41985 | | } H 525 | 0.3353340 | 3.17909 | 0.0514426 | 3.35486 | 9.9324028 | 3.40336 || 9.8562475 | 3.42681 .530 3360952 18598 } .0525835 36171 .9336786 41028 | .8575942 43378 535 3368686 19288 || .0537426 .36858 || .9349749 41721 .8589627 44075 -540 8376545 19979 .0549200 .37546 | .9362921 42415 | .8603533 AATTA 545 3384530 20670 .0561163 38236 .9376305 43110 | .8617665 45475 550 | 0.3392641 | 3.21361 | 0.0573318 | 3.38926 ]} 9.9389905 | 3.43806 } 9.8632028 | 3.46177 555 .3400883 22053 |} .0585668 39616 || .9403725 44504 || .8646625 .46880 .560 3409258 22747 || .0598216 .40308 .9417769 45204 | .8661460 47585 565 3417768 123444 f} .0610966 .410038 9432042 45905 8676538 48292 570 3426415 24143 ff 0623923 41700 9446547 .46608 8691865 49001 .575 | 0.3435203 | 3.24844 | 0.0637089 | 3.42400 | 9.9461289 | 3.47313 } 9.8707443 | 3.49711 -580 3444135 125547 § .0650469 43102 9476273 .48020 | .8723279 50424 585 3453213 26252 | .0664068 43805 # .9491503 48728 |} .8739378 51140 .590 3462439 26960 | .0677889 44511 ff .9506984 49440 f .8755746 51859 595 3471817 27671 .0691938 .45220 9522722 50155 8772387 52581 .600 | 0.3481352 | 3.28385 | 0.0706219 | 3.45931 | 9.9538720 | 3.50873 } 9.8789308 | 3.53306 | -605 3491044 29104 | .0720735 46645 9554987 51594 8806513 54033 i| .610 .8500898 .29826 | .0735493 47362 | .9571527 52319 | 8824010 54763 615 .3510917 .30550 | .0750497 48081 -9588346 .53047 }| .8841803 .55498 620 8521105 .31278 | .0765751 48805 | .9605450 53779 8859901 56236 | 625 | 0.3531466 | 3.32010 } 0.0781263 | 3.49534 | 9.9622846 | 3.54516 | 9.8878310 | 3.56979 .630 3542004 .82746 |} .0797036 50266 | .9640540 .55257 || .8897038 57726 | .635 3552723 33486 | .0813080~] .51002 | .9658539 56001 | .8916092 58478 640 3563626 134230 | .0829399 51742 | .9676851 .56750 |} .8935480 59234 | 645 8574719 .34980 0845999 52488 |} .9695482 .57505 || .8955210 59995 | 650 | 0.3586005 | 3.35735 | 0.0862889 | 3.53239 | 9.9714441 | 3.58264 | 9.8975290 | 3.60761 655 3597490 36495 0880074. 53995 | .9733735 59028 ff .8995728 .61532 i| -660 3609178 37261 || .0897560 54757 | .9753374 .59798 9016534 62309 665 3621075 .38034 |} .0915358 55526 || .9773364 .60573 | .9037717 63093 670 3633187 .38813 .0933476 56301 9793717 .61354 | .9059286_| .63883 .675 | 0.3645519 | 3.39599 1 0.0951921 | 3.57081 | 9.9814440 | 3.62142 } 9.9081254 | 3.64680 .680 3658077 .40392 | .0970703 57869 9835545 62936 | .9103631 65484 685 .3670868 41191 | .0989830 58665 | .9857040 63738 || .9126428 66294 690 .3683897 41997 | .1009312 59467 | .9878939 64547 | .9149655 67111 695 3697172 42811 f .1029158 60277 9901251 65364 || .9173325 .67936 | H ! | 700 | 0.3710699 | 3.43633 || 0.1049381 | 3.61095 } 9.9923988 | 3.66190 | 9.9197451 | 3.68770 705 3724486 44464 } .1069990 61921 } .9947164 67025 | .9222048 .69613 710 .3738540 45304 | .1090996 62756 | .9970793 .67869 | .9247131 70465 || “715 3752870 46153 | .1112412 .63599 |) 9.9994889 68724 9272713 71327 .720 3767484. 47011 1134250 64450 | 0.0019466 .69589 | .9298809 72198 | 1725 | 0.3782393 | 3.47880 || 0.1156523 | 3.65310 || 0.0044542 | 3.70465 | 9.9325436 | 3.73078 .730 3797604 48758 } 1179244 66179 | .0070132 (71352 || .9352612 .73967 735 3813128 49647 | .1202426 67056 || .0096253 £72251 || .9380354 74867 740 8828975 .50546 | .1226084 | . .67942 .0122922 .73161 | .9408680 175777 | 745 8845155 51455 |} .1250231 .68837 } .0150159 74082 } .9437609 76697 | 750 | 0.3861679 | 3.52374 | 0.1274884 | 3.69741 | 0.0177985 | 3.75015 | 9.9467161 | 3.77627 — — TABLES FOR DETERMINING THE VALUES OF © AND ITS DERIVATIVES. | (0 LOGARITHMIC VALUES OF —2- a pd) log var. for } i) log var. for} 19) ut) 28) p?) log —*- ‘001 of c. eg — ‘eat oon |) Les =e log ~ log = log + 9.737888 —@® f 9.692131 —@ 9.65434 9.62216 9.59413 9.56931 -737894 0.3222 | .692137 0.3222 -65435 -62217 -59414 -56932 -737909 -O9L1 § -692151 -5911 -65436 -62218 -59415 -56933 -737934 -7643 | -692176 -7782 -65439 -62220 09417 -56936 -737967 .8921 .692211 -9031 65442 -62224 -59421 .56939 9.738011 0.9868 } 9.692256 0.9956 9.65447 9.62229 9.59426 9.56944 .738064 1.0682 | -692310 0.0719 -65452 -62234 -59431 -56949 .738128 .1367 | 692374 1.1399 -65458 -62240 -59437 .56955 -738201 .1931 | -692448 1987 -65466 -62248 -59445 -56963 «738284 +2455 | .692532 2504 -65474 -62257 -59454 .56972 9.738377 1.2923 § 9.692626 1.2967 9.65484 9.62266 9.59464 9.56982 -738480 .3344 | -692730 3404 -65495 -62277 -59475 -56993 -738593 .3711 | .692845 3784 65506 -62289 -59487 -57005 -738715 4065 | .692969 -4133 .65518 -62302 -99500 -57018 - 738848 -4393 | -693104 -4472 -65532 -62315 -59514 -57032 9.738991 1.4698 | 9.693249 1.4771 9.65547 9.62330 9.59529 9.57047 -739143 4983 jf -693404 -5065 65562 .62346 -09545 -57063 -739306 -5238 | .693569 5315 -65579 -62363 -59562 -57080 -739477 -5478 | -693744 .5563 -65597 -62382 -59580 -57098 -739659 .5740 -693930 -5821 -65616 .62401 59599 -57117 9.739852 1.5977 | 9.694126 1.6043 9.65635 9.62421 9.59619 9.57138 -740055 -6181 | .694332 -6263 -65656 -62442 -59640 -57160 «740267 6375 | -694549 -6474 -65678 -62464 -59663 .57182 .740489 6571 | -694776 6665 65701 .62487 -59687 .97205 -740721 -6766 4 -695013 .6857 -65726 -62511 -59711 01229 9.740964 1.6955 9.695261 1.7042 9.65751 9.62536 9.59736 9.57255 -741217 7127 | -695519 -7217 -65777 -62562 .59763 -57281 -741480 -7300 | -695788 7388 -65804 -62589 59791 .57309 -741754 -7459 | .696067 7544 -65833 -62618 -59819 -57338 -742038 -7619 ff -696356 7701 -65863 -62648 .59848 -57368 9.742332 1.7774 4 9.696656 1.7853 9.65893 9.62678 9.59879 9.57400 -742637 -7924 §F -696966 -8000 -65924 -62710 -o9911 -57432 -742952 -8069 | 697287 .8143 -65957 62742 -59943 -57465 -743278 .8209 | .697618 .8280 .65991 -62776 -59977 -57499 743614 .8344 | .697960 8420 -66025 -62811 -60012 i530 9.743961 1.8476 } 9.698313 1.8549 9.66061 9.62847 9.60049 9.57572 -744318 .8609. | .698676 -8675 .66098 -62885 -60087 -57609 .744686 8733 .699050 .8808 -66136 .62923 -60126 -57648 -745065 8854 | .699436 .8943 66175 .62962 -60165 .57688 -745455 .8976 | .699833 -9063 -66215 .63003 -60206 -57729 9.745855 1.9096 | 9.700243 1.9185 9.66257 9.63045 9.60249 9.5777: -746266 -9212 Ff -700663 -9299 -66300 -65088 -60292 .O7816 || -746688 9325 § -701095 -9415 -66343 -63132 -60337 .57860_ || -747122 9435 -701537 -9523 .66387 -63177 -60383 -57905 -747566 .9547 -701991 9633 -66433 -63223 -60430 .97952 9.748022 1.9652 | 9.702456 1.9731 9.66480 9.63270 9.60478 9.58000 -748489 -9745 | -702931 .9832 -66529 -63319 -60527 -58049 -748967 .9854 -703418 1.9934 { -66579 .63369 -60577 .58100 -749456 1.9956 | -703915 2.0030 | 66629 -63419 -60628 .08152 -749957 2.0060 -704425 .0137 -66680 -63471 .60680 .58205 9.750470 2.0162 | 9.704947 2.0237 } 9.66733 9.63524 9.60734 9.58259 ————— TABLES FOR DETERMINING THE VALUES OF Be AND ITS DERIVATIVES. 5 9.750470 -750994 -751530 -752078 -752638 9.753210 «753794 -754390 -754999 -755620 9.756253 -756900 -757558 -758230 -758914 9.759611 -760322 -761047 -761784 762535 9.763300 -764079 -764871 .765678 -766499 9.767334 -768184 -769050 -769929 -770824 9.771735 -772661 -773602 «774559 -775532 oO -776521 «777527 -778550 -779589 9.781721 «782814 -783923 785050 -786197 9.787362 -788546 .789749 -790972 -792215 9.793478 - 780646 © log var. for 001 of c. | 2.0154 | -0253 .0350 | 0445 | 0539 | 2.0630 .0719 | .0810 | .0899 | .0986 | 2.1072 | 1156 | .1239 J .1323 | -1406 2.1489 | 1569 | 1650 | .1732 | .1807 | 2.1884 1962 | -2039 2117 | 2191 2.2269 | 2345 | 2420 | 2494 | 2567 2.2639 | 2711 .2783 | -2856 12927 | 2.2999 | 3071 3143 | 3214 | 3286 | 2.3357 | -3428 | -3496 .3568 | .3638 2.3709 | 3777 | .3849 3920 | 3990 | 2.4057 3) LOGARITHMIC VALUES OF —2- a p) log var. for | p(9) A 28) 3?) log ~b ‘001 ofa. | log + log + log ~- log -+ 9.704947 2.0237 } 9.66733 9.63524 9.60734 9.58259 -705481 .0338 | -66787 -63579 -60789 -58315 -706028 0434 | -66842 -63634 -60845 -58372 -706587 -0531 | -66898 -63691 -60902 -98430 -707158 -0622 | -66957 -63750 -60962 -58490 9.707741 2.0715 | 9.67016 9.63809 9.61022 9.58551 -708337 -0803 | -67076 -63870 .61083 -58612 -708945 -0892 | -67137 -63932 .61146 -58675 -709564 -0980 } -67200 -63996 -61210 -08739 -710197 -1065 | -67264 -64061 -61275 .08805 9.710842 2.1153 9.67330 9.64128 9.61342 9.58872 -711500 1235 | -67396 -64196 -61410 -58940 -712171 -1319 } -67464 64265 -61479 -59010 .712855 -1405 -67533 -64335 -61550 -59081 .7138552 -1489 | -67604 .64407 -61622 09154 9.714263 2.1572 | 9.67676 9.64480 9.61695 9.59228 -714988 -1655 | .67750 -64554 -61770 -59303 -715727 .1735 | -67825 -64630 -61846 -59380 -716479 -1813 | -67901 -64707 -61924 .09458 /717245 -1892 | -67979 -64786 -62003 -59538 9.718025 2.1971 } 9.68058 9.64866 9.62084 9.59618 -718819 .2049 | -68139 -64947 -62166 -59700 _-719628 .2127 -68221 -65030 .62249 .59784 -720452 .2204 § -68505 -65114 -62334 -59869 .721290 2281 | -68390 -65200 .62421 _ -59956 9.722143 2.2358 } 9.68477 9.65287 9.62509 9.60045 -723011 2433 | -68565 -65376 -62599 -60136 -723894 2507 | -68655 -65466 .62690 -60228 -724792 .2581 | .68745 -65559 .62783 -60322 -725705 -2653 | .68838 .65652 .62877 -60417 9.726634 2.2725 | 9.68932 9.65747 9.62973 9.60513 -727578 2797 | -69028 -65844 -63070 -60611 -728538 -2869 § -69125 | -65942 .63169 60711 -729514 -2940 f -69224 -66042 -63270 -60812 -730505 .3013 | -69325 66144 .63372 -60917 9.731514 2.3086 } 9.69428 9.66248 9.63475 9.61022 732540 -3160 | -69532 -66353 -63580 -61129 -733583 .3233 -69638 .66460 -63688 -61238 -734645 -3304 | -69746 -66569 .63797 -61348 «735724 .3375 -69856 -66680 -63908 61461 9.736821 2.3446 | 9.69966 9.66791 9.64022 9.61574 -737936 .3517 -70079 -66905 -64137 -61692 -739069 .3587 | -70194 -67022 -64254 -61812 -740221 -3657 | -70311 |} -67141 .64373 61935 -7A1391 3727 -70429 -67261 .64494 -62058 9.742580 2.3797 | 9.70549 9.67383 9.64617 9.62183 -743789 .3867 | -70672 -67508 -64743 -62310 -745018 .3939 | -10797 -67635 -64870 -62440 -746266 A009 | -70923 -67763 -65000 -62571 «747535 4081 | «71051 -67893 .65132 .62704 9.748825 2.4150 9.71182 9.68026 9.65266 9.62840 TABLES FOR DETERMINING THE VALUES OF 2® AND ITS DERIVATIVES. laa —<————) Ee (0 (or) 1 LOGARITHMIC VALUES OF : a (4) el (5) : (6) (7) (8) (9) b log var. for b log var. for } b b b b log i 001 of « | log + 001 of a | log + log o}) log 3 log Oey loz einai lor ey lor rs or cree oa, a wi 9 B? 5 al pi f=) « pe 5 oe Be =) a pe a? +9.5268252 -+-+-0.5682179 +-1.5682180 +:2.5224605 +3.4255504 +4.2706484 a2 +9.2073119 —0.2054196 —1.6889414 —2.8588090 —3.8971069 —4.8347436 a4 9.0653399 —9.5463043 +1.0462084 +-2.6871765 +3.9409679 +5.0166585 af 8.9703643 —9.1922130 -0.2352761 -—1.8700532 —3.5974309 —4.8900626 a8 8.8976491 —8.9384579 +9.7904561 —0.9318112 +-2.6593168 +-4.4254283 ql 8.8381032 —8.7368913 9.4732818 —0.3755407 -+1.6307492 —3.3923716 al? 8.7873497 —8.5678872 92271350 —9.9626214 1.0060926 —2.2830750 al4 -+8.7429307 —8.4213789 9.0260938 —9.6290049 0.5415519 —1.5846506 al6 8.7033201 —8.2914656 +8. 8562818 —9.3463657 0.1707002 —1.0489863 al8 86675010 —8.1743672 +8. 7093425 —9.0993890 -9.8618412 —0.6057986 | @20 8.6347593 —8.0675042 8.5798437 —8.8787761 9.5979913 —0.2223090 i q22 8.6045716 —7.9690301 8.4640573 —8.6784273 9.3682395 —9.8798852 ati +8.5765428 —7.8775729 +8.3593185 —8.4941026 9.1651830 —9.5662041 I] q@26 +8.5503661 —7.7920522 -+8.2636600 —8.3227280 8.9834735 —9.2733277 | I Powers of, a ‘oe D, po) od De ot) a? Ds ptt?) ot De ot?) a Dy (12) | a oS Tauare log oS pe log a pe 5 log at pe log sat FO 7 | a? +9.5083418 +-0.5875231 -++-1.6289158 -+2.6289158 +3.5831583 +-4.4862482 a2 9.1902787 —0.2300891 —1.7550865 -| —2.9722348 —4.0642824 —5.0642824 at 9.0495455 Bae: 5756293 +1.1152368 -+2.8046272 +4.1132964 +5.2527521 ad 8.9556411 9.2256368 0.3085255 —1.9904750 —3.7731624 —5.1302153 a3 8.8838608 _8.97553 58 -+-9.8609192 —1.0550089 -+2.8372855 +4.6682848 ald +8. 8251385 —8.7772635 -+9.5453948 —0.5016665 ---1.8098247 —3.6373347 al2 8.7751153 —8.6112584 9.2966176 —0.0919487 -+-1.1851409 —2.5302996 al4 8.7313488 —8.4675049 +9.0948396 —9.7618367 -0.7198127 —1.8349419 ql6 8.6923246 —8.3401421 8.9242830 —9.4850034 0.3466756 —1.3036584 ql8 -L8. 6570356 —8.2254225 +8.7766454 —9.2401260 —L0.0351507 —0.8665692 | 20 8.6247750 —8.1207929 +8.6465207 —9.0239023 9.7681640 —0.4912748 a22 8.5950262 —8.0244282 --8.5301901 —8.8282356 9.5350080 —0.1595579 | a4 8.5673995 —7.9349743 +-8.4249892 —8.6488982 9.3284478 —9.8597170 i} q26 +8.5415923 —7.8519462 +-8.3289457 —8.4828361 9.1432694 —9.5843549 SS SSS SERIES FOR DETERMINING THE VALUES OF 0® AND ITS DERIVATIVES. 43 LOG COEFFICIENTS OF THE POWERS OF @. | Powers of ar Oe : a D, ys) Pe D Ooo) oe D3 a?) oe: Dt p(s) © D p13) a °S is 5 all x2 7 log opi log Tarp log op = log a pr = a0 +9.4913085 -+-0.6052519 +1.6844331 +2.7258258 +-3.7258258 +4.6800683 a2 +9.1744843 —0.2523084 —1.8150705 —3.0747017 —4.2143089 —5.2683366 at +-9.0348223 —9.6018732 -+1.1777047 +2.9104912 +-4.2676086 +15 .4622206 aS +8.9418527 —9.2553117 -+0.3724148 —2.0987823 —3.9303704 —5.3431579 a8 +-8.8708958 —9.0083430 +9.9250372 —1.1660456 +-2.9963254 -+-4.8835891 ql0 +8.8129038 —8.8129039 -+9.6073958 —0.6147041 +1.9709083 —3.8541404 al2 8.7635334 —8.6494833 —++9.3602251 —0.2074551 1.3460206 —2.7504203 alt 8.7203533 —8.5081058 +9.1579208 —9.8799920 —0.8803458 —2.0560178 ql6 8.6818593 —8.3829425 8.9867952 —9.6039936 0.5061988 —1.5274218 qi8 8.6470514 —8.2702724 8.8385981 —9.3641317 --0.1931121 —1.0938681 @20 +8.6152297 —8.1675634 +8.7079525 —9.1511073 9.9241505 —0.7231561 a +8.5858829 —8.0730084 +8.5911541 —8.9587904 9.6887312 —0.3972342 a2t +8.5586256 —7.9852682 8.4855439 —8.7829812 9.4797595 —0.1044932 qh +8.5331590 —7.9033201 8.3891496 —8.6206213 9.2920344 —9.8379853 Powers of at DP y®) a! Dt p?) «lO p> y(9) a p20) a2 D, p20) a® D® p(10) log Sa = 8 - 2 08 = t log — i. ofS 5 - : log = i a B 6 pi a? pt w 6 ar 6 a? +3.5504892 +-4.3286404 -++5.0276105 --0.8692480 -+1.8692480 +-2.8235105 a2 —3.8306691 —4.6016417 —5.1157465 —0.5045488 —1.9177604 —3.0539393 ai +3.7377454 +4.6141274 +5.2313061 —9.8444969 -+1.1980561 +2.7915914 aS —3.2929649 —4.3721462 —5.1327767 —9.4902214 0.3103372 —1.9019875 a8 +-2.2695187 +3.8149424 -4.7877245 —9.2368834 +-9.7814475 —0.9091387 qld 1.1580679 —2.7107658 —4.1534165 —9.0362239 +9.3830115 —0.3140332 gl2 0.4446582 —1.5590758 2.9663195 —8.8685333 -+9.0561187 —9.8753576 al4 -+9.8800815 —0.8510769 1.6656694 —8.7236808 8.7752576 —9.5264328 ql6 9.3916055 —0.3358277 0.6207094 —8.5957154 8.5267393 —9.2366687 | ql8 8.9407888 —9.9357315 —9.5245714 —8.4808186 8.3022385 —8.9889307 @20 +8.4955194 —9.6104595 —9.8502736 —8.3763796 8.0962429 —8.7725202 azz +8.0062649 —9.3358673 —9.7399401 —8.2805253 7.9048621 —8.5802930 azt -+7.2834143 —9.0969135 —9.5734112 —8.1918647 -++7..7252090 —8.4072467 Powers of at DS p(t) o® pt oy a D> p(10) a pet) a D, om) a® 10 oe log z log - log 2 log 2 log ops a @ pe? Bi? pM ab 6! 5 a8 [e aA B° +3.7265804 +-4.5716785 +5.3498298 -+0.8885531 -++1.9299458 ++-2.2929458 —4.0539393 —4.9340801 —5.6660997 —0.5295311 —1.9919291 —3.1813628 +3.9863590 +-4.9789846 +5.7846840 —9.8742256 1.2840853 +2.9336080 —3.5554083 —4.7512369 —5.6867987 —9.5239776 0.4070709 —2.0531846 +-2.5428102 +4.2044619 -L-5.3505899 —9.2741001 -+9.8880594 —1.0652448 1.4440987 —3.1045829 —4.7191795 —9.0764462 +9.4989245 —0.4719546 0.7480065 —1.9458065 +3.5441036 —8.9113908 -+-9.1809532 —0.0330568 0.2075078 —1.2178904 2.2995123 —8.7688663 8.9087975 —9.682'7036 9.7529392 —0.6736069 Tias27087 —8.6429742 8.6689098 —9.3909122 9.3515837 —0.2413970 -L0.7262120 —8.5299345 8.4530947 —9.1409322 +8.9837165 —9.8857399 -++9.9690896 —8.4271690 8.2559630 —8.9222998 +8.6353832 —9.5855171 —8.1495270 —8.3328308 8.0737506 —8.7280452 +8.2942457 —9.3252488 —9.2796669 —8.2455500 +-7.9037041 —8.5530938 44 SERIES FOR DETERMINING THE VALUES OF oe AND ITS DERIVATIVES. [ i LOG COEFFICIENTS OF THE POWERS OF a. Powers of Be D3 oe) i @ Dt pa 8 DP p() a g2) oe D, Se a Dt oe) a log 25 og asa log yale log = 3 5 log aor log aye a? -+3.8841883 -+-4.7872782 -+5.6323763 --0.9062819 -+1.9854631 -+-3.0268558 a2 —4.2443399 —5.2046788 —6.0551829 —0.5520063 —2.0583348 —3.2945607 at +-4.1962330 +5.2754141 -+6.2023168 —9.9007284 +-1.3601209 +3.0585618 af —3.7771807 —5.0615905 —6.1171159 —9.5539408 —-+-0.5055677 —2.1860606 a8 +2.7735204 +4.5245260 +5.7902188 —9.3070689 -++9.9328078 —1.2029610 qld 1.6836121 —3.4302486 —5.1646981 —9.1120497 9.5990642 —0.6121807 qi2 0.9978052 —2.2721385 -+3.9960709 —8.9493226 9.2881409 —0.1741381 | al4 0.4699147 —1.5837168 2.7663615 —8.8088714 9.0227514 —9.8235499 qlé 0.0312468 —0.9830938 1.9535877 —8.6848364 8.7894428 —9.5308603 a8 9.6501229 —0.5353043 1.3033967 —8.5734708 --8.5801015 —9.2796327 20 +9.3081801 —0.1620742 -++0.7274119 —8.4722208 +8.3894100 —9.0596089 az 8.9949767 —9.8439239 0.1919566 —8.3792624 8.2136752 —8.8638996 ars 8.6985355 —9.5675322 9.6145070 —8.2932417 8.0502026 —8.6877340 Powers of| at D3 ptt) 1 a? Dt pf?) al D° Ore) a Bp) & 10), om) 2 pa a log a iat OS Be a log is log ae log Fp log ros a? .0268558 | +4.9810983 | +5.8841883 | -+1.7538545 | 42.7538545 | -+-1.8093718 ae) —4.4111603 —5.4359432 —6.3702645 —1.8179720 —2.9554998 —1.8840054 ai +4.3784473 ++5.5269955 +6.5431207 +-1.1144544 +2.6486141 +1.1891914 af —3.9695033 —5.3253849 —6.4715129 —-+-0.2435490 —1.6994811 0.3256103 8 +-2.9734198 | +-4.7965683 | +16.1537157 | -+-9.7321501 —0.6336635 9.8204600 qld -+-1.8903509 —3.7078557 —5.5344717 9.3519389 —9.9540007 9.4456437 gl2 +1.2116515 —2.5650467 4.3711407 9.0440696 —9.4208136 9.1424797 al4 0.6918574 —1.7477473 2.1485242 8.7831029 —8.9685343 8.8856534 al6 0.2625935 —1.3651767 1.3483653 8.5554353 —8.5667556 8.6616562 ql8 9.8923506 —0.7309881 0.7181354 + 8.3528354 —8.1974184 8.4623356 20 9.5639199 —0.4226375 0.1834208 +-8.1699061 —7.8478193 +8 .2823486 a22 9.2657845 —0.0940097 9.7072379 +8.0028837 —7.5052857 -+8.1179885 I! q24 +8.9913590 —9.8066683 9.2650538 Powers of a® D pa) a p(l2) o® D, pz) log ere ek log ELS, loz ee Ge a a? (oe a8 ps 5 at pe a ++-2.8507745 ++-1.8605244 +-2.9397056 az —3.0750739 —1.9488616 —3.1819476 at -+2.7886585 1.2563714 +-2.9116769 aS —1.8587518 0.3990389 —1.9967340 a3 —0.8116862 9.8992840 —0.9639272 qld —0.1509997 9.5291729 —0.3171937 al2 —9.6377598 9.2301490 —9.8179724 ql4 —9.2071979 +8.9769939 —9.4018570 ql6 —8.8301137 -+8.7562746 —9.0400482 als —8.4900709 --8.5598978 —8.7166293 20 —8.1764964 +8.3825710 —8.4215217 a2 —7.8820120 -+8.2206235 —8.1483558 i al aaa aces See SUPPLEMENT. Ir now remains to take from these Tables the especial values of 5“) and its deriva- tives, which are needed in the perturbative theories of the planetary motions. The present Supplement will only include those coefficients which pertain to the prin- cipal Planets; those for the Asteroids being reserved for a future occasion. In determining the values of a, the following values of the masses and mean motions, which are those adopted in the American Ephemeris and Nautical Alma- nac, will be used. Mercury, ae = aaa n' = 5381016.218 Venus, me = aa nt = 2106641.4388 The Earth, mt aaa nil == 1295977.440 Mars, i = — nv = 689051.030 Jupiter, mY = oa nY = 109256.719 Saturn, m= a nm! = 43996.127 Uranus, mt = oe nv= —= 15424.5094 Neptune, = nv — —7872.771382 We have, then, for the value of «, the ratio of the mean distances of any two planets, as Mercury and Venus, the formula nil \ 2 alan O— G-)? ( ae 3 ) > which takes into account the correction, necessary in the perturbative theory, due to the masses. But if each planet is considered with reference to the Earth, the values of the mean distances ai, aU, a™, &c., may first be found, since a™' = 1, and then the values of a. We find for Mercury, a’ == 0.38709870 log a’ = 9.58782172 Venus, ai =~ —0.72333227 log a" == 9.85933784 The Earth, at = _ 1.00000000 log a'™ = 0.00000000 Mars, av = _ 1.52369140 log aY = 0.18289702 Jupiter, avy = 5,.20280136 log aY == 0.71623725 Saturn, a' = 9.53885533, log a’! = 0.97949626 Uranus, a" = 19.18357126 log aY" = 1.28292946 Neptune, av"! = 30.03680569 log a" = 1.47765375 46 Hence, for Mercury and Venus, Mercury and The Earth, Mercury and Mars, Mercury and Jupiter, Mercury and Saturn, Mercury and Uranus, Mercury and Neptune, Venus and The Earth, Venus and Mars, Venus and Jupiter, Venus and Saturn, Venus and Uranus, Venus and Neptune, The Earth and Mars, The Earth and Jupiter, The Earth and Saturn, The Earth and Uranus, The Earth and Neptune, Mars and Jupiter, Mars and Saturn, Mars and Uranus, Mars and Neptune, Jupiter and Saturn, Jupiter and Uranus, Jupiter and Neptune, Saturn and Uranus, Saturn and Neptune, Uranus and Neptune, With these values of « and 8? we enter the Tables and take out the required SUPPLEMENT. « = 0.5351603 log « = 9.7284839 o = 0.3870987 log « = 9.5878217 a = 0.2540532 log a = 9.4049247 a = 0.0744020 log o = 8.8715845 o = 0.0405813 log « = 8.6083254 a = 0.0201787 log « = 8.3048923 a = 0.0128875 log « = 8.1101680 a = 0.7233323 log a = 9.8593378 a = 0.4747236 log « = 9.6764408 a = 0.1390275 log « = 9.1431006 a = 0.0758301 log « = 8.8798416 a = 0.0377058 log « = 8.5764084. a = 0.0240815 o = 0.6563009 a = 0.1922042 a = 0.1048344. o = 0.0521279 a = 0.0332925 o = 0.2928598 a = 0.1597353 a = 0.0794269 o = 0.0507275 o = 0.5454825 o = 0.2712113 o = 0.17382142 a = 0.4972408 oa = 0.38175722 a = 0.6386689 log a = 8.3816841 log « = 9.8171030 log « = 9.2837628 log « = 9.0205037 log « = 8.7170705 log « = 8.5223463 log « = 9.4666598 log « = 9.2034008 log a = 8.8999676 log « = 8.7052433 log « = 9.7367410 log o = 9.4333078 log w = 9.2385835 log « = 9.6965668 log « = 9.5018425 log o = 9.8052757 coefficients, which are found on the following pages. log 62 = 9.6035107 log 62 = 9.2461455 log 62 — 8.8388256 log fp? = 7.7455797 log 62 = 7.2173667 log 6? = 6.6099614 log 62 = 6.2204080 log 6? = 0.0403481 log 6? = 9.4637832 log 6? = 8.2946777 log 62 = 7.7621877 log 6? = '7.1534347 t=} log 6? = 6.7636201 log 62 = 9.8788884 log 6? = 8.5838733 log 6? = 8.0458069 log 2 — 7.4353228 log 6? = 7.0451741 log 62 = 8.9722626 log 62 = 8.4180265 log 62 = 7.8026836 log 62 = 7.4116055 log 62 = 9.6268336 log 62 = 8.8997962 log 6? = 8.4903967 log 62 = 9.5164820 log 62 = 9.0498539 log 6? = 9.8381548 SUPPLEMENT. 47 MERCURY AND VENUS. a log oY log « D, a) log «2 D? wo log «® D3 uw log a* D* Be 0 0.3368936 99.6206871 99.8972897 0.2388589 0.8016751 1 99.7822639 99.8922032 99.8418921 0.2669438 0.7985490 2 99.3919845 99.7578828 99.9878240 0.2639757 0.8170165 3 99.0444586 99.5682264 99.9860814 0.3492156 0.8295626 4 98.7168905 99.3555162 99.9084175 0.3914858 0.8842750 5 98.4009294 99.1300174 99.7873191 0.3775499 0.9354354 6 98.092563 98.896347 99.638442 0.3195425 0.9550919 a 97.789597 98.656996 99.470354 0.228810 8 97.49060 98.413474 99.288216 9 97.19490 98.166718 a log « U) log «” D, of) log a? Dp) log a? o) 2 by = a 0 0.3531933 0.5947884 1.1362336 0.5632360 1 0.2107051 0.6129323 1.1227699 2 0.0156280 0.5544420 1.1137060 0.4107724 3 99.8048651 0.4467261 1.0786698 4 99.5788115 0.3073166 1.0125432 5 99.3448135 0.1467052 0.9191260 6 99.1052495 99.9693565 a 98.8615637 ICTS: TG WU Te Se eV IN ID) AN TBDID, 19, ATR IB Le a log wD log « D, uo) log a” D? o) log a? D? a0) log «* Dt oy 0 0.3184766 99.2546919 99.3989310 99.4220427 99.7628838 1 99.6139899 99.6668702 99.2622822 99.5008233 99.7371661 2 99.0798287 99.4111232 99.5250938 99.4562433 99.7872022 3 99.5899659 99.0885481 99.4435846 99.6221510 99.7828049 4 98.1207040 98.7394582 99.2505507 99.6353560 5 97.6633767 98.3760072 99.0025367 6 97.213840 98.0035704 98.7215190 of 96.76980 97.6249551 8 96 32984 : a log « oy log «* D, oy) log u? D2 oy) log o” ae 0 0.0459805 99.9373245 0.2584646 99.8858911 1 99.7853941 0.0068851 0.2138736 2 99.4615006 99.8803230 0.2202039 99.5589618 3 99.1118471 99.6682696 0.1450095 4 98.7481282 5 98.3755292 MERCURY AND MARS. 6 log b) log « D, U) log D. o? log a D3 o log a DEL 0 0.3082438 98.8424025 98.9049136 98.5490181 98.7173894 1 99.4157453 99.4374778 98.6272822 98.7368905 98.6196100 2 98.6969416 $9.0101961 99.0578698 98.5895868 98.7510792 3 98.0232940 98.5090174 98.8315886 98.9130185 98.6765937 4 97.3705928 97.9793098 98.4698494 98.8042736 5 96.7300025 97.4344104 98.0460740 a log « wy) log a? D, oy log «? D2 De) log a” Oe 0 99.7708872 99.2594445 99.4148023 99.2858964 1 99.3413761 99.4415556 99.2872887 2 98.8396194 99.1903507 99.3590295 98.6705902 3 98.3096765 98.8193952 99.1976237 SUPPLEMENT. MERCURY AND JUPITER. a log oD log « D, wo log a” D? ? log a? D3 BW log at Dt } 0 0.3016325 97.7458802 97.7512851 96.3240081 96 .3404635 1 98.8724882 98.8742957 96.9719581 96.9819147 95.8193051 2 97.6192343 97.9212700 97.9252836 96.3693077 96.3848826 3 96.4116879 96.8595133 97.1923042 97.1993128 95.8853453 4 95.225311 95.827914 a log a b) log ? D, log «® D? 6) log a? 1 x 0 99.1780369 97.5765287 97.5913778 98.0592196 1 98.2248103 98.2337851 97.0263193 2 97.1930041 97.4982470 97.5148215 96.4373878 3 96.1313849 96.6112183 96.9189960 a log so log «a D, OY log a? Dt We log a® D3 a log at Dt up 0 0.3012093 97.2174553 97.2190649 95.2650906 95.2700362 1 98.6085938 98.6091299 96.1786498 96.1816249 94.4943723 z 97.0920105 97.3933388 97.3945312 95.3107115 95.3153870 3 95.6211696 96.0984995 96.4000520 96.4021379 94.5610483 4 94.1715118 94.7737328 1 log « o® log a” D, uD log a® Dt oD log «2 Bp 0 98.9109658 96.7814557 96.7859097 97.5221507 1 97.6951141 97.6977926 95.9650543 2 96.4002605 96.7025422 96.7075262 95.3779943 3 95.0754879 95.5534144 95.8564546 a tog 0 log « D, UP log a” D? uo log a D3 o log at DE 0 0 0.3010745 96.6099831 96.6103814 94.0494867 94.0507129 1 98.3049585 98.3050908 95.2672278 95.2679644 92.9744565 2 96.4849193 96.7860233 36 .7863180 94.0952106 94.0963708 3 94.7106341 95.1878071 95.4889658 95.4894822 93.0413363 a log « 0 log @? D, bY log a? D2 wo) log a? 0 98.6063203 95.8694720 95.8705767 96.9119197 1 97.0872375 97.0879007 94.7487026 2 95.4890174 95.7903568 95.7915942 94.1622404 ~ SUPPLEMENT. 49 eee | a log oP log « D, o log oe D? B® log a Ds 6 log a Dt KO | 0 0.3010482 96.2204167 96.2205795 93.2702259 93.2707270 1 98.1101949 98.1102487 94.6828366 94.6831374 92.0003003 2 96.0954270 96.3964873 96.3966076 93.3159697 93.3164439 s 3 é : Ai a log « oD log a” D, oD log a® D2 oD log o* o 0 98.4113602 95.2849716 95.2854233 96.5218167 1 96.6975924 96.6978632 93.9692959 2 94.9046608 95.2058173 95.2063234 93.3829501 log uy) log « D, BW log ae D? oe log & D3 oD log a* Dt wp log a D> Dey 0 0.3777387 0.0751753 0.6062955 1.3304800 2.2339265 3.2571104 1 99.9742423 0.2158375 0.5955403 1.3366398 2.2349877 3.2581326 2 99.7222879 0.1752740 0.6510807 1.3429395 2.2404308 3.2609114 3 99.5096630 0.0996032 0.6782990 1.3697966 2.2484968 3.2659903 4 99.3155264 0.0078221 0.6768729 1.4000746 2.2645398 3.2732901 5 99.1322252 99.9065691 0.6533964 1.4221359 2.2869730 3.2844533 6 98.956047 99.7990095 0.6132848 1.4315468 2.3107746 3.3002061 7 98.784955 99.686930 0.5604115 1.4277420 2.3311298 3.3194820 8 98.617623 99.571455 0.4975245 1.4116546 2.3448582 3.3399585 9 98.453251 99.453263 0.4265994 1.3846568 2.3503817 3.3590269 98.291240 99.332957 0.3491038 1.3481201 2.3472192 3.3744826 98.131160 99.210872 0.2661455 1.3033678 2.3355127 3.3847833 97.972728 99.087305 0.1785773 1.2514069 2.3157346 3.3890323 97.809310 98.962477 0.0870730 1.1931751 2.2885064 3.3868287 log a uD log a Dy ) log a De Be log a* DB ey log a Ds uo log a® D> Ke 0.8590131 1.5254362 2.4126655 0.8073433 1.5253162 2.4098989 0.7277921 1.5068774 2.4040576 0.6341595 1.4719142 2.3923886 0.5318658 1.4235885 2.3731955 0.4236621 1.3645764 2.3459447 0.3111523 1.2969468 2.3107387 0.1953592 1.2222139 2.2682820 0.0769784 1.1416746 2.2190160 99.9565006 1.0561729 2.1636585 3.2949178 4.4657772 5.6871063 99.8342894 0.9664059 2.1028268 3.2569379 4.4433426 5.6737091 99.7106216 0.8731223 2.0370794 3.2139903 4.4169447 5.6577201 99.5857112 0.7766490 1.9669190 3.1663382 4.3865409 5.6388507 log & Oe log a D, BY) 1.6520288 1.6085195 1.0169577 2.2415088 0.9206974 2.1682542 0.8216328 2.0912966 SUPPLEMENT. we VENUS AND MAIR Se eo 96.1645717 96.6445102 96.9525494 i log 0%) log « D, bi) log «? D? 0) log « D3 ul) log a DE oP 0 0.3283132 99.4769896 99.6938783 99.9122567 0.3810500 1 99.7173584 99.8005488 99.6119497 99.9555499 0.3723979 2 99.2735258 99.6229528 99.7993513 99.9412687 0.3998361 3 98.8731656 99.3848599 99.7725747 0.0571017 0.4094658 4 98.4930603 99.1221164 99.6547601 0.0909596 0.4862474 5 98.1247182 98.8458657 99.4881571 6 97.764075 98.561057 99.2913313 7 97.408846 98.270329 a log @ wt log « D, wy) log «° D2 ae log a oe 0 0.2234242 0.3284515 0.7758352 0.2777165 1 0.0390136 0.3616490 0.7538055 2 99.7989772 0.2810544 0.7474236 0.0667512 3 99.5354049 0.1372379 0.6997284 4 99.2587233 5 98.9736609 ; log B) log « D, v0) log a D2 vo) log a? D3 wo) log «* Dt ul) 0 0.3031463 98.2957335 98.3145632 97.4310860 97.4866127 1 99.1462'753 99.1526329 97.7991402 97.8334042 97.2076815 2 98.1647907 98.4693659 98.4834389 97.4752552 97.5280039 3 97.2288875 97.7084935 98.0157400 98.0401876 97.2715070 4 96.314102 96.9180814 97.3990491 97.7096849 5 95.41152 96.112051 .) log « bl) log a” D, vi) log a® D? ui) log a” U7) 0 99.4631797 98.4100228 98.4604358 98.6396471 1 98.7792220 98.8102149 98.1417438 2 98.0181761 98.3339507 98.3897984 97.5462166 3 97.2276932 97.7143505 98.0388280 ’ VENUS AND SATURN. a log oD log « D, uP log a io Be) log a? D3 uD log a# pt oD 0 0.3016559 97.7624999 97.7681145 96.3573617 96.3744455 1 98.8807804 98.8826583 96.9969247 97.0072649 95.8610681 2 97.6357877 97.9378624 97.9420319 96 .4026436 96.4188144 3 96.4365002 96.9143552 97.2172126 97 .2244928 95.9270734 4 95.2583823 95.8610061 96.3392568 96.6431106 a log « Be log a# D, u@ log a® De @ log a2 oD 0 99.1865049 97.6015951 97.6170106 98.0763161 1 98.2415003 98.2508215 97.0598027 2 97.2179397 97.5253450 97.5405529 96.4707681 SUPPLEMENT. VENUS AND URANUS. 51 ; log Uf) log « D,, o) log a? Do) log a? D3 0) log «* Dt uf) 0 0.3011847 97.1535110 97.1549003 95.1370825 95.1413554 1 98.5766400 98.5771026 96.0826950 96.0852642 94.3342873 2 97.0281355 97.3294231 97.3304520 95.1827220 95.1867614 3 95.5253753 96.0026771 96.3041581 96.3059585 94.4010004 4 94.0437995 94.6459986 a log « 04) log a” D,, 0) log a? D2 0) log a? 0) 0 98.8788285 96.6853988 96.6892460 97.4577049 1 97.6310965 97.6334096 95.8369102 2 96.3043381 96.6064484 96.6107545 95.2499591 VENUS AND NEPTUNE. log vf) log « D, b log a” D2 wo log a® D? b log at DE of 0.3010933 96.7636511 96.7642173 94.3569146 94.3586608 98.3817785 98.3819670 95.4977600 95.4988080 93.3587986 96.6385344 96.9396695 96.9400890 94.4026241 94.4042749 94.9410424 95.4182373 95.7194509 95.7201858 93.4256500 log « oy) log a? D i op log ow Dt oD log a o 98.6832809 96.1000820 96.1016540 97.0659721 97.2409619 97.2419058 95.0562346 95.7195243 96.0209948 96.0227555 94.4696891 = THE EARTH AND MARS. t log o{)) log « D,, b) log «? D? 0) log a? D3 v()) log at Dé vl? 0 0.3600512 99.9063288 0.3318839 0.9141702 1.6847103 1 99.9055625 0.0892258 0.3104128 0.9251659 1.6854936 2 99.6080871 0.0215561 0.3924579 0.9311108 1.6940369 3 99.3514193 99.9108645 0.4165453 0.9736804 1.7048208 4 99.1138839 99.7812022 0.3958855 1.0125710 1.7307937 5 98.887518 99.6406607 0.3448559 1.0303987 1.7642993 6 98.668488 99.4930083 0.2725474 1.0249435 7 98.454661 99.340324 0.1846741 0.9987475 8 98.244734 99.183856 9 98.037747 99.024519 a log « 0”) log a” D, 0”) log a? D? ol) log a? 0) 0 0.6531967 1.1628096 1.9145598 1.2140322 1 0.5750996 1.1657938 1.9096196 2 0.4610026 1.1367583 1.9017179 1.1418640 3 0.3297791 1.0816108 1.8836598 4 0.1883851 1.0069848 1.8522916 5 0.0402136 0.9176828 1.8074144 6 99.8871919 0.8170486 52 SUPPLEMENT. THE EARTH AND JUPITER. ”) log SS log « D, log a? D? oe log «® D8 OW log a* Dt ae 0 0.5051074 98.5859021 98.6218017 98.0209251 98.1228757 1 99 .2898787 99.3021396 98.2375153 98.3018635 97.9506914 2 98.4493848 98.7572747 98.7843211 98.0636724 98.1609219 3 97.6543084 98.1362460 98.4493285 98.4960014 98.0117776 4 96.880286 97.4860667 97.9706649 98.2903438 5 96.118424 96.8204336 6 95.364507 96.145214 7 94.616139 95.463471 } log « op log a” DE BS log a Da oe log a? BS) 0 99.6214901 98.8565780 98.9497818 98.9687006 1 99.0753228 99.1337764 98.7422899 2 98.4539620 98.7832731 97.8856386 98.1384352 3 97.7936485 98.2991609 98.6447454 4 97.1379483 } log of log « D, vo log a? D2 of) log «? D, oY) log «* D4 of) 0 0.3022290 98.0464055 98.0571258 96 .9279665 96.9601872 1 99.0223022 99.0259018 97.4236915 97.4433442 96.5760501 2 97.9180673 98.2211014 98.2290828 96.9728170 97.0033601 3 96 .8594899 97.3380151 97.6425563 97.6564655 96.6412072 4 95.822063 96.4252059 96.9044969 97.2109487 5 94.796844 95.4967015 a log «DQ — log o” D, bY log «® D2 uy log a? a 0 99.3323249 98.0307485 98.0598969 98.3718510 1 98.5271291 98.5448684 97.6335748 2 97.6439443 97.9533446 97.9857812 97.0420271 3 96.7310949 97.2136156 9'7.5280162 O log ot? log « D, op log a Dt o? log a? iD OY log «+ D* Oe 0 0.3015256 97.4354695 97.4381242 95.7016881 95.7098238 1 98.7175135 98.7183990 96.5058565 96.5107585 95.0404733 2 97.3096947 97.6112174 97.6131856 95.7472204 95.7549146 3 95.9476085 96.4250747 96.7269674 96.7304084 95.1069740 4 94.606 7012 95.2090280 95.6866818 } log a Oe log a? D, Nee log a® D By) log oe oe 0 99.0207590 97.1091469 97.1164784 97.7425453 1 97.9134779 97.9178933 96.4022975 2 96.7273112 97.0304071 97.0386052 95.8147221 3 95.5112547 95.9897052 96.2940507 53 SUPPLEMENT. +. Sanaatia a log af) log « D, W) log a? D2 vo) log a® D3 vo”) log a* Dt ol) 0 0.3011507 97.0452335 97.0463171 94.9203609 94.9236944 1 98.5225269 98.5228872 95.9202246 95.9222280 94.0632816 2 96.9199546 97.2211851 97.2219871 | 94.9660264 94.9691775 3 95.3631295 95.8403912 96.1417725 96.1431767 94.1300459 a log « 6) log a” D, b”) log a® D? 0) log a? 0) 0 98.8244597 96.5227863 96.5257875 97.3487309 1 97.5227166 97.5245204 95.6199996 2 96.1419128 96.4437851 96.4471449 95.0331992 3 94.7311760 95.2088388 95.5112218 log o@) log « D, 6 log a Dt a log a® De SY log at pt o 0 0.3107113 98.9770487 99.0599399 98.8300984 99.0453381 1 99.4811814 99.5103889 98.8332179 98.9762844 98.9776184 2 98.8245306 99.1420587 99.2058544 98.8690316 99.0762273 3 98.2128292 98.7015819 99.0317499 99.1398730 99.0315969 4 97.6219911 98.2330619 98.7283933 99.0746535 5 97.043213 97.7495567 98.3646694 6 96.472329 97.2567116 97.9657798 7 95.90695 96.7574834 8 95.34575 log «@ ot log a? D, oe log «® Dt BD log o# oD 99.8548398 99.4'756985 99.6755213 99.4671301 99.4835937 99.6149205 99.5814924 99.0423516 99.4097419 99.6250671 98.9550827 98.5735187 99.0944484 99.4974752 98.0898551 t log a) log « D, of log oe De ot) log & DS Be log at Dt of) 0 0.3038316 98.4194228 98.4442570 97.6817908 97.7540338 1 99.2076032 99.2160220 97.9857638 98.0307110 97.5230775 2 98.2865336 98.5922635 98.6108769 97.7254579 97.7941901 3 97.4109882 97.8914051 98.2006829 98.2329418 97.5859297 4 96.5565380 97.1611435 97.6433727 97.9571530 5 95.714274 96.415321 6 94.879965 95.659857 D log « o log a D, On log a3 BD wy log a” Oe 0 99.5296467 98.5995041 98.6652666 98.7770123 1 98.9049807 98.9456991 98.3962028 2 98.2038928 98.5244111 98.5970262 97.7977385 3 97.4735386 97.9632879 98.2952057 54 SUPPLEMENT. MARS AND URANUS. a log oD log « D, of) log a D2 u? log a ps up log a* Dt up 0 0.3017169 97.8030264 97.8091849 96.4387118 96.4574277 1 98.9009978 98.9030588 97.0578109 97.0691483 95.9629399 2 97.6761412 97.9783178 97.9828929 96.4859476 96.5016662 3 96.4969847 96.9749090 97.2779470 97.2859339 960288542 4 95.3389952 95.9416747 96.4200358 a log o D, o log a D? o log a” s 0 99.2071792 97.6627331 97.6796282 98.1180826 1 98.2822098 98.2924315 97.1414900 2 97.2787446 97.5845753 97.6034263 96.5521871 3 96.2454874 96.7257004 97.0344186 log &D log a D, oD log a D: a log o® Db oD) log até Dt ot? 0 0.3015100 97.4117444 97.4142587 95.6541612 95.6618697 1 98.7056629 98.7065011 96.4702454 96.4748870 94.9810173 2 97.2860140 97.5875105 97.5893744 95.6997056 95.7069953 3 95.9120994 96.3895471 96.6913938 96.6946528 95.0475415 4 94,.5593641 95.1616763 95.6393018 } log o Ow log oe D, ot log a iy ol) log a Be) 0 99.0087906 97.0734690 97.0804149 97.7185002 1 97.8897057 97.8938878 96.3546840 2 96.6917194 96.9947059 97.0024735 95.7671776 3 95.4638396 95.9422196 96.2463897 JUPITER AND SATURN. i log of) loga Dv!) | log a D200) | log a? D3 0) | log a* DEG) | log a? DB a 0 0.3385227 | 99.6447536 99.9323668 0.2943834 0.8737065 1.5571443 1 99.7929617 99.9080126 99.8807510 0.3204252 0.8712043 1.5610525 2 99.4112293 99.7803232 0.0203404 0.3188200 0.8884925 1.5658199 3 99.0721127 99.5982403 0.0219675 0.3995635 0.9011930 1.5798031 4 98.7528969 99.3934022 99.9503069 0.4424607 0.9527604 1.5958171 5 98.445260 99.1759112 99.8362007 0.4325812 1.0028484 1.6320201 6 98.145206 98.9503245 99.6947800 0.3803462 1.0245924 1.673991 7 97.850517 98.7190975 99.5343998 0.2962794 1.0130524 1.7122581 8 97.559818 98.483710 99.3601200 0.1880990 0.9715115 1.7254699 9 97.272369 98.245141 99.1752269 0.0612446 10 96.98714 98.00416 11 | 96.70391 97.76098 a | loga ol) log o” D, Od log a? D? u log a* D3 OH log OD) 0 | 0.3762360 0.6405825 1.1986313 1.8182258 0.6137241 1 | 0.2401571 0.6567683 1.1862536 1.8459979 2 | 0.0555698 0.6014522 1.1770313 1.8554065 0.4698123 3 | 99.8196384 0.4991413 1.1438034 1.8414177 4 | 99.6315700 0.3661981 1.0814342 1.8164763 5 | 99.4056399 0.2121088 0.9931214 1.7744894 | 6 99.1741927 0.0426529 | 0.834073 1.7135764 7 | 98.9386574 99.8615625 0.7563142 1.6344562 8 | 98.6999680 99.6713775 0.6150429 9 | 98.4587713 99.4738784 0.4620858 SUPPLEMENT. oy) JUPITER AND URANUS. a log Be log « D, OW log o De Je log & De OW) log a Dt oD 0 0.3092856 98.9038847 98.9750571 98.6769679 98.8656377 1 99.4456908 99.4705769 98.7211775 98.8451251 98.7823853 2 98.7554468 99.0704995 99.1249909 98.7168378 98.8980896 3 98.1102711 98.5972679 98.9230322 99.0157985 98.8380776 4 97.486006 98.0957127 98.5882625 98.9276587 5 96.873837 97.5790530 98.1921618 6 96 .269539 97.0529904 97.7605062 7 95.670777 96.520507 a log « log ? D, 0} log a® D2 6) log oo) 0 99.8086496 99.3576948 99.5322513 99.3671643 1 99.4060486 99.5195467 99.4207972 2 98.9321593 99.2899439 99.4788381 98.7999575 3 98.4303359 98.9447839 99.3335720 4 97.9135406 5 97.3874000 0 log wD? log « D, } log ae Dt a log & Db of? log a Dt uD 0 0.3043311 98.4920408 98.5212246 97.8294469 97.9135311 1 99.2435350 99.2534573 98.0954862 98.1481025 97.7091037 2 98.3577319 98.6643058 98.6862239 97.8727521 97.9528337 3 97.5174107 97.9984222 98.3091854 98.3471076 97.7712573 4 96.698170 97.3032334 97.7863873 98.1024699 5 95.891104 96.5925262 6 95.091992 95.872200 log « op log ae D, Oe log & De } log a? BY) 0 99.5693244 98.7113098 98.7879789 98.8595382 1 98.9791094 99.0268276 98.5465870 2 98.3129556 98.6369224 98.7214024 97.9460003 3 97.6176584 98.1096632 98.4469597 4 96 .9068966 } log 0 log « D,, b log a” D2 of) log «® DB 2 log «* DE UD 0 0.3313200 99.5310896 99.7692508 0.0542514 0.5374908 1 99.7419927 99.8345228 99.6981179 0.0711778 0.5313225 2 99.3188110 99.6739420 99.8691952 0.0618363 0.5549586 3 98.9388512 99.4547104 99.8528345 0.1653903 0.5661350 4 98.5790462 99.2113929 99.7509771 0.2034016 0.6339224 5 98.230944 98.9548198 99.6022336 6 97.890500 98.6898232 99.4241234 a 97.555494 98.418992 a log @ 6 log «2 D eh oD log ae D ) log oe Be) 0 0.2707586 0.4273481 0.9090815 0.3820620 1 0.1028521 0.4541657 0.8907357 2 99.8815026 0.3825507 0.8829489 0.1946360 3 99.6372755 0.2530913 0.8404206 4 99.3802273 5 99.1149516 56 SUPPLEMENT. SATURN AND NEPTUNE. i log v) log « D, b”) log «? D2 o) log a? D3 ot) log a* Dt of) 0 0.3124955 99.0555102 99.1528574 98.9955021 99.2422368 1 99.5190405 99.5536677 98.9537897 99.1200212 99.1890516 2 98.8978754 99.2185249 99.2939236 99.0332935 99.2713572 3 98.3215112 98.8124824 99.1482174 99.2753084 99.2409713 4 97.765950 98.3787471 98.8776094 99.2325567 5 97.222425 97.9801765 98.5478353 6 96.686750 97.472343 B log a Oe log & D, wy) log a? D? oy) log a” wt) 0 99.9060934 99.6037404 99.8337030 99.5787130 1 99.5675621 99.7205960 99.7562985 2 99.1606227 99.5399608 99.7865741 99.1230705 3 98.7265189 99.2555761 99.6760942 4 98.2777608 5 97.8198198 URANUS AND NEPTUNE. b log 0”) log « D, vf) log a” D? b') log a D3 0) log at DEO 0 0.3560705 99.8638782 0.2648420 0.8115144 1.5497002 n 99.8877784 0.0586025 0.2397216 0.8242115 1.5502635 2 99.5777458 99.9827065 0.3297006 0.8296527 1.5598299 3 99.8088556 99.8618339 0.3517696 0.877171 1.5712163 4 99.0592408 99.7213150 0.3246251 0.9177603 1.6003951 5 98.8208746 99.5695925 0.2650304 0.9330233 1.6368631 6 98.589898 99.4105746 0.1830624 0.9219949 1.6663271 1 98.364156 99.2464174 0.0848955 0.8883071 1.6808770 8 98.142317 99.078414 99.9745172 0.8359697 1.6782061 9 97.923459 98.907462 99.8546237 0.7683861 10 97.70712 98.734127 99. 7271213 0.6882557 11 97.49272 98.558858 99.5934081 12 97.27994 98.381556 99.4544996 a log « Bo log o” D, oD log a® D# o log a” oD 0 0.6048327 1.0748668 1.7937073 1.1101211 1 0.5187735 1.0791600 1.7879788 2 0.3946344 1.0467691 1.7796214 1.0287654 3 0.2526312 0.9853565 1.7595863 4 0.1001034 0.9027548 1.7242974 5 99.9405998 0.8044232 1.6737988 6 99.7761207 0.6940781 1.6095105 7 99.6079077 0.5742955 15332226 8 99.4367866 0.4469509 1.4465602 SMITHSONIAN CONTRIBUTIONS TO KNOWLEDGE. ASTEROID SUPPLEMENT TO NEW TABLES VALUES OF 6° AND ITS DERIVATIVES. BY JOHN D. RUNKLE, ASSISTANT IN THE OFFICE OF THE AMERICAN EPHEMERIS AND NAUTICAL ALMANAC. ACCEPTED FOR PUBLICATION BY THE SMITHSONIAN INSTITUTION, NOVEMBER, 1855. COMMISSION TO WHICH THIS PAPER HAS BEEN REFERRED. Bensamin Peirce, Cuarues H. Davis. JosepH Henry, Secretary. Tue following pages contain the values of 6® and its derivatives for all the Asteroids except those having large inclinations and eccentricities ; and is the completion of the paper lately published by the Smithsonian Institution, entitled “* New Tables for determining the Values of the Coefficients, in the Perturbative Function of Planetary Motion, which depend upon the Ratio of the Mean Distances.” CAMBRIDGE: ELECTROTYPED AND PRINTED BY METCALF AND COMPANY. ASTEROID SUPPLEMENT. Tue large, and still increasing, number of the Asteroids has served to augment the labors of astronomers in a rapid ratio; so much so, that nothing short of gen- eral tables, by means of which their ephemerides can be rapidly computed, will ever reduce this department of astronomical labor to anything like its just proportion. The Asteroid problem must always remain one of a purely scientific character ; and such results, based upon a solid foundation, can hardly be expected, so long as so much mechanical labor is required merely to prevent these bodies from being lost. The great work of Gauss, Theoria Motus Corporum Celestium, and the subsequent labors of many other distinguished astronomers, leave little to be desired so far as the determination of their orbits is concerned. Such, however, is by no means the case with regard to their perturbations by the larger planets. While the variations of the elements of those having small eccentricities and incli- nations may be obtained through the development of the usual form of the pertur- bative function, there are others for which this method is practically nearly impos- sible for any close approximation. This fact has led to the suggestion of new theories of their general perturbations; and the study which is now bestowed upon this problem, in this country as well as in Europe, warrants the confident expectation that it will erelong be presented in its simplest and most practical form. In order to facilitate as much as possible the computation of the perturbations of those to which the usual theory of development is applicable, I have thought it best to take from the Tables the necessary constants, 0) and its derivatives, depend- ing upon the ratio of the mean distances, giving at the same time a simple table for computing the variation of these constants relatively to this ratio, in order that they may readily be corrected for any change in the Asteroid’s mean distance. This correction will be necessary for those Asteroids more recently discovered, and whose mean distances are not therefore very well known. If, then, m and mp are the mean motion and mass of the Earth, and 7 is the mean motion of the Asteroid in a Julian year, its mean distance a will be Adopting the following values of n, the corresponding values of a are found to be for OOOO BOOTS GOOOH OOOO @OSOQ GOOOOH OGOOWO) GEE) @©® Ceres, Pallas, Juno, Vesta, Astrea, Hebe, Tris, Flora, Metis, Hygeia, Parthenope, Clio, Egeria, Irene, Eunomia, Psyche, Thetis, Melpomene, Fortuna, Massalia, Lutetia, Calliope, Thalia, Themis, Phocea, Proserpine, Euterpe, Bellona, Amphitrite, Urania, Euphrosyne, Pomona, Polymnia, Circe, Leucothea, Atalanta, Fides, Leda, Leetitia, Harmonia, Daphne, Isis, Hence, since or, if a — sin 6, we have for ASTEROID SUPPLEMENT. n = 281110.5 n = 281174.6 n = 297282.4 n = 357318.7 n = 313428.6 n = 342978.4 n = 351620.0 n = 396782.4 n = 351546.5 n = 231877.3 n = 337564.7 n = 363291.7 n = 313296.1 n = 811778.8 n = 301543.6 n = 259387.5 n = 333324.5 n = 372571.0 n = 346696.3 n = 346935.0 n = $41251.3 n = 260561.4 n = 304604.2 n == 230157.6 n = 348415.7 n == 299449.4 n = 360561.4 n = 279486.4 n = 317485.8 n = 356829.1 nm = 227218.7 n = 312088 9 n = 353282.6 n = 294022.0 N = 252728.1 n = 284199.7 n = 301801.1 n = 285726.3 n = 281889.5 n = 379644.5 n = 353182.1 log a = 0.4424798 log a = 0.4424188 log a. = 0.4262850 log a = 0.8730274 log a = 0.4109720 log a = 0.3848866 log a = 0.38776818 loz a = 0.3426962 log a = 0.3777426 log a = 0.4982256 log a = 0.3894930 log a = 0.3682274 log a = 0.4110944 log a = 0.4125000 log a = 0.4221644 log a = 0.4657652 log a = 0.3931530 log a = 0.3609250 log a = 0.3817650 log a = 0.38815646 log a = 0.3863482 log a = 0.4644578 log a = 0.4192406 log a = 0.50038 10 log a = 0.3803328 log a = 0.4241822 log a = 03770784 log a = 0.4441574 log a = 0.4072482 log a = 0.3734242 log a = 0.5041018 log a = 0.4122586 log a = 0.3763164 log a = 0.4294780 log a = 0.4732954 log a = 0.4393088 log a = 0.4219174 log a = 0.43877644 log a = 0.4416786 log a = 0.3554798 log a = 0.3763988 n = 340776.8 log a = 0.38867512 oy oe a B leas 6? = tan? d, a = 2.770000 a = 2.769579 a = 2.668609 a = 2.360627 a = 2.576155 a = 2.425977 a = 2.386063 a = 2.201386 a = 2.386397 a = 3.149385 a = 2.451845 a = 2.334680 a = 2.576881 a = 2.585235 a = 2.643409 a = 2.922572 a = 2 472595 a = 2.295752 a = 2.408602 a = 2.407490 a = 2.484155 a = 2.913788 a = 2.625672 a = 3.165053 a = 2.400672 a = 2.655720 a = 2.382750 a = 2.780721 a = 2.554160 a = 2.362785 a = 3.192286 a = 2.583799 a = 2.378573 a = 2.688302 a = 2.973688 a = 2.749849 a = 2.641906 a = 2.740088 a = 2.764895 @ = 2.267148 a = 2.379024 a = 2.436415 ASTEROID SUPPLEMENT. MERCURY AND VENUS AND ASTEROID a log a log 3” a log a log 6? @ Ceres, | 0.1397469 | 9.1453419 | 8.2992490 || 0.2611807 | 9.4168580 | 8.8643882 @) Pallas, | 0.1897681 | 9.1454079 | 8.2993834 || 0.2611704 | 9.4169240 | 8.8645298 @) Juno, | 0.1450564 | 9.1615367 | 8.3323090 || 0.2710521 | 9.4380528 | 8.8992460 @ Vesta, 0.1639812 | 9.2147943 | 8.4414266 | 0.3064153 | 9.4863104 | 9.0154400 | G6) Astrea, | 0.1502622 | 9.1768497 | 8.3636172 || 0.2807797 | 9.4483658 | 8.9323950 | © Hebe, | 0.1595641 | 9.2029351 | 8.4170708 || 0.2981612 | 9.4744512 | 8.9893366 @ tis, | 0.1622333 | 9.2101399 | 8.4318632 | 0.3031489 | 9.4816560 | 9.0051782 | Flora, | 0.1758432 | 9.2451255 | 8.5038916 || 0.38285804 | 9.5166416 | 9.0829018 @) Metis, | 0.1622106 | 9.2100791 | 8.4317386 || 0.3031065 | 9.4815952 | 9.0050436 | @) Hygeia, | 0.1229125 | 9.0895961 | 8.1858034 || 0.2296742 | 9.8611122 | 8.7457598 @) Parthenope, | 0.1578802 | 9.1983287 | 8.4076200 || 0.2950155 | 9.4698448 | 8.9792348 | @) Clio, 0.1658037 | 9.2195943 | 8.4512948 || 0.3098207 | 9.4911104 | 9.0260468 | @) Egeria, | 0.1502191 | 9.1767273 | 8.3633672 || 0.2807006 | 9.4482434 | 8.9821294 @) Irene, | 0.1497344 | 9.1753217 | 8.3604912 || 0.2797936 | 9.4468378 | 8.9290786 @ Eunomia, 0.1464392 | 9.1656573 | 8.3407292 || 0.2736361 | 9.4871734 | 8.9081472 @6) Psyche, ) 0.1824514 | 9.1220565 | 8.2518000 || 0.2474985 | 9.3935726 | 8.8145976 @ Thetis, 0.1565556 | 9.1946687 | 8.4001144 || 0.2925397 | 9.4661848 | 8.9712234 @) Melpomene, | 0.1686152 | 9.2268967 | 8.4663196 || 0.3150742 | 9.4984128 | 9.0422318 @) Fortuna, 0.1607151 | 9.2060567 | 8.4234'782 || 0.8003121 | 9.4775728 | 8.9961938 @0) Massalia, | 0.1607893 | 9.2062571 | 8.4238896 || 0.3004507 | 9.4777732 | 8.9966344 @i) Lutetia, } 0.1590280 | 9.2014735 | 8.4140716 0.2971596 | 9.4729896 | 8.9861286 @2) Calliope, | 0.1828507 | 9.1233639 | 8.2544612 || 0.2482447 | 9.3948800 | 8.8173836 @3) Thalia, | 0.1474284 | 9.1685811 | 8.3467060 || 0.2754845 | 9.4400972 | 8.9144712 | @4) Themis, 0.1223040 | 9.0874407 | 8.1814266 || 0.2285372 | 9.8589568 | 8.7412102 @5) Phocea, 0.1612460 | 9.2074889 | 8.4264188 || 0.30138041 | 9.4790050 | 8.9993426 @6) Proserpine, | 0.1457604 | 9.1636395 | 8.8366054 || 0.2723677 | 9.4351556 | 8.9037866 @7) Euterpe, | 0.1624588 | 9.2107438 | 8.4831028 || 0.3035704 | 9.4822594 | 9.0065074 @8) Bellona, | 0.1392080 | 9.1486643 | 8.2958274 || 0.2601240 | 9.4151804 | 8.8607884 99 Amphitrite, | 0.1515562 | 9.1805735 | 8.3712386 || 0.2831977 | 9.4520896 | 8.9404862 Urania, | 0.1638316 | 9.2148975 | 8.4406112 || 0.8061354 | 9.4859136 | 9.0145640 @) Euphrosyne, | 0.1212607 | 9.0837199 | 8.17388780 || 0.2265876 | 9.3552360 | 8.7333624 | 63) Pomona, ! 0.1498178 | 9.1755631 | 8.3609852 || 0.2799491 | 9.4470792 | 8.9296028 | | @3) Polymnia, | 0.1627441 | 9.2115053 | 8.4846682 | 0.3041035 | 9.4830214 | 9.0081858 68 Ciree, | 0.1439938 | 9.15834387 | 8.3257866 || 0.2690666 | 9.4298598 | 8.8923570 | @5) Leucothea, | 0.1301746 | 9.1145263 | 8.2364750 || 0.2432441 9.3860424 | 8.7985724 | 66) Atalanta, 0.1407709 | 9.1485129 | 8.3057184 || 0.26380444 | 9.4200290 | 8.8711982 | 6) Fides, 0.1465225 | 9.1659043 | 8.3412542 || 0.2737918 | 9.4374204 | 8.9086812 68) Leda, 0.1412724 | 9.1500573 | 8.3088698 || 0.2639814 | 9.4215734 | 8.8745172 Letitia, 0.1400049 | 9.1461431 | 8.3008832 || 0.2616130 | 9.4176594 | 8.8661084 @ Harmonia, | 0.1707426 | 9.2323419 | 84775334 | 0.3190422 | 9.5038580 | 9.0543398 @) Daphne, | 0.1627133 | 9.2114229 | 8.4344990 | 0.8040458 | 9.4829390 | 9.0080048 | @) Isis, 0.1588805 | 9.2010705 | 8.41382448 | 0.2968840 | 9.4725866 | 8.9852450 ASTEROID SUPPLEMENT. THE EARTH AND MARS AND ASTEROID a log a log Bp? a log a log £” @) Ceres, | 0.3610108 | 9.5575202 | 9.1756850 || 0.5499526 | 9.7403172 | 9.6370508 @) Pallas, | 0.3610657 | 9.5575862 | 9.1758370 || 0.5501526 | 9.7404832 | 9.63875268 () Juno, | 0.3747270 | 9.5787150 | 9.2131442 || 0.5709682 | 9.7566120 | 9.6845672 | @) Vesta, | 0.4236162 | 9.6269726 | 9.3398400 || 0.6454604 | 9.8098696 | 9.8537870 | @) Astrea, 0.3881754 | 9.5890280 | 9.2489844 || 0.5914594 | 9.7719250 | 9.7308190 ©) Hebe, j 0.4122051 | 9.6151134 | 9.3111086 || 0.6280734 9.7980104 | 9.8138890 @ _ Iris, | 0.4191005 | 9.6223182 | 9.3285220 || 0.6385800 | 9.8052152 || 9.8379504 Flora, } 0.4542593 | 9.6573038 | 9.4149788 |) 0.6921510 | 9.8402008 | 9.9636242 @) Metis, 0.4190419 | 9.6222574 | 9.3283752 || 0.6384949 | 9.8051574 | 9.8377554 @ Hygeia, | 0.317524 | 9.5017744 | 9.0497024 | 0.4838060 | 9.6846714 | 9.4851526 @) Parthenope, | 0.4078561 | 9.6105070 | 9.3000288 || 0.6214469 | 9.7934040 | 9.7987786 @) Clio, | 0.4283242 | 9.6317726 | 9.3515690 || 0.6526339 | 9.8146696 | 9.8703756 @) Egeria, 0.3880660 | 9.5889056 | 9.2486962 || 0.5912928 | 9.7718026 | 9.7304432 (4 Irene, } 0.3868121 | 9.5875000 | 9.2453892 || 0.5893821 | 9.7703970 | 9.7261280 @) Eunomia, 0.3782993 | 9.5778356 | 9.2227462 || 0.5764114 | 9.7607326 | 9.6968516 @® Psyche, | 0.3421644 | 9.5842348 | 9.1225462 |) 0.5213528 | 9.7171318 | 9.5720184 @ _ Thetis, | 0.4044334 | 9.6068470 | 9.2912624 || 0.6162317 | 9.789'7440 | 9.7869150 Melpomene, || 0.4355872 | 9.6390750 | 9.3695238 || 0.6637003 | 9.8219720 | 9.8961430 Fortuna, | 0.4151787 | 9.6182350 | 9.3186354 |) 0.6326040 | 9.8011320 | 9.8242486 @0) Massalia, 0.4153703 | 9.61843854 | 9.3191196 || 0.6328961 | 9.8013324 | 9.8245836 @i) Lutetia, } 0.4108202 | 9.6136518 | 9.8075842 || 0.6259631 | 9.7965488 | 9.8090718 @) Calliope, | 0.3431960 | 9.5355422 | 9.1255090 || 0.5229247 | 9.7184392 | 9.5756132 Thalia, 0.8808547 | 9.5807594 | 9.2295784 || 0.5803050 | 9.7636564 | 9.7056382 24) Themis, | 0.3159504 | 9.4996190 | 9.0449108 || 0.4814110 | 9.6825160 | 9.4795332 @8) Phocea, | 0.4165500 | 9.6196672 | 9.8220986 || 0.6346937 | 9.8025642 | 9.8290350 @6) Proserpine, ) 0.8765458 | 9.5758178 | 9.2180402 || 0.5737395 | 9.7587148 | 9.6908214 @7) Euterpe, | 0.4196832 | 9.6229216 | 9.3299862 || 0.6394677 | 9.8058186 | 9.8399906 @8) Bellona, 0.3596190 | 9.5558426 | 9.1718296 || 0.5479441 | 9.7387396 | 9.6325348 @9) Amphitrite, | 0.38915180 | 9.5927518 | 9.2577668 || 0.5965527 | 9.7756488 | 9.7423274 Urania, } 0.4232294 | 9.6265758 | 9.38388734 || 0.6448709 | 9.8094728 | 9.8524280 61) Euphrosyne,} 0.8132551 | 9.4958982 | 9.1366518 || 0.4773042 | 9.6787952 | 9.4698718 62) Pomona, | 0.38870272 | 9.5877414 | 9.2459566 || 0.5897100 | 9.7706384 | 9.7268680 @3) Polymnia, | 0.4204209 | 9.6236835 | 9.3318370 || 0.6405906 | 9.8065806 | 9.8425712 3 Circe, H 0.3719820 | 9.5705220 | 9.2057244 || 0.5667858 | 9.7534190 | 9.6751256 85) Leucothea, | 0.3362828 | 9.5267046 | 9.1055276 || 0.5123911 | 9.7096016 | 9.5514684 36) Atalanta, | 0.8636564 | 9.5606912 | 9.1829862 || 0.5541000 | 9.7435882 | 9.6464614 @) Fides, 0.8785145 | 9.5780826 | 9.2233228 || 0.5767394 | 9.7609796 | 9.6975898 68) Leda, | 0.3649519 | 9.5622356 | 9.1865478 || 0.5560740 | 9.7451326 | 9.6509244 39) Leetitia, | 0.38616774 | 9.5583214 | 9.1'775288 || 0.5510848 | 9.7412184 | 9.6396362 @) Harmonia, | 0.4410828 | 9.6445202 | 9.3830044 || 0.6720742 | 9.8274172 | 9.9158034 8 Pepune. } 0.4203405 | 9.6236012 | 9.3316372 || 0.6404691 | 9.8064982 | 9.8422938 49) Isis, | 9.4104392 | 9.6132488 i| | 9.3066132 | 0.6253682 | 9.7961358 | 9.8077146 ASTEROID SUPPLEMENT. JUPITER AND ASTEROID 0 log a @ Ceres, 0.5324055 | 9.7262425 @) Pallas, | 0.5328246 | 9.7261765 (@) Juno, | 0.5129176 | 9.7100477 @ Vesta, | 0.453723 | 9.6567901 G) Astrea, 0.4951477 | 9.6947347 @) Hebe, | 0.4662826 | 9.6686493 @imins) | 0.4586110 | 9.6614445 Flora, 0.4231154 | 9.6264589 @) Metis, | 0.4586752 | 9.6615053 @ Hygeia, | 0.6053246 | 9.7819883 @ Parthenope, | 0.4712547 | 9.6732557 @) Clio, | 0.4487351 | 9.6519901 ® Egeria, 0.4952871 | 9.6948571 @ Irene, 0.4968928 | 9.6962627 @ Eunomia, | 0.5080741 | 9.7059271 @ Psyche, | 0.5617304 | 9.7495279 @) Thetis, | 0.4752430 | 9.6769157 Melpomene, | 0.4412530 | 9.6446877 Fortuna, | 0.4629432 | 9.6655277 @0) Massalia, 0.4627295 | 9.6653273 @i) Lutetia, | 0.4678547 | 9.6701109 ® Calliope, | 0.5600419 | 9.7482205 Thalia, 0.5046651 | 9.7030033 @) Themis, | 0.6083363 | 9.7841437 @5) Phoceea, } 0.4614190 | 9.6640955 CB) Proserpine, | 0.5104402 | 9.'7079449 @7) Euterpe, | 0.4579743 | 9.6608411 @) Bellona, | 0.5344660 | 9.7279201 69 Amphitrite, | 0.4909202 | 9.6910109 Urania, ‘| 0.4541370 | 9.6571869 @) Euphrosyne,} 0.6135706 | 9.7878645 @2) Pomona, | 0.4966167 | 9.6960213 @3) Polymnia, | 0.4571714 | 9.6600791 Circe, | 0.5167026 | 9.7132407 @5) Leucothea, | 0.5715551 | 9.7570581 Atalanta, | 0.5285322 | 9.7230715 @ Fides, 0.5077852 | 9.7056801 6) Leda, | 0.5266561 | 9.7215271 Letitia, | 0.5314241 | 9.7254413 @ Harmonia, | 0.4357551 | 9.6392425 @) Daphne, 0.4572582 | 9.6601615 @) Isis, | 0.4682889 | 9.6705139 SATURN AND log f? a log a log 6? 9.5972418 || 0.2903912 | 9.4629835 | 8.9642268 9.5970576 || 0.2903471 | 9.4629175 | 8.9640826 9.5526778 || 0.2797620 | 9.4467887 | 8.9289720 9.4136850 || 0.2474749 | 9.8935311 | 8.8145096 9.5116208 || 0.2700696 | 9.4314757 | 8.8958426 | 9.4437696 || 0.2543257 | 9.4053903 | 8.8398212 | 9.4254400 || 0.2501414 | 9.8981855 | 8.8244328 | 9.3385890 || 0.2307809 | 9.3631999 | 8.7501690 | 9.4255938 || 0.2501764 | 9.38982463 | 8.8245618 9.7621738 || 0.38301637 | 9.5187293 | 9.0875848 9.4555768 || 0.2570376 | 9.4099967 | 8.8496782 9.4016310 || 0.2447547 | 9.8887311 | 8.8042904 9.5119454 || 0.2701457 | 9.4315981 | 8.8961064 9.5156748 || 0.2710215 | 9.4330037 | 8.8991400 9.5415322 || 0.2771201 | 9.4426681 | 8.9200382 9.6637084 || 0.3063860 | 9.4862689 | 9.0153486 9.4650096 || 0.2592130 | 9.4136567 | 8.8575210 9.3834198 || 0.2406737 | 9.8814287 | 8.7887714 9.4358076 || 0.2525042 | 9.4022687 | 8.8331494 9.4352980 || 0.2528878 | 9.4020683 | 8.8327214 9.4475086 || 0.2551831 | 9.4068519 | 8.8429470 9.6598932 || 0.8054651 | 9.4849615 | 9.0124638 9.5336678 || 0.2752608 | 9.4897443 | 8.9137078 9.7689974 || 0.3318063 | 9.5208847 | 9.0924256 9.4321654 || 0.2516730 | 9.4008365 | 8.8300908 9.5469810 || 0.2784107 | 9.4446859 | 8.9244112 9.4239124 || 0.2497941 | 9.3975821 | 8.8231452 9.6019316 || 0.2915151 | 9.4646611 | 8.9678920 9.5017814 || 0.2677638 | 9.4277519 | 8.8878142 9.4146848 || 0.2477010 | 9.3939279 | 8.8153552 9.7808704 || 0.3346613 | 9.5246055 | 9.1007972 9.5150332 || 0.2708709 | 9.4827623 | 8.8986186 9.4219850 || 0.2493562 | 9.8968201 | 8.8215198 9.5613672 || 0.2818265 | 9.4499817 | 8.9359044 9.6858902 || 0.3117448 | 9.4937991 | 9.0319994 9.5884168 || 0.2882793 | 9.4598125 | 8.9573054 9.5408658 || 0.2769626 | 9.4424211 | 8.9195028 9.5841354 || 0.2872553 | 9.4582681 | 8.9539372 9.5950066 || 0.2898560 | 9.4621823 | 8.9624776 9.3699368 || 0.2376750 | 9.3759835 | 8.7772206 9.4221928 || 0.2494034 | 9.3969025 | 8.8216958 9.4485410 || 0.2554200 | 9.4072549 | 8.8438088 ASTEROID SUPPLEMENT. URANUS AND NEPTUNE AND ASTEROID a log a log 6? a | log a log 6? @ Ceres, 0.1448944 | 9.1595503 | 8.3282512 || 0.0922202 | 8.9648260 | 7.9333614 @) Pallas, | 0.1443724 | 9.1594843 | 8.3281162 || 0.0922062 | 8.9647600 | 7.9332282 (3) Juno, | 0.1891091 | 9.14388555 | 8.2951978 || 0.0888446 | 8.9486312 | 7.9007042 @_ Vesta, | 0.12380546 | 9.0900979 | 8.1868222 || 0.0785911 | 8.8953736 | 7.7934380 G) Astrea, | 0.1342896 | 9.1280425 | 8.2639882 || 0.0857666 | 8.9333182 | 7.8698428 @) Hebe, } 0.1264611 | 9.1019571 | 8.2109160 || 0.0807668 | 8.9072328 | '7.8173020 @ Iris, 0.1248805 | 9.0947523 | 8.1962758 || 0.0794379 | 8.9000280 | 7.8028050 Flora, | 0.1147537 | 9.0597667 | 8.1252904 || 0.0782896 | 8.8650424 | '7.7324240 @) Metis, / 0.1243979 | 9.0948131 | 8.1963996 || 0.0794491 | 8.9000888 | '7.8029278 @) Hygeia, | 0.1641709 | 9.2152961 | 8.4424582 || 0.1048508 | 9.0205718 | 8.0459446 (i) Parthenope, | 0.1278096 | 9.1065635 | 8.2202800 || 0.0816280 | 8.9118392 | '7.8265820 @) Clio, | 0.1217021 | 9.0852979 | 8.1770762 || 0.0777273 | 8.8905736 | 7.7837792 @) Egeria, | 0.1348275 | 9.1281649 | 8.2642376 || 0.0857908 | 8.9334406 | '7.8700892 (@) Irene, | 0.1347629 | 9.1295705 | 8.2671008 || 0.0860689 | 8.9348462 | 7.8729216 @ Eunomia, | 0.1877955 | 9.13892349 | 8.2867952 || 0.0880057 | 8.9445106 | 7.8923978 @ Psyche, | 0.1523476 | 9.1828357 | 8.3758704 || 0.0972997 | 8.9881114 7.9803538 @ Thetis, | 0.1288912 | 9.1102235 | 8.2277226 || 0.0823188 | 8.9154992 | 7.8339506 @s) Melpomene, | 0.1196729 | 9.0779955 | 8.1622562 || 0.0764313 | 8.8832712 | 7.7690870 @) Fortuna, 0.1255554 | 9.0988355 | 8.2045718 || 0.0801883 | 8.9041112 | '7.8110240 @0) Massalia, | 0.1254978 | 9.0986351 | 8.2041646 || 0.0801513 | 8.9089108 | 7.8106206 @i) Lutetia, } 0.1268875 | 9.1034187 | 8.2138866 || 0.0810391 | 8.9086944 | '7.8202504 Q2) Calliope, | 0.1518891 | 9.1815283 | 8.3731932 || 0.0970072 | 8.9868040 | 7.9777144 P } @3) Thalia, | 0.1868709 | 9.13863111 | 8.2789702 || 0.0874151 | 8.9415868 | 7.8865052 @4) Themis, | 0.1649877 | 9.2174515 | 8.4468886 || 0.1053726 | 9.0227272 | 8.0503034 @5) Phocwa, | 0.1251421 | 9.0974033 | 8.2016610 || 0.0799243 | 8.9026790 | 7.8081412 @e) Proserpine, | 0.1884371 | 9.1412527 | 8.2909096 || 0.0884155 | 8.9465284 | 7.8964652 @7) Euterpe, | 0.1242078 | 9.0941489 | 8.1950500 || 0.0793276 | 8.8994246 | 7.8015908 @8) Bellona, | 0.1449532 | 9.1612279 | 8.3316786 || 0.0925771 | 8.9665036 | '7.9367454 Amphitrite, | 0.13831431 | 9.1243187 | 8.2564048 || 0.0850344 | 8.9295944 | '7.8623406 Urania, | 0.1231671 | 9.0904947 | 8.1876282 || 0.0786630 | 8.8957704 | '7.7942364. @i) Euphrosyne,} 0.1664073 | 9.2211723 | 8.4545402 || 0.1062742 | 9.0264480 | 8.0578292 62) Pomona, | 0.1346880 | 9.1293291 | 8.2666090 || 0.0860211 | 8.9346048 | 7.8724852 @3) Polymnia, 0.1239906 | 9.0933869 | 8.1935024 || 0.0791886 | 8.8986626 | 7.8000572 Circe, | 0.1401356 | 9.1465485 | 8.8017102 || 0.0895002 | 8.9518242 | 7.9071412 @5) Leucothea, | 0.1550122 | 9.1903659 | 8.38912946 || 0.0990014 | 8.9956416 | 7.9955608 G6 Atalanta, | 0.1483439 | 9.1563793 | 8.8217752 | 0.0915493 | 8.9616550 | 7.9269652 67 Fides, 0.1377171 | 9.1389879 | 8.2862920 || 0.0879557 | 8.9442686 | 7.8919002 68 Leda, | 0.1428351 | 9.1548349 | 8.3186218 || 0.0912243 | 8.9601106 | 7.9238506 Letitia, 0.1441281 | 9.1587491 | 8.3266150 || 0.0920502 | 8.9640248 | 7.9317454 @ Harmonia, | 0.1181817 | 9.0725503 | 81512096 || 0.0754790 | 8.8778260 | 7.7581332 @) Daphne, | 9.1240136 | 9.0934693 | 8.1936694 || 0.0792036 | 8.8987450 | '7.8002230 42) Isis, | 0.1270053 | 9.1038217 | 8.2147060 || 0.0811143 | 8.9090974 | 7.8210616 ASTEROID SUPPLEMENT. 9 The want of accuracy in the mean distances of many of the Asteroids renders some simple and expeditious means desirable for correcting the coefficients for changes in the value of the argument a. The following formulas and _ tables enable us to compute these changes with every possible facility and accuracy, and leave nothing to be desired in the numerical solution of the problem. Denote by A;, B,, C,, D,, &c. the variations of the tabulated functions for a change of .001 in the argument a, the logarithms of which at any value of a are found in the general Tables. If 4 denotes a difference of the function correspond- ing to a change 4a = .001 in the argument, and J is the modulus of the common system of logarithms, we readily find the following formulas, VARIATIONS oF Loe bY. Alles 6 =7A) ——— for all values of 7. VARIATIONS OF FIRST DERIVATIVES. A log « D. 3!) = B.+ (i+ 2 6) ¥O for all values of i except i = 0, for which the formula is Alog a D.b) = B+ (24 26%) “2. VARIATIONS OF SECOND DERIVATIVES. A loge? D2 3) = C,+ (6 + 49%) VA" for all values of 7 except 7 = 0, and 1, for which the formulas are Aloga’ Dz b') = C,+ (2+ 48 Ay aes. ieee 1 A = Gh Gee aga) eee VARIATIONS OF THIRD .DERIVATIVES. Alog a? Di 0) = D, + (i+ 6 #2) “2# for all values of ¢ except i = 0, 1, and 2, for which the formulas are Aloga® DV = D+ (4-664 UAE, A log a® D2 by = D, -— (3b 6B) ——— ne MA Aloga’ D?b) = D, + (4 + 6 B2) ——* VARIATIONS OF FOURTH DERIVATIVES. A log a! Di 3) = E, + (+ 8 6) “44 for all values of 7 except 7 = 0, 1, 2, and 3, for which the formulas are Pie 10: A arp ok (A Bp) ae Nig WO = Jes (Cha ep) = Maa SEER Maa Aloga Dj 0) — By (5-8 42) ——— A loga D, bo = E, + (5 + 8 B2) ——— VARIATIONS OF FIFTH DERIVATIVES. MaAa Aloga’ D? bY = F, + (i+ 10?) for all values of 7 except 7 = 0, 1, 2, 3, and 4, for rich the formulas are 9 10 ASTEROID SUPPLEMENT. Maa Alogi) Dine (62810 63) Allog @ DROP = mG =e 10 6) Ae Alora DEO) r= (6 teml0le yee Maa A log a D53® — F, + (5+ 10 62) M42 Maa A log a pine (6 + 10 5%) MA VARIATIONS OF LOG ab". log 00) (GE (Gee ieeya2) ae for all values of 7. VARIATIONS OF FIRST DERIVATIVES. i Mi Aon 0), WO == tat (6. 1 tL Gea) BAS for all values of ¢ except i = 0, for which the formula is 1 A lees 1), 6 = ih Te (Ge Bee) BES, VARIATIONS OF SECOND DERIVATIVES. A log Ds) = K+ @ +1486) “4 for all values of ¢ except ¢ = 0, ad 1, for which the formulas are M A log a’ D0) = K, + (3+86)™"%, A log a? Dio) = K+ (44.86%) 25. VARIATIONS OF LOG a” DY. Allog a? Oly Te EL GG 4eto\ tt giaay Aaa for all values of 7. It will be observed, that, in all these variations, simple multiples of oS: and 9 ge Ma te Sa and 2 ew ——* $a, it will only be necessary to multiply them by 1, 2, 3, 4, —* occur. then for a change of a in the argument we compute the terms &e. to have the aualions of all the coefficients arising from these terms. The other terms, A; da, B, 8a, C, 8a, &c., of the variations are as readily found, since the logarithms of A;, B;, C,, &c., which are given in the general Tables, are all to be increased by the same constant log Sa. If, besides, we have tables from which Maa and 2 6?“ Maa he! able to esiupils the variations of all the coefficients needed for any Asteroid in a few minutes. Such are the Tables given on the following pages. The unit place corresponds to the fifth decimal place of the logarithm to be corrected, while the unit place of A;, B;, C;, &c. corresponds to aie. last decimal in the tabulated function, which is satel the seventh. The logarithms of b® and its derivatives, found in the following pages, have been computed in duplicate to seven decimals; but only five are printed, which is ample to give all desired accuracy in the final result. —— can be taken for any value of a by simple inspection, we shall ASTEROID SUPPLEMENT. Maa 2p2 Maa a MAa 282 Maa a MaAa a a a a a 1447.6 2.6 090] 482.5 7.8 150] 289.5 1400.9 2.7 || O91] 477.2 7.9 151) 287.6 1357.2 2.8 || .092] 472.0 8.0 152] 285.7 1316.0 2.8 093 | 467.0 8.1 153} 283.8 1277.3 2.9 094 | 462.0 8.2 154] 282.0 1240.8 3.0 095} 457.2 8.3 155] 280.2 1206.4 3.2 096 | 452.4 8.4 156] 278.4 1173.7 3.3 097 | 447.7 8.5 157] 276.6 1142.9 3.4 098 | 443.2 8.6 || .158] 274.8 1113.6 3.4 099 | 438.7 8.7 159] 273.1 1085.8 3.5 100} 434.3 8.8 160] 271.4 1059.3 3.6 101 | 430.0 8.9 161] 269.7 1034.1 3.6 102 | 425.8 9.0 162} 268.0 1010.0 317) 103 | 421.6 9.1 163] 266.4 987.0 3.8 104 | 417.6 9.2 164| 264.8 965.1 3.9 105 | 413.6 9.2 165} 263.2 944.1 4.0 106 | 409.7 9.3 166] 261.6 924.0 4.1 107 | 405.9 9.4 || .167] 260.0 904.8 4.2 108 | 402.1 9.5 168] 258.5 886.3 4.3 109 | 398.4 9.6 169] 257.0 868.7 4.4 110} 394.8 9.7 170] 255.5 851.5 4.4 111] 391.3 9.8 171} 254.0 835.2 4.5 112} 387.7 9.9 172} 252.5 819.4 46 113 | 384.3 10.0 173 | 251.0 804.2 4.7 114] 380.9 10.0 174] 249.6 789.6 4.8 115 | 377.6 10.1 175 | 248.2 775.5 4.9 116] 374.4 10.2 176 | 246.8 761.9 5.0 117 | 371.2 10.3 177 | 245.4 748.8 5.1 118] 368.0 10.4 178} 244.0 736.1 5.2 119 | 364.9 10.5 179 | 242.6 723.8 5.2 120] 361.9 10.6 180} 241.2 711.9 53 121] 358.9 10.7 181] 239.9 700.5 5A 122 | 356.0 10.8 182} 238.6 689.4 55 123 | 353 10.8 183] 297.3 678.6 5.6 124 | 350.2 10.9 184} 236.0 668.1 5.7 125] 347.4 11.0 185] 234.7 658.0 5.8 126 | 344.7 11.1 186] 233.4 648.2 5.9 127] 342.0 11.2 187} 232.2 638.7 6.0 128] 339.3 11.3 188} 230.9 629.4 6.0 129] 336.7 11.4 189} 229.7 620.4 6.1 130] 334.1 11.5 190] 228.5 611.7 6.2 131) 331.5 11.6 191] 227.3 603.2 6.3 132] 329.0 11.6 192] 226.1 594.9 6.4 133] 326.5 11.7 193] 224.9 586.9 6.5 134] 324.1 11.8 194] 223.8 579.1 6.6 135] 321.7 11.9 195} 222.7 571.4 6.7 136] 319.3 12.0 196] 221.6 564.0 6.8 137] 317.0 12.1 197} 220.5 556.8 6.8 138] 314.7 12.2 198] 219.4 549.7 6.9 139} 312.4 12.3 199} 218.3 542.9 7.0 140] 310.2 12.4 200] 217.2 536.1 7.0 141] 308.0 12.4 201} 216.1 529.6 7.1 142] 305.8 12.5 202} 215.0 523.2 7.2 143 | 303.7 12.6 || .203]| 213.9 517.0 eS 1441 301.6 12.7. || .204] 219.8 | 510.9 74 145] 299.5 12.8 || 205] 211.8 505.0 WED. 146 | 297.4 12.9 206] 210.7 499.2 7.5 147| 295.4 13.0 207 | 209.7 493.5 7.6 148] 293.4 13.1 .208| 208.7 488.0 “oll 149] 291.4 13.2 .209| 207.7 482.5 7.8 150} 289.5 13.3 210] 206.7 ee a anrteke BERBER Be wo a el Le sel oe eel oe I a eel mown wwnwwrd~ 2 OOO oe ole oon) wu 0° SCODDDD DOWD MD M~-F~2~F BPW YNBABAGA ABIAAAGDA AANA naan Ce ee FRR RRR OC BODDID APWNHNE DODAD ARWHH SHODND TNRWHWH SCOMHAT ARUP WW HM OODA AARWNHN BPH OOD See Soe eee SS See e rs eae ee | HOT Or wwwnwn»wn wwnwwr» SSIRQS GVIGID GAAADA Aaaan wmwwnwwnwn wWNHNWYWD WNWWWW WwWwww wwnwwnnd wonnwn wOwWWWNH WNWWNWD ASTEROID SUPPLEMENT. a Maa . MAa a Maa 22 Maa a MAa 2p2 Masa a a a a a 330] 131.6 32.1 390} 111.3 39.9 450) 96.4 49.0 331 | 131.2 32.2 391] 111.1 40.0 451] 96.2 49.1 332] 130.8 32.3 392] 110.8 40.1 452] 96.0 49.3 333 | 130.4 32.5 393] 110.5 40.3 453] 95.8 49.5 334 | 130.0 32.6 394] 110.2 40.4 454] 95.6 49.6 335 | 129.6 32.8 395} 109.9 40.6 4551 95.4 49.8 336 | 129.2 32.9 396} 109.6 40.7 .456| 95.2 50.0 337 | 128.9 33.0 397 | 109.4 40.8 457) 95.0 50.1 338 | 128.5 33.1 398] 109.1 41.0 458] 94.8 50.3 339 | 128.1 33.2 399] 108.8 41.2 459} 94.6 50.5 340 | 127.7 33.3 400] 108.6 41.3 460} 94.4 50.6 341} 127.3 33.4 401} 108.3 41.4 461] 94.2 50.8 342 | 126.9 33.6 402] 108.0 41.6 462] 94.0 51.0 343 ] 126.6 33.7 403! 107.8 41.7 .463| 93.8 51.1 344 | 126.2 33.9 404} 107.5 41.9 464] 93.6 51.3 345 | 125.8 34.0 405] 107.2 41.0 465] 93.4 51.5 346 | 125.5 34.1 406} 107.0 42.1 466] 93. 51.6 347 | 125.1 34.2 407} 106.7 42.3 .467| 93.0 51.8 348 | 124.7 34.3 408} 106.4 42.5 468] 92.8 52.0 349 | 124.4 34.4 409} 106.2 42.6 469] 92.6 52.2 350} 124.0 34.5 |; .410] 105.9 42.7 470] 92.4 52.4 351 | 123.6 34.7 411] 105.6 42.9 471 92.2 52.6 352 | 123.3 34.8 412| 105.4 43.0 472] 92.0 52.7 353 | 122.9 35.0 413] 105.1 43.1 473 | 91.8 52.9 354] 122.6 35.1 414} 104.8 43.3 474| 91.6 53.1 355 | 122.3 35.2 415| 104.6 43.4 475] 91.4 53.2 356 | 121.9 35.3 416] 104.3 43.6 476| 91.2 53.4 357 | 121.6 35.5 417 | 104.1 43.8 477 | 91.0 53.6 358] 121.3 35.6 418] 103.9 43.9 .478| 90.8 53.8 359 | 120.9 35.8 419] 103.6 44.0 479 | 90.6 54.0 360] 120.6 35.9 420] 103.3 44,2 480] 90.4 54.2 361] 120.3 36.0 421] 103.1 44.3 481 90.3 54.3 362 | 119.9 36.1 422] 102.8 44.5 482] 90.1 54.5 363 | 119.6 36.3 423] 102.6 44.7 483 89.9 54.7 364 | 119.3 36.5 424] 102.4 44.8 484 89.7 54.8 365 | 118.9 36.6 425] 102.1 45.0 485 89.5 55.0 366 | 118.6 36.7 426] 101.9 45.2 486 89.3 55.2 367 | 118.3 36.8 427| 101.7 45.3 487 89.1 55.4 368] 117.9 36.9 428] 101.4 45.5 .488 88.9 55.6 369] 117.6 37.1 429} 101.2 45.6 489 88.7 55.8 370] 117.3 37.2 430| 101.0 45.7 490 88.6 55.9 371] 117.0 37.4 431} 100.7 45.9 AQ 88.4 56.1 372] 116.7 37.5 432] 100.5 46.1 492] 88.2 56.3 373] 116.4 37.6 || .433] 100.3 46.2 493 88.0 56.5 374] 116.1 37.7. || .434] 100.0 46.4 494 87.8 56.7 Ie 375} 115.8 37.9 435] 99.8 46.6 495 87.6 56.9 376 | 115.5 38.0 436] 99.6 46.7 496 87.5 57.1 377} 115.2 38.2 437 99.3 46.9 497 87.3 57.3 378] 114.9 38.3 \) 488] 99.1 47.0 498 87.1 57.5 379] 114.6 38.4 || .439] 98.9 47.1 499} 87.0 57.7 380} 114.3 38.5 440] 98.6 47.3 .500 86.8 57.9 381] 114.0 38.7 441 98.4 47.5 501 86.6 58.1 382] 113.7 38.8 || .442]) 98.9 47.6 502 86.5 58.3 383] 113.4 39.0 || .443 97.9 47.8 .503 86.3 58.5 384] 113.1 39.1 || 444) 97.7 48.0 504 86.1 58.6 385] 112.8 39.2 445| 97.5 48.1 505 86.0 58.8 386] 112.5 39.4 446] 97.2 48.3 506 85.8 59.1 387| 112.2 39.5 447] 97.0 48.5 .507| 85.6 59.3 388} 111.9 39.6 448] 96.8 48.6 508] 85.5 59.5 389} 111.6 39.8 449} 96.6 48.8 509] 85.3 59.7 | .390] 111.3 39.9 450] 96.4 49.0 510] 85.1 59.9 Sob DOnm RNUHOO DYORW HOODY ARwWNH SCODNUD RWHHS OHUDMR WHWHSS BDNYBHUR WHNHRSOOS BRAUN wo vo 02 Go 0 OO ON Oi ASTEROID SUPPLEMENT. [ooo oo o)xo oe 2) = ee OO anDnDone ~ wt 3 ~3 +3 2 OCconoe o foe dhs I iS SS SS eS SS SS 2 BS BD EEE III OD wo KKK RK oO COCO So NOD ODWe DM DAHWO~F Crd a] (WS) WwWAMVO CHwWRA RDOKDW WARNS SHURA Dox wD 2 ID 1) Maa lope Aa | a Maa ope ihe a MAa ope Ae a a a a 76.2 73.3 -630 68.9. 90.8 -690 63.0 114.5 76.1 73.5 631 68.8 91.1 691 62.9 114.9 75.9 73.8 -632 68.7 91.4 .692 62.8 115.4 75.8 74.1 -633 68.6 91.8 .693 62.7 115.9 75.7 74.3 .634 68.5 92.6 694 62.6 116.3 75.5 74.6 -635 68.3 92.4 695 62.5 116.8 75.4 74.9 636 68.2 92.8 696 62.4 117.3 75.3 75.1 637 68.1 93.1 AE 62.4 117.7 Cael 75.4 | .638 68.0 93.4 .698 62.3 118.2 75.0 Woe: .639 67.9 93.8 699 62.2 118.7 74.9 75.9 640 67.8 94.1 -700 62.1 119.2 74.7 76.2 641 67.7 94.5 -701 62.0 119.7 74.6 | 76.5 || .642| 67.6 | 94.9 || .702] 61.9 | 120.2 74.5 | 76.7 || .643| 67.5 | 95. || .703] 61.8 | 120.7 74.3 | 77.0 BM GIA | 688 704) 617 | 1212 74.2 77,3 .645 67.3 95.9 .705 61.6 We 7/ 74.1 77.5 646 67.2 96.2 -706 61.6 122.2 73.9 77.8 -647 67.1 96.6 .707 61.5 | 122.7 73.8 78.1 .648 67.0 97.0 -708 61.4 123.3 Wer 78.3 649 66.9 97.3 .709 61.3 123.8 Seo) 78.6 -650 66.8 97.7 .710 61.2 124.3 73.4 78.9 651 66.7 98.1 Se lil 61.1 124.9 73.3 79.1 652 66.6 98.4 AP 61.0 125.4 73.1 79.4 653 66.5 98.8 .713 60.9 125.9 73.0 | 79.7 |) .654| 66.4 | 99.2 || 714] 60.8 | 126.5 72.9 80.0 655 66.3 99.6 Bile 60.8 127.0 1228 80.3 656 66.2 100.0 .716 60.7 127.6 WaT 80.6 -657 66.1 100.4 STAI 60.6 128.2: 72.6 80.9- .658 66.0 100.8 .718 60.5 esi 72.4 | 81.2 || .659] 65.9 | 101.2 || .719| 60.4 |- 129.3 72.3 81.4 .660 65.8 101.6 .720 60.3 129.9 72.2 81.7 661 65.7 102.0 Seal 60.2 130.4 72.0 82.0 .662 65.6 102.4 a2 60.1 131.0 71.9 82.3 .663 65.5 102.8 5B 60.0 131.6 71.8 82.6 -664 65.4 103.2 7124 60.0 132.2 riileards 82.9 -665 65.3 103.6 .725 59.9 132.8 71.6 83.2 .666 65.2 104.0 .726 59.8 133.4 71.5 83.5 667 65.1 104.4 Bh 59.7 134.0 ipleess 83.8 .668 65.0 104.8 .728 59.6 134.6 yi?) 84.0 .669 64.9 105.3 3129 59.5 135.2 ToLal: 84.2 .670 64.8 105.7 .730 59.4 135.8 71.0 84.5 671 64.7 106.1 nies 59.3 136.4 70.9 84.8 | coz 64.6 106.5 .732 59.2 137.0 70.8 85.1 | .673 64.5 106.9 .733 59.2 137.6 70.7 85.4 674 64.4 107.3 «734 59.1 138.2 70.6 85.7 675 64.3 107.8 ew 59.0 138.9 70.5 86.0 .676 64.2 108.2 .73 58.9 139.5 70.3 86.3 677 64.1 108.6 SUB 58.8 140.1 70.2 86 7 .678 64.0 109.1 IS 7/sxs} 58.7 140.8 70.1 | 87.0 || .679| 64.0 | 109.5 || .739| 58.6 | 141.4 | 70.0 87.3 .680 63.9 109.9 | -740 58.5 142.1 69.9 87.7 .681 65. 110.4 | .741 58.5 142.8 69.8 88.0 .682 63.7 110.8 | .742 58.5 143.4 69.7 88.4 683 63.6 111.2 | -743 58.4 144.1 69.6 88.8 .684 63.5 111.7 | .744 58.3 144.8 69.5 89.1 .685 63.4 112.1 | -745 58.2 145.4 69.3 89.4 .686 63.3 112.6 | .746 58.1 146.1 69.2 89.8 687 63.2 US| aera: 58.0 146.8 69.1 90.1 .688 63.2 113.5 || .748 57.9 147.4 69.0 90.4 .689 63.1 114.0 || .749 57.8 | 148.1 68.9 | 90.8 .690 63.0 114.5 || .750 57.8 | 148.9 14 ASTEROID SUPPLEMENT. CERES AND MERCURY. i log of) log « D, b\) log a” D2 Ui) log «® D2 o") log «* DE o 0 0.30317 98.30032 98.31934 97.44036 97.49643 1 99.14855 99.15497 97.80605 97.84066 97.21934 2 98.16931 98.47392 98.48814 97.48451 97.53778 3 97.23565 97.71528 98.02259 98.04729 97,28313 z log « 0) log «” D, 0 log « D2 log a” UY 0 98.46562 98.41702 98.46794 98.64467 1 98.78387 98.81518 98.15114 2 98.02506 98.34098 98.39738 97.55551 CERES AND VENUS. z log of log « D,, 0" log a” D2 v()) log «® D3 ol) log «* Div 0 0.30866 98.86817 98.93419 98.60257 98.77923 1 99.42831 99.45131 98.66661 98.78204 98.68770 2 98.72151 99.03548 99.08592 98.64286 98.81241 3 98.05983 98.54607 98.86992 98.95594 98.74416 a log « Te log oD, 6} log « D2 s@ log Be 0 99.78661 99.30053 99.46371 99.31967 1 99.36843 99.47402 99.34309 2 98.87840 99.23198 99.40891 98.72471 CERES AND THE EARTH. a log uo log « D, By log a” ioe oe log a® D? oy log at pt OS 0 0.31606 99.18307 99.30863 99.26745 99.57212 1 99.58006 99.62555 99.15090 99.36112 99.53802 2 99.01518 99.34214 99.44058 99.30306 99.59821 3 98.49481 98.99028 99.33731 99.50149 99.58608 i log « 0) log «” D, 0) log a D2 UD log «7 U 0 99.99388 99.81579 0.10171 99.77113 1 99.70620 99.90075 0.04682 2 99.35318 99.75615 0.06022 99.40046 CERES AND MARS. . ; log b' log « D, 0? log a” D? uf) log «? D3 vl) log a* Dé 6) 0 0.33926 99.65530 99.94784 0.31880 0.90544 1 99.79764 99.91499 99.89782 0.34400 0.90318 2 99.41961 99.79015 0.03469 0.34294 0.91998 3 99.08414 99.61133 0.03771 0.42177 0.93272 a log a OY log oe Dy Be) log oe De 3 log oo s@ 0 0.38646 0.66077 1.22618 0.63611 1 0.25313 0.67615 1.21425 2 0.07178 1.20498 0.49583 0.62218 wnt ae ASTEROID SUPPLEMENT. 15 Gide lS). ANID Ad) UIP I Wek. reits a log vf) log « D, 6) log «” D2 of log «® D3 vo log a* Db) 0 0.33647 99.61422 99.88792 0.22399 0.78240 1 99.77938 99.88798 99.83147 0.25264 0.77910 2 99.38678 99.75185 99.97913 0.24928 0.79789 3 99.03698 99.56013 99.97645 0.33576 0.81039 4 98.70714 99.34528 99.89714 0.37783 0.86597 5 98.38892 99.11660 99.77413 0.36276 0.91738 a log « 6 log a” D, b log a® D2 u) log «1 0 0.34707 0.58255 1.11957 0.54981 1 0.20283 0.60124 1.10580 2 0.00871 0.54188 1.09679 0.39499 3 99.79282 0.43268 1.06126 0 log Be log « D, SY log of Dt Oe log oe D o log at Dt op 0 0.31054 98.96893 99.05044 98.81306 99.02522 1 99.4725 99.50595 98.82077 98.96 160 98.95587 2 98.81690 99.13413 99.19682 98.85210 99.05628 3 98.20150 98.69005 99.01969 99.12600 99.01005 4 97.59598 97.89490 98.71290 99.05833 a log « 0 log o” D, 0) log a® D2 bo log 0) 0 99.84964 99.46254 99.65943 99.45585 1 99.47496 99.60419 99.56356 2 99.03012 99.39638 99.60864 98.93780 3 98.55765 98.92597 99.47918 a log 0 log « D, 6 log o? D? o(? log a D3 v) log a* DE 0”) 0 0.30331 98.32939 98.34970 97.49922 97.55890 1 99.16298 99.16984 97.84989 97.88680 97.29334 2 98.19797 98.50283 98.51802 97.54326 97.59998 3 97.27853 97.75834 98.06608 98.09245 97.35693 a log « uo} log of D, a) log ae DA B®) log of @ 0 99.48114 98.46148 98.51570 98.67667 1 98.81339 98.84678 98.21080 2 98.06871 98.38565 98.44566 97.61455 CERES AND NEPTUNE. a log 0 log « D, 0) log a” DU) log a? D3 uP log at DE 0 0 0.30196 97.93382 97.94212 96.70148 96.72657 1 98.96622 98.96900 97.25439 97.26964 96.29212 2 97.80626 98.10884 98.11501 97.74653 96.77030 3 96.69198 97.17019 97.47393 97.48469 96.35768 >. log « a log oe DE o log a D> Be log oe BO wore co 99.27420 98.41373 97.47500 97.86031 98.42748 97.78251 9788298 97.40558 97.80777 98.25376 96.81523 16 ASTEROID SUPPLEMENT. PALLAS AND MERCURY. The values of a for Pallas and the principal Planets are so near the correspond- ing ones for Ceres, that the coefficients for Pallas are readily obtained from those for Ceres by means of the formulas and tables on pages 63 — 67. The inclination and eccentricity of Pallas are so great, however, that its pertur- bations cannot be obtained to any great degree of approximation through the usual development without a disproportionate amount of labor. The values of b and its derivatives for Pallas will, therefore, probably never be needed for the computation of its perturbations ; and especially for the action of Jupiter and Saturn. JUNO AND MERCURY. The inclination of Juno is 13°, and the eccentricity is 0.27. Both of these ele- ments are large; and the eccentricity especially is too great to render it necessary to give the coefficients for this Planet. If, however, all or any of them shall ever be needed, they may readily be found from the corresponding ones for Proserpine given hereafter. To illustrate the use of the formulas for computing the variations of the co- efficients corresponding to a change in the argument a, we will find the value of log a* Di bP for Juno and J pues from the dilie of the same coefficient for Proser- pine and Jupiter. The formula is Alogat Div) = E,-+ (44.86%) MS. For Proserpine and Jupiter, a = 0.5104402. For Juno and Jupiter, a = 0.5129176, Cla 2.4774. With a = 0.5116790, the mean of the above values, which must be used when we wish to take second differences into account, find from the Tables, pp. 25 and 67, log E, = 2.0408, i ee = 84.9, 2p? ae = 60.2. Then, Boa = Sou ee ya = 210.3, 2p? et ta = 149.1. Hence, Aloga’ Di bY) = + 272.1 + 4 x 210.3 + 4 x 149.1 = 1709.7. From the general Tables we find for Proserpine and Jupiter, log a’ D2 b°? = 0.6459610, For Juno and Jupiter, log a’ Dt bP = 0.6630584, Aloga’ Di bf = 1709.74. Products of 210.3 and 149.1 by 1, 2, 3, 4, &c. give the corrections corresponding to these terms for all the coefficients. ASTEROID SUPPLEMENT. VESTA AND MERCURY. 17 a log op log « D, 6 log oe D a log a De of log at Ds © 0 0.30398 98.44290 95.46907 97.72948 97.80538 1 99.21922 99.22810 98.02122 98.06852 97.58314 2 98.30958 98.61556 98.63519 97.77304 97.84527 3 97.44544 97.92604 98.23577 98.26976 97.64578 a log a 0 log a” D, 0) log a? D2 uf log a oY 0 99,54242 98.65560 98.70472 98,80352 1 98.92892 98.97179 98.44473 2 98.23915 98.56072 98,63700 97,84562 } log a log « D, log & Dp a) log a D of) log at Ds Bo 0 0.31167 99.02069 99.11137 98.92194 99.15432 1 99.50227 99.53438 98.90023 99.05583 99.09495 2 98.86513 99.18463 99 .25466 98.96026 99.18423 8 98.27346 98.76341 99.09655 99.21489 99.14781 ) log « oD log oo D, ae log a D? log oe OY) 0 99.88312 99.54672 99.76291 99.52861 1 99,53019 99.67325 99.67839 2 99.10813 99.48194 99.71429 99.04830 } log oP log ¢ D, Be log & ae a) log a D a) log at Dt 3 0 0.32224 99.35018 99.52280 99.63057 0.02356 1 99.65878 99.72521 99.41169 99.69217 0.00669 2 99.16442 99.50256 99.64054 99.66268 0.04549 3 98.71404 99.21755 99.58475 99.81091 0.04882 ) log « oD log a” D, uD log «? D? wo log wu? 0 0.11907 0.10255 0.47486 0.04725 1 99.89277 0.15441 0.44158 2 99.60619 0.04944 0.44090 99.77389 a log b log « D, 0? log a” D? vi) log a® D3 of) log «* Dt 6) 0 0.35757 99.88016 0.29046 0.85080 1.60134 1 99.89462 0.07029 0.26679 0.86281 1.60200 2 99.58946 99.99762 0.35366 0.86847 1.61116 3 99.32531 99.88072 0.37657 0.91340 1.62232 t log « Oe log oe D, oe log a Dt a log oe ee 0 0.62323 1.10845 1.83985 1.14968 1 0.54028 1.11221 1.83444 2 0.42006 1.08114 1.82625 1.07195 3 18 ASTEROID SUPPLEMENT. ee a log 0? log « D, oP log a” D2 vo"? log « DE UD log «* DE vp 0 0.32570 99.42566 99.62370 99.79754 0.23479 1 99.69378 99.76887 99.53061 99.84765 0.22325 Q 99.22984 99.57437 99.73427 99.82785 0.25485 3 98.80959 99.31773 99.69651 99.95619 0.26241 4 98.40969 99.03594 99.56268 99.98494 0.34853 5 98.02159 98.74042 99.37837 a log a ae log oe D, o log o® De L@ log ea ne 0 0.18011 0.23606 0.65211 0.18211 i 99.97927 0.27617 0.62600 2 99.72084 0.18628 0.62148 99.94711 3 99.43830 0.02802 0.56838 VESTA AND SATURN. a log Bf “log « D, OY log a” D2 uP log «® D3 0 log ut DE of 0 0.30786 98.81790 98.87724 98.49819 98.65898 1 99.40378 99.42437 98.58992 98.69423 98.55504 2 98.67352 98.986 12 99.03131 98.53902 98.69314 3 97.98845 98.47371 98.79512 98.87240 98.61250 4 97.32433 97.93269 98.42250 98.75513 a log « log &” D, 0 - log « D2 v log a” 6 0 99.75608 99.22050 99.36870 99.25415 1 99.31571 99.41098 99.23443 2 98.80275 99.15091 99.31202 98.61926 3 98.26151 99,98244 99.14386 Z log 0 log « D, bD log «? D? b(? log « D3 oO log «* DEB”) 0 0.30268 98.18765 98.20241 97.21267 97.25611 1 99.09258 99.09753 97.63628 97.66324 96.93329 2 98.05802 98.36182 98.37283 97.25718 97.29888 3 97.06907 99.54813 97.85402 97.87317 96.99779 a log « 0 log e” D, 0 log e® D2 6D log a” 0 0 99.40602 98.24525 98.28506 98.52230 1 9866975 98.69411 97.92079 2 97.85593 98.16850 98.21271 9782726 VESTA AND NERP@DUNE. a log o@) log « D, OS log a D? BY log a Db wo log at Dt op 0 0.30170 97.79377 97.79980 96.42014 96.43847 1 98.89638 98.89840 97.04391 97.05501 95.93968 2 97.66693 97.96908 97.97356 96.46538 9648274 3 96.48318 96.96109 97.26408 97.27190 96.00561 a log a uD log & D, Oo log oo Be sD log oe o 0 9920246 97.64877 97.66532 98.10854 1 98.27291 98.28292 97.12283 2 97.26486 97.57059 97.58906 96.53359 ASTEROID SUPPLEMENT. 19 ASTRAMA AND MERCURY. a log BY log a D, 0? log a” D2 ) log «® Do!) log a DE o 0 0.30351 98.36485 98.38684 97.57107 97.63543 1 99.18056 99.18800 97.90339 97.94328 97.38372 2 98.23289 98.53807 98.55452 97.61497 97.67617 3 97.33076 97.81080 98.11911 98.14766 97.44703 a log « ee log a D, ee log a Dt IO log a we 0 99.50016 98.51577 98.57429 98.71595 1 98.84943 98.88546 98.28370 2 98.12195 98.44021 98.50493 97.68663 a log o log « D, oS log oe De ol) log we Dt gw) log at Dt op 0 0.30990 98.93678 99.01303 98.74570 98.94599 1 99.46167 99.48542 98.77152 98.90577 98.86996 2 98.78659 99.10271 99.16121 98.78517 98.97775 3 98.15652 98.64428 98.97193 99.07134 98.92491 z log a uD log oe D, 6@ log & D? oe log oe oO 0 99.82924 99.41060 99.59619 99.41166 1 99.44084 99.56207 99.49280 2 98.98170 99.34361 99.54409 98.86954 ) log Be log a D, a) log a De a) log a D3 ol) log at pt Te 0 0.31857 99.25758 99.40262 99.42831 99.77067 1 99.61535 99.66855 99.26679 99.50653 99.74525 2 99 .08242 99.41391 99.52854 99.46245 99.79491 3 98.59377 99.09249 99.44766 99.63748 99.79079 a log a oD log oe 1D), uD log a De oe log oe Nee 0 0.04813 99.94227 0.26489 99.89063 1 99.78861 0.01125 0.22068 2 99.46587 99.88538 0.22676 99.56540 ; log 6) log « D, 0? log a* D? vi) log o® D3 0) log at Dt 6) 0 0.34652 99.75234 0.09270 0.54564 1.20115 1 99.84012 99.98042 0.05580 0.56406 1.20064 2 99.49501 99.88011 0.16920 0.56699 1.21354 3 99.19183 99.72986 0.18309 0.62974 1.22609 a log « op log oe D, 6 log a DP y@ log a s@ 0 0.48415 0.84980 1.48475 0.84911 1 0.37451 0.85893 1.47627 2 0.22138 0.81613 1.46706 0.73925 20 ASTEROID SUPPLEMENT. (ACS Ray AY OA ND a) Ra aaah i a log b) log « D, 0°) log oD? of) log a? D? u) log « DE OD 0 0.33103 99.52609 99.76223 0.02294 0.52295 1 99.73973 99.83136 99.69014 0.06042 0.51657 2 99.31466 99.66924 99.86269 0.05066 0.54054 3 98.93285 99.44812 99.84542 0.15531 0.55160 4 98.57116 99.20322 99.74221 0.19299 0.62018 5 98.22121 98.94486 99.59177 a log a OS log a De oD log a De o log of BY 0 0.26631 0.41815 0.89666 0.37227 1 0.09692 0.44552 0.87799 2 99.87387 0.37311 0.87032 0.18275 : 3 99.62789 0.24236 0.82733 Z log 6) log « D, 0D log a” D2 vo" log «® D3 oP log a* DE vo’ 0 0.30921 98.89990 98.97047 98.66865 98.85595 1 99.44375 99.46842 98.71508 98.83805 98.77179 2 98.75166 99.06659 99.12061 98.70856 98.88848 3 98.10465 98.59156 98.91711 99.00910 98.82757 4 97.47855 98.08819 98.58060 98.91965 D log « 8 log a” D, 0) log a® D2 bY log a 0) 0 99.80617 99.35130 99.52455 99.36182 1 99.40184 99.51443 99.41209 2 98.92615 99.28345 99.47098 98.79154 3 98.42252 98.93664 99.32470 a log of log « D, bP ‘log a DvP log a? D3 0 log «* DE 0 0 0.30300 98.26497 98.28254 97.36887 97.42082 1 99.13100 99.13694 97.75277 _ 97.78178 97.12949 2 - 98.13444 98.43877 98.45190 97.41314 97.46250 3 97.18346 97.66290 97.96972 97.99253 97.19352 a log « DY log a” D, 0D log «® D2 oD log a? 0 0 99.44683 98.36306 98.41021 98.60602 1 98.74803 98.77698 98.07874 2 97.97200 98.28678 98.33906 97.48383 a log bp log « D, 0 log o” Dv) log a D3 vo) log a Dt up) 0 0.30183 97.87024 97.8742 96.57370 96.59547 1 98.93452 98.93692 97.15882 97.17202 96.13202 2 97.74303 98.04540 98.05074 96.61885 96.63946 3 96.59724 97.07530 97.37867 97.38798 96.1977 a log a Se) log o D, o log of D ® log oe o? 0 99.24156 97.76422 97.78387 98.18762 1 98.34978 98.36168 97.2711 2 97.37960 97.68623 97.70814 96.68731 The inclination of Hebe is 14° 47’, and its eccentricity is 0.202. ASTEROID SUPPLEMENT. al HEBE AND MERCURY. Both of these elements are so large that the coefficients for this Planet need not be They may, however, if needed, be readily found from the corre- sponding ones for Lutetia and Mercury, Lutetia and Venus, &c., by means of the variation formulas, as the values of 6a are all less than 0.0025. given. Tee) A IND) ML IO WIR WC a log oe log « D, oY log a Dt ul) log we De uf) log at Dt o 0 0.30392 98.43330 98.45892 97.70999 97.78437 1 99.21448 99.22316 98.00673 98.05306 97.55858 2 98.30016 98.60604 98.62525 97.75359 9782437 3 97.43136 97.91189 98.21143 98.25470 97.62131 a log « Oe log a D, BY log a Dt op log oe oy 0 99.53719 98.62084 98.68857 98.79267 n 98.91913 98.96111 98.42489 2 98.22474 98.54588 98.62063 97.82604 t log ot) log « D, ob log 2 D2 ol!) log «® D? a!) log a* D* 6 ters t=) a 5 a D aod 5 a £ 0 0.31143 99.01032 99.09909 98.90007 99.12828 1 99.49726 99.52866 98.88428 99.03683 99.06699 2 98.85573 99.17452 99.24302 98.93854 99.15843 3 98.25909 98.74873 99.08115 99.19698 99.12013 a log « log o” D, b9 log a D? 6) log a” UO 0 99.87634 99.52979 99.74200 99.51386 1 99.51909 99.65928 99.65528 2 99,09249 99.46472 99.69294 98.02609 z log 6) log « D, 0 log 2 Dv’) log o® D3?) log a* D* 1 ost 5 act =) Cy c—) Cay 5 at 0 0.32175 99.33863 99.50760 99.60519 99.99164 1 99.65339 99.71631 99.39355 99.66871 99.97383 2 99.15429 99.49153 99.62640 99.63757 0.01386 3 98.69922 9920208 99.56765 99.78900 0.01640 a log « log a” D, 0 log a® D? 6) log a” 0 0 0.10999 0.08236 0.44823 0.02720 1 99.87969 _ 0.13619 0.41372 2 99.58867 0.02875 0.41375 99.74765 22 ASTEROID SUPPLEMENT. IRIS AND MARS. (®) log 04 log « D, 6") log a” D2 log o® D3 v”) log «* Dt 0 0 0.35605 9986367 0.26451 0.81100 1.54903 1 99.88769 0.05845 0.23937 0.82371 1.54959 2 99.57759 99.98251 0.32939 0.82915 1.55916 3 99.30864 99.86159 0.35145 0.87670 1.57055 a log « uf log & D, BO log a? D WO log a oe Oo 0.60459 1.07443 1.79311 1.10961 1 0.51849 1.07873 1.78737 2 0.39430 1.04632 1.77901 1.02820 a log UD log « D, 0°) log o? D? oP log «® D3 uP log «* Dt ot) 0 0.32629 99.43770 99.64004 9982435 0.26890 1 99.69933 99.77625 99.54965 99.87279 0.25808 2 99.24014 99.58578 99.74943 99.85436 0.28865 58 98.82460 99.33354 99.71434 99.97970 0.29676 4 98.42939 99 .05627 99.58434 0.00975 0.38061 5 98.04575 98.76532 99.40425 a log a ue log oe D, ee log of D: oD log oe Be 0° 0.19013 0.25760 0.68088 0.20423 1 99.99321 0.29601 0.65579 2 99.73915 0.20837 0.65078 99.97502 3 99.46111 0.05356 0.59900 z log 0) log « D, 0°) log a” D? 6) log «? D3 oP log «* Dz oD 0 0.30802 98.82790 98.8885 L 98.51892 98.68277 1 99.40867 99.42971 98.60516 98.71161 98.58137 2 98.68308 98.99595 99.04214 98.55965 98.71674 3 98.00268 98.48813 98.81001 98.88895 98.63864 4 97.34323 97.95173 98.44183 98.77518 ) log « Uf log «” D, 0) log a? D? 0 log a” 6) 0 99.76211 99.23638 99.38747 99.26706 1 9932618 99.42342 99.16598 2 98.81780 99.16699 99.33116 98.64019 3 98.28117 98.78986 99.16577 IRIS AND URANUS z log 0 log « D, b') log a® D2 log a? D3 6) log a* DE 6) 0 0.30272 98.19712 98.21220- 97.23179 97.27665 1 99.09729 99.10237 97.65054 97.67808 96.95730 2 98.06739 98.37124 9838250 97.27627 97.31885 3 97.08310 9756220 97.86819 97.88776 97.02174 t log a ue) log & D, o® log ae D> 3o log fe ee 0 99.41100 98.25965 98.30031 98.53249 1 98.67933 98.70421 97.94011 2 97.87014 98.18297 98.22810 97.34642 a ASTEROID SUPPLEMENT. 23 IERIE) AV IND) IN, BP 00 UN 1. @) a log 0G log « D, 0) log ” D2 UY log o° Du) log «* D* ? 0 0.30172 97.80315 97.80931 96.43896 96.45768 1 98.90106 98.90312 97.05799 97.06933 95.96324 2 97.67627 97.97844 97.98302 96.48419 96.50191 3 96.497 17 96.97509 97.27813 97.28612 96.02916 a log « Bo log & D, o@ log «® D2 DS log Be 0 99.20724 97.66292 97.67981 98.11821 1 98.28233 98.29256 97.14173 2 97.27893 97.58476 97.60361 96.55243 ELORA AND MERCURY. i log 6? log « D, 0 log a DP oli log «? Dt of) log at D3 6 0 0.30443 98.50559 98.53565 97.85703 97.94351 1 99.25023 99.26046 98.11597 98.17014 97.74388 2 98.37099 98.67773 98.70033 97.90026 97.98264 3 97.53722 98.01835 98.32941 98.36850 97.80589 a log @ D log a D, vo log oe Dt o@ log Pa Oe 0 99.57679 98.73222 98.81110 98.87511 1 98.99296 99.04211 98.57473 2 98.33330 98.65797 98.74485 97.97371 t log Up) log « D, log «? D2 v') log a® D3 ol) log «* Dt oD) 0 0.31335 99.08897 99.19313 99.06645 99.32758 1 99.53512 99.57233. - 99.00536 99.18235 99.27993 2 98.92889 99.25104 99.33195 99.10371 99.35592 3 98.36740 98.85944 99.19785 99.33388 99.33090 log a Ne log a” D, b® log a? Dz of log o uD 0 99.92855 99.65888 99.90267 99.62780 1 99.60366 99.76681 99.83271 2 99.21110 * | 99.59610 99.85700 98.19529 a log 0? log « D, b')) log o* Dz ol) log a® D3 B) log a* DE oD 0 0.32576 99.42699 99.62550 99.80049 0.23854 1 99.69439 99.76968 99.53274 99.85041 0.22708 2 99.23098 99.57563 99.73594 99.83077 0.25856 3 98.81125 99.31947 99.69848 99.95877 0.26619 a log « oD log a ID). uD log a® D uD) log oe Be) 0 0.18121 0.23843 0.65527 0.18453 1 99.98080 0.27834 0.62927 P) 99.72286 0.18870 0.62470 99.95017 24 ASTEROID SUPPLEMENT. FLORA AND MARS. a log b log « D, 0? log a” D? o) log a? D3 u()) log a* DE vo) 0 0.36896 0.03121 0.54698 1.23993 2.11572 1 99.94198 0.19101 0.53182 1.24805 2.11674 2 99.66925 0.13864 0.59900 1.25445 2.12349 3 99.43658 0.04739 0.62561 1.28804 2.13287 z log « 0) log «” D, 0) log o® D2 0 log a” 0 0 0.83115 1.45944 2.31773 1.58424 1 0.76792 1.46044 2.31409 2 0.67300 1.43746 2.30725 1.52857 a log Uf) log « D, 0? log o* D2 vo log a® DB log «* Dé 0 0.32218 99.34891 99.52112 99.62776 0.02002 1 99.65819 99,72245 99.40968 99.68957 0.00306 2 99.16331 99.50134 99.63898 99.65990 0.04386 3 98.71214 99.21584 99.58286 9980849 0.04523 4 98.28198 98.90453 99.42355 99.82740 5 9786343 98.57920 99,21149 Z log « b log a” D, bY log «® Dz o) log a” 0 0 0.11806 0.10032 0.47191 0.04503 1 99.89132 0.15239 0.43850 2 99.60426 0.04715 0.43983 99.77099 3 9929229 99.86576 0.37570 i log oD log « D, UP log «? D? 6) log o® D3 op? log a* Dt of 0 0.30695 98.75311 93.80476 98.36423 98.50628 1 99.37208 99.38991 98.49127 98.58264 98.38505 2 98.61134 98.92237 98.96157 98.40568 98.54 164 3 97.89585 98.38001 98.69865 98.76588 98.44368 4 97.20136 97.80886 98.29693 98.62524 a log « OS log a D, o? log oe Dp } log Pa o} 0 99.71753 99.11804 99.24864 99.17182 1 99.24814 99.33144 99.09557 2 98.70530 99.04724 99.18967 98.48409 3 98.13396 98.63782 99.00276 a log oD log « D, op? log of D 6) log of Dt o? log at Dt oe 0 0.30247 98.12601 98.13885 97.08834 97.12673 1 99.06192 99.06624 97.54347 97.56697 96.77723 2 97.99699 98.30043 98.31000 97.13301 97.16943 3 96.97770 97.45650 97.76175 97.77841 96.84203 a log a ee log oe D, ey log oe D uo) log oe ee 0 99.37374 98.15153 98.18630 98.45628 1 98.60745 98.62867 97.79526 2g 97.76341 98.07447 98.11312 97.20267 ASTEROID SUPPLEMENT. 25 : i log oP log « D, 1 log «? D? uf) log a? DB of) log «* DE 0? 0 0.30161 97.73272 97.73796 96.29759 96.31357 1 98.86592 98.86767 96.95218 96.96176 95.78623 2 97.60612 97.90813 97.91202 96.34290 96 .35802 3 96.39203 96 .86963 97.17256 97.17937 95.85230 a log « oD log oe D, B® log oo D D log of Be) 0 99.17133 97.55668 97,.57110 98.04569 1 98,21160 98.22030 96,99980 2 _ 97.17325 97.47837 97.49446 96.41095 log } log « D, ee log oe Dt o) log & De oo) log at Dt BO 0 0.30592 98.43318 98.45879 97.70973 97.78410 1 99.21441 99.22310 98.00653 98.05285 97.55826 2 98.30004 98.60592 98.62512 97.75334 97.82410 3 97.43118 97.91187 98.22124 98.25451 97.62099 ) log a uD log ae D, oe log oe D? B@ log oe oD 0 99.53712 98.62065 98.68836 98.79253 1 98.91900 98.96097 98.42463 2 98.22455 98.54568 98.62042 97.82578 Z log vi) log « D, log a” D? 6.) log «® D3 oi) log * Dt 1 0 0.31143 99.01015 99.09894 98.89979 99.12794 1 99.49720 99.52859 98.88408 99.03658 99 .06663 2 98.85560 99.17439 99.24286 98.93826 99.15810 3 98.25890 98.74854 99.08095 99.19675 99.11977 ) log a iO) log e” D, oD log a? De “> log a” OS) 0 99.87625 99.52957 99.74173 99.51367 1 99.51894 99.65910 99.65498 2 99,09228 99.46450 96.69266 99.02580 a log oP log « D, o') log «? D2 2!) log a D3 vo) log «* D3 0) 0 0.32174 99.33848 99.50740 99.60486 99.99122 1 99.65332 99.71622 99.39332 99.66840 99.97341 2 99.15416 99.49139 99.62622 99 .63724 0.01345 3 98.69902 99.20188 99.56743 99.78872 0.01598 a log « uo} log a DE uD log a De ie) log oo 6? 0 0.10988 0.08210 0.44788 0.02694 1 99.87991 0.13595 0.41336 2 99.58844 0.02848 0.41340 99.74732 ASTEROID SUPPLEMENT. MO aS) ANN DS IVicAU Ss a log uP log «a D, uw? log a” D2 W log a? D ol) log a* Dt oD 0 0.35603 99.86346 0.26419 0.81051 1.54838 1 99.88760 0.05830 0.23903 0.82332 1.54894 2 99.5745 99.98233 0.32909 0.82866 1.55852 3 99.30843 99.86135 0.35114 0.87624 1.56991 a log « he log a D, 5D log oe Dt oD log ae BO 0 0.60437 1.07401 1.79253 1.10912 1 0.51823 1.07832 1.78680 2 0.39399 1.04589 1.77843 1.02767 METIS AND JUPITER. a log 0 log « D, 6) log a” D? oP log a® DB oP log at DE 0 0 0.32630 99.43785 99 64025 99 82470 0 26934 1 99.69440 99.77635 99.54990 99.87312 0.25854 2 99.24028 99.58588 99.74963 99.85472 0.28910 3 98.82480 99.33375 99.71458 99.98000 0.29721 4 98.42965 99.05653 99.58462 0.01047 0.38104 5 98.04629 - 98.76565 99.40458 a log a Be log oe 1D), ee log a De Be log om ® 0 0.19026. 0.25788 0.68127 0.20452 1 99.99339 0.29627 0.65618 D) 99.73939 0.20866 0.65117 99.97538 3 99.46141 0.05389 0.59940 METIS AND SATURN. a log U') log « D, bP log oD? o log «® D3 vo? log a DE Uf) 0 0.30811 98.82803 98.88866 98.51919 98.68308 1 99.40873 99.42978 98.60536 98.71183 98.58171 2 98.68318 98.99608 99.04228 98.55991 98.72305 3 98.00286 98.48831 98.81020 98.88817 98.63898 4 97.34347 97.95198 98.44209 98.77544 a log « U0) log «” D, 0) log a? D? 0) log «0 0 99.76218 99.23662 99.38771 99.26723 1 9932631 99.42359 9925626 2 98.81799 99.16720 99.33140 98.64046 3 98.28143 98.79012 99.16606 a log 0 log « D,, bD log a? D2 b(? log a? D3 1 log at DE b") 0 0.30272 98.19724 98.21233 97.23204 97.27691 1 99.09735 99.10243 97.65073 97,67827 6.95762 2 98.06751 98.37137 98,38262 97.27652 97.31911 3 97.08328 97.56239 9786838 97.88796 97.02205 a log c uo} log a DE uD log o® D 30 log a oD 0 99.41107 98.25984 98.30051 98.53263 1 98.67945 98.70434 97.94036 2 97.87023 8.18316 98.22830 97.34667 ASTEROID SUPPLEMENT. METIS AND NEPTUNE. log Be log « D, BD 2 72 7(¢ log a Dy, BO log a? D3 oP log at Dt BY 27 0 0.30172 97.80327 97.80943 96.43920 96.45793 1 98.90112 98.90318 97.05818 97.06952 95.96355 2 97.67638 97.97856 97.98314 96.48444 96.50217 3 96.49735 96.97527 97.27831 97.28630 96.02947 z log « 09 log oD, b log o® D2 oY log a” 1D 0 99.20730 97.66310 97.68001 98.11834 1 98.28246 98.29268 97.14198 2 97.27911 97.58494 97.60381 96.55268 z log o} log « D, Oe log oe Dt Be log ee D oD) log a 1D o 0 0.30268 98.18663 98.20135 97.21061 97.25445 1 99.09207 99.09703 97.63474 97.66164 96.93071 2 98.05701 98.36080 98.37178 97.25513 97.29673 3 97.06756 97.54662 97.85249 97.87160 96.99520 1 log « i log a D, BO log a Dt o@) log of oe 0 99.40549 98.24368 98.28342 98.52120 1 98.66871 98.69302 97.91871 2 97.85439 98.16694 98.21106 97.32520 log Up) log « D, 0? log «? D2 vi) log o° D’ of) log a* Di oP 0 0.30690 98.74868 98.79987 98.35509 98.49607 1 99.36993 99.38756 98.48453 98.57523 98.37348 2 98.60708 98.91799 98.95683 98.39658 98.53149 3 97.88950 98.37356 98.69202 98.75867 98.43218 z log « bY) log o” D, oD log a D2 U log a? 1 0 99.71493 99.11105 99.24064 99.16632 1 99.24352 99.32613 99.08613 ’ 2 98.69862 99.04019 99.18155 98.47485 log 0) log « D, v'? log «7 D2 of) log o® D3 2) log «* DE bY 0.31249 99.05536 99.15267 98.99518 99.24185 99.51897 99.55358 98.95355 99.11974 99.18864 98.8973 99.21838 99.29375 99.03297 99.27097 98.32130 98.81227 99.14799 99.27504 99.24056 log « Be) log oe D, y@ log a De w) log a” 6) 99.90599 99.56740 99.16039 99.60349 99.72039 99.53970 99.83339 99.75595 99.78625 99.57849 99.12274 28 ASTEROID SUPPLEMENT. HYGEIA AND MARS. a log oD log « D, oP log of D DY log & Bs a log ot Dt uw) 0 0.32950 99.49891 99.72425 99.96156 0.44417 1 99.72737 99.81424 99.64681 0.00217 0.43659 2 99.29197 99.64364 99.82750 99.99000 0.46242 3 98.89995 99.41328 99.80509 0.10074 0.47274 a log « of) log a” D, bD log a? D? o log a” of) 0 0.24239 0.36837 0.82948 0.31955 1 0.06477 0.39884 0.80902 2 99.83240 0.32198 0.80200 0.11835 HYGEIA AND JUPITER. a log UP log « D, 0 log ? D? oP log a? D3 uD log «* DE op 0 0.34917 99.78487 0.14229 0.62262 1.30187 1 99.85416 0.00288 0.10918 0.63916 1.30176 2 99.51958 99.91012 0.21536 0.64302 1.31358 3 99.22673 99.76883 0.23209 0.70099 1.32587 4 98.95340 99.60669 0.19103 0.74383 1.36192 5 98.69145 99.43279 0.11374 0.75242 1.40383 a log a 09 log a” D,, bY log a? Dz 0 log a? 0 0 0.51840 0.91456 1.57357 1.92344 1 0.41604 0.92205 1.56601 2 0.27176 0.88254 1.55698 0.82258 3 0.10828 0.80808 1.53281 ; log b log « D, vf) log a” D2 bY log «® D2 ov) log a* Dib) 0 0.31359 9909372 99.19887 99.07653 99.33975 1 99.53857 99.57499 99.01268 99.19124 99.29285 2 98.93347 99.25565 99.33737 99.11372 99.36798 3 98.37409 98.86608 99.20488 99.34223 99.34369 4 97.83526 98.44901 98.94983 99.30957 a log « i log oe D, ® log of ing o log oe Oe 0 99.93177 99.66671 99.91252 99.63484 1 99.58879 99.7342 99.84244 P) 99.21826 99.60409 99.86706 99.20556 3 98.80079 99.33430 99.76423 HYGEIA AND URANUS. a log 0 log « D, 0) log «” Dz oP log a D3 0 log «* DE 1? 0 0.30399 98.44393 98.47016 - 97.73159 97.80764 1 99.21974 99.22864 98.02278 98.07019 97.58579 2 98.31059 98.61659 98.63626 99.7514 97.84752 3 97.44695 97.92756 98.23731 98.27138 97.64842 a log a oe log oe D, De log of De Oe log a wD 0 9954298 98.63719 98.70646 98.80470 1 98.92997 98.97294 98.44687 2 98.24070 98.56232 98.63876 97.84773 ASTEROID SUPPLEMENT. 29 HYGHITA AND NEPTUNE: ) log up log « D,, ey log oe D oD log ea io? oy) log ow 1 OM 0 0.30223 98.04654 98.05727 96.92824 96.96047 1 99.02237 99.02597 97.42390 97.44356 96.57640 2 97.91820 98.22124 98.22922 96.97309 97.00365 3 96.85969 97.33822 97.64276 97.65668 96.64155 a log « 0 log oD, 0 log a D2 oy log ? 0 0 99.33240 98.03096 98.06011 98.37200 1 98.52727 98.54501 97.63385 2 97.64415 97.95355 97.98600 97.04231 PUI EISEN QIE 1. A IN ID) IME aC) la eG } log IO log « D, 6 log os Dt wt) log a De wl) log as Ds wo? 0 0.30377 98.40898 98.43225 97.66060 97.73127 n 99.20243 99.21066 97.97000 98.01394 97.49639 2 98.27628 98.58190 98.60008 97.70431 97.77154 3 97.39566 97.87600 98.18508 98.21660 9755934 a log « 6 log « D, 6 log a° D* vo) log a7 0) 0 99.52399 98.58347 98.64778 98.76527 I 98.89434 98.93414 98.37465 2 98.18822 98.50828 98.57932 97.77646 7 log v') log « D, 0 log «” D2 v') log a? D3 vl) log a* Dt 0) 0 0.31086 98.98410 99.06820 98.84490 99.06284 1 99.48459 99.51425 98.84403 98.98906 98.99651 2 98.83115 99.14894 99.21370 98.88373 99.09357 3 98.22265 98.71158 99.04221 99.15193 99.05032 a log « BY log a” D, 6) log a D2 uo log «7 bY 0 99.85987 99.48713 99.68953 99.47696 1 99.49110 99.62426 99.59708 2 99.05297 99.42136 99.63937 98.97009 a log oD log « D, oD log ” D2 2) log «® D3 vi) log a* DE 0 0.32056 99.30957 99.39762 99.54153 99.91180 1 99.63980 99.69906 99.34739 99.61007 99.89148 2 99.12868 99.46375 99.59104 99.57456 99.93476 3 98.66169 99.16298 99.52463 99.73423 99.93514 ) log « Be) log Pa D, uD log oe Dt BQ log oe uD 0 0.08745 0.03181 0.38178 99.97741 1 99.84684 0.09080 0.32600 D) 99.54461 99.97699 0.34599 99.68195 30 ASTEROID SUPPLEMENT. PARTHENOPE AND MARS. a log 0) log « D, 0? log a” D? o") log a? D3 uf) log «* Dt of) 0 0.35241 99.82990 0.20092 0.71320 1.42061 1 99.87043 0.02950 0.17186 0.72777 1.42087 2 99.54785 99.94511 0.27000 0.73251 1.43154 3 99.26673 ~ 99.81389 0.28957 0.78524 1.44344 7 log « of log a” D, bD log a? D2 oY log «6 0 0.55943 0.99119 1.67876 1.01222 1 0.46516 0.99701 1.67215 2 0.33081 0.96107 1.66341 0.92115 Z log 0? log « D, b? log «? D2 of) log «® D3 0 log a* Dib) 0 0.32787 99.46858 99.68228 99.89338 0.35693 1 99.71351 99.79532 99.59859 99.9374 0.34784 De 99.26641 99.61500 99.78860 99.92261 0.37592 3 98.86282 99.37391 99.76010 0.04044 0.38525 4 98.47951 99.10809 99.63972 0.07354 0.46351 5 98.10797 98.82872 99.47016 a log a oY log ea D, uO) log oe D oD log oe oD ~O 0.21622 0.31321 0.75537 0.26181 1 0.02917 0.34748 0.73271 2 99.78616 0.26542 0.72659 0.04703 3 99.51952 0.11929 0.67805 - Z log b) log « D,, bP log a” D2 log a? D3 o log a* Dt oP 0 0.30842 98.85334 98.91732 98.57210 98.74359 1 99.42108 99.44334. 98.64397 98.75602 98.64849 2 98.70738 99.02094 99.06976 98.61219 98.77706 3 98.03882 98.52476 98.84786 _ 98.93121 98.70525 4 97.39120 98.00008 98.49096 9882622 0) log « 9 log oe De oe log a Dt oD log oe oD 0 99. 77754 99.27687 98.43551 99.30018 1 99,35285 99.45530 99.31095 2 98.85608 99.20800 99.38015 98.69355 3 98.33117 98.84168 99.22170 a log 0 log « D, 0 log «” Db? log o® D3 b) log a* Div) 0 0.30282 98.22117 98.23709 97.28036 97.32762 1 99.10924 99.11461 97.28677 97.71582 97.01827 2 98.09117 98.39519 98.40706 97.32477 97.36964 3 97.11870 97.59791 97,904.19 97.92485 9708259 a log a OW log a Dy oD log a iy Be) log a” w ) 99.42367 98.29628 98.33914 98.55845 1 98.70366 98.72992 97.98920 2 97.90625 98.21973 98.26728 97.39510 ASTEROID SUPPLEMENT. 31 Jee. Jey ah Tet 1D, IN, ©)IE ID, va INE ID) INT 1 JP 00 WU IN 0.07095 0.46919 Z log 0 log « D, 0 log «? D2 Ut log o D3 uf) log at DEO) 0 0.30176 97.82694 97.83345 96.48674 9650650 i 98.91293 98.91511 97.09375 97.10572 96.02309 2 97.69995 98.00219 98.00702 96.53194 96.55064 3 96.53267 97.01064 97.31379 97.32222 96.08894 a log a oD log oe D, BO log a D? ) log of vw 0 99.21940 97.69883 97.65666 98.14279 1 98.30624 98.31704 97.18973 2 97.31463 97.62073 97.64062 96.60026 a log 0) log « D, 0 log a” D2 ol) log a® D3 vi) log a* DE vf) 0 0.30405 98.45280 98.47955 97.74960 97.82709 1 99.22413 99.23320 98.03618 98.08451 97.60849 2 98.31928 98.62539 98.64545 97.79311 97.86687 3 97.45995 97.94064 98.25057 98.28531 97.67104 z log « UY log a” D, bY log @ D2 0 log a7 BY 0 99.54781 98.65084 98.72142 98.81475 1 98.93902 98.98283 98.46522 2 98.25402 98.57605 98.65392 97.86582 ig’ log of) log « D, 0? log «D2 I) log «® D2 uf) log «* DE 0? 0 0.31192 99.03142 99.12411 98.94458 99.18131 1 99.50744 99.54031 98.91672 99.07554 99.12390 2 98.87545 99.19508 99.26673 98.98274 99.21098 3 98.28830 98.77855 99.11247 99.23345 99.17646 ) log a BO log oe D, a log & De ue) log oe u) 0 99.89016 99.56425 99.78462 99.54394 1 99.54169 99.68785 99.70234 2 99.12430 99.49978 99.73645 99.07130 Z log 0) log « D, b'? log a” D2 y()) log a D3 a) log a* Dt 6) 0 0.32276 99.36216 99.53862 99.65693 0.05677 1 99.66436 99.73083 99.43050 99.71658 0.04084 2 99.17489 99.51398 99.65526 99.68877 0.07840 3 98.72936 99.23355 99.60248 99.83372 0.08250 a log « Be log oc D, BY) log oe De Be log oe ee 0 0.12855 0.12356 0.50262 0.06821 1 99.90639 0.17342 0.47057 2 99.62436 99.80117 32 ASTEROID SUPPLEMENT. OOO). IN IDE MME san Ta S)< () log « D, BD log ? D2 uy) log a® DEB) log at Dt Be log Oy i 0 0.35920 99.89764 0.31780 0.89264 1.65637 1 99.90185 0.08297 0.29560 0.90397 1.65712 2 99.60175 0.01344 0.37926 0.90983 1.66587 3 99.34261 99.90067 0.40297 0.95340 1.67678 Z log « UY log a” D,, oD log a? D2 log a? 0 0 0.64297 1.14431 1.88914 1.19210 1 0.56325 1.14755 1.88405 2 0.44710 1.11784 1.87604 1.11808 a log 0 log « D, 0) log 7 D? UD log a® D8 vo? log a DE op Oo 0.32510 99.41333 99,60703 99.7012 0.19996 1 99.68809 99.76134 99.51113 99.82199 0.18764 2 99.21925 99.56264 99.71880 99.80074 0.22032 3 98.79414 99.30147 99.67824 99.93219 0.22730 4 98.38941 99.01502 99.54043 99.95955 0.31578 5 ~ -97,99650 98.71479 99.35177 a log « 0 log «” D, oY log « D2 bo log «0 : 0 0.16993 0.21405 0.62276 0.15961 n 99.96503 0.25595 0.59558 2 99.70209 0.16377 0.59160 99.91858 3 99.41490 0.00184 0.53712 a log 0") log « D, b) log «? D? of log «? D3 o(? log a* DE vo") 0 0.30771 98.80761 98.86565 98.47687 98.63455 1 99.89875 99.41887 98.57423 98.67638 98.52796 2 98.66367 98.97600 99.02018 98.51780 98.66890 3 97.97378 98.45885 98.7980 98.85539 98.58561 4 97.30486 97.91807 98.40259 98.73448 a log a UY log a” D, UD log a? D? o) log «” 0 99.74990 99.20417 99.34945 99.24090 1 99.30495 9939822 99.21229 2 98.78727 99.13438 99.29240 98.59773 3 98.24126 98.74857 99.12134 a log AW) log « D, Be log oe Db oD? log a D 5 log at Di op) 0 0.30265 98.1788 98.19232 97.19297 97.24498 1 99.08773 99.09259 97.62158 97.64795 96.90855 2 98.04835 98.35209 98.36286 97.23750 97.27832 3 97.05461 97.55363 97.83940 97.85814 96.97310 a log « 64) log a? D, oD log a? D2 oY log a 0) 0 99.40090 98.23038 98.26856 98.51180 1 98.65987 98.68360 97.90089 2 97.84127 98.15359 98.19687 97.30751 ASTEROID SUPPLEMENT. 33 CLIO AND NEPTUNE. EGERIA AND 1 log of) log « D, bY log «? D2 U) log o° D3 vo log a* Div) 0 0.30169 97.78411 97.79001 96.40073 96 .41867 1 - 98.89156 98.89353 97.02939 97.04025 95.91537 2 97.65730 97.95943 97.96381 96.44599 96.46296 3 96.46875 96.94664 9724959 97.25724 95.98134 a log a oY log o? D, 0 log o? D2 bY log a” 6) 0 99.15752 97.63419 97.65038 92.09857 1 98.26320 98.27300 97.10335 2 97.25036 97.55599 97.57405 96.51417 1 log 0) log « D, 0 log o” D2!) log a® D3 v()) log a* DE bY 0 0.30350 98.36460 98.38657 97.57056 97.63489 1 99.18044 99.18787 97.90301 97.94288 97.38308 2 98.23264 98.53782 98.55427 97.61447 97.67563 3 97.33039 98.81043 98.11873 98.14726 97.44639 a log « ey log at D, ee log a Dt SO log a we 0 99.50003 98.51539 98.57387 98.71567 1 98.84917 98.88526 98.28318 2 98.12157 98.43983 98.50451 97.68612 a log Be log « D, o log a Dt Bi) log a Db ue log at Dt “6 0 0.30989 98.93652 99.01272 98.74514 98.94532 1 99.46154 99.48827 98.77110 98.90329 98.86924 2 98.78633 99.10244 99.16092 98.78461 98.97711 3 98.15615 98.64389 98.97154 99.07089 98.92420 Z log « OS log Pa D, BO) log a Dt Be log oe oD 0 99.82907 99.41017 99.59566 99.41129 1 99.44055 99.56172 99.4922] 2 98.98130 99.34319 99.54355 98.86898 log 6) log « D, 6 log a” D2 of) log a? DB o')) log a* Dt 6) 0.31874 99.25729 99.40224 99.42767 99.76988 99.61521 99.66838 99.26633 99.50595 99.74443 99.08215 99.41362 99.52819 99.46182 99.79413 98.59338 99.09209 99.44723 99.63694 99.78998 log « o) log ao D, uD log a Dt SY log oe uD 0.04791 99.94177 0.26423 99.89015 99.78828 0.01080 0.21999 99.46543 99.88486 0.22609 99.56475 34 ASTEROID SUPPLEMENT. EGERIA AND MARS. 1) i log 0% log « D, 0? log o D2 ut) log a D3 ul) log a* Dt 0) 0 0.34648 99.75195 0.09211 0.54472 1.19994 1 99.83995 99.98015 0.05516 0.56316 1.19943 2 99.49471 99.87975 0.16865 0.56608 1.21235 3 99.19141 99.72989 0.18250 0.62889 1.22490 7 log « Ut) log «? D, 0 log a? D? 0 log a? 0 0 0.48374 0.84903 1.48369 0.84823 1 0.37401 0.85818 1.47520 2 0.22078 0.81534 1.46599 0:73825 EGERIA AND JUPITER. D log 0? log « D,, UD Jog o? D2 oD log a® D8 0 log a DE oP 0 0.33105 99.52643 99.76270 0.02369 0.52392 1 99.73988 99.83157 99.69068 0.06114 0.51756 2 99.31494 99.66956 99.86313 0.05140 0.54150 3 98.93325 99.44873 99.84591 0.15598 0.55257 4 98.57172 99.20376 99.74272 0.19368 0.62109 5 98.22189 98.94552 99.59247 i log a 0 log o D, bP log a? D? a log a? 0) 0 0.26661 0.41876 0.89748 0.37292 1 0.09731 0.44610 0.87884 ; 2 99.87438 0.37374 - 0.87116 0.18354 3 99.62852 0.24308 0.82820 a log b") log « D, 0) log a” D2 bo) log o® D3 uD log a* Dé oD 0 0.30922 98.90016 98.97078 98.66920 98.85659 1 99.44388 99.46856 98.71549 98.83852 98.77250 2 98.75192 99.06685 99.12091 98.70912 - 98.88912 3 98.10502 98.59194 98.91753 99.00954 98.82827 4 97.47905 98.08869 98.58111 98.92018 a log « oY log «” D, 0 log «® D? o log a? 0 0 99.80634 99.35171 99.52507 99.36217 1 99.40212 99.51477 99.41267 Q 98.92656 99.28389 99.47151 98.79210 3 98.42304 98.93718 9932530 t log eu log a D, wD log a D: Se log & Ds BD log at Dt of) 0 0.30300 98.26522 98.28280 97.36937 97.42137 1 99.13113 99.13706 97.75315 97.78516 97.13012 2 98.13468 98.43902 98.45215 97.41344 97.46303 3 97.18383 97.66327 97.97010 97.99292 97.19415 a log « oD log oe D, oD log a D w) log Pa SY 0 99.44697. | ~«98.36344 98.41062 98.60629 1 98.74828 98.7724 98.07925 2 97.97237 98.28716 98.33947 97.48434 ASTEROID SUPPLEMENT. 30 EGERIA AND NEPTUNE. a log of) log « D, 0) log «” D2 of) log o® D3 o? log a* Dz UD 0 0.30183 97.87049 97.87767 96.57420 96.59597 1 98.93464 98.93705 97.15919 97.17240 96.13264 2 97.74328 98.04565 98.05099 96.61935 96.63997 3 96.59760 - 97.07566 97.37904 97.38835 96.19839 a log « bY log o” D, 0) log «® D? 6 log «7 1 0 99.24168 97.76459 97.78425 98.18788 1 98.35002 98.36193 97.27761- 2 97.37997 97.68660 97.70853 96.68780 z log 0) log « D, 0 log «? D2 u)) log a? D3 0) log a* DE uf) 0 0.30349 98.36172 98.38355 97.56471 97.62865 1 99.17901 99.18640 97.89866 97.93829 97.37539 2 98.22980 98.53495 98.55130 97.60863 97.66942 3 97.32615 97.80615 98.11442 98.14277 97.43906 a log a 0) log a” D, LD log o° D2 o log a” bY 0 99.49848 98.51097 98.56909 98.71247 1 98.84624 98.88210 98.27725 2 98.11724 98.43539 98.49968 97.68025 IRENE AND VENUS. 1 log vf) log « D, b log «” D2) log o® DE ol) log o* Di 0 0.30984 98.93344 99.00915 98.73870 98.93778 1 99.46005 99.48660 98.76639 98.89778 98.86103 2 98.78343 99.09943 99.15752 98.77820 98.96962 3 98.15183 98.63950 98.96696 99.06567 98.91606 i log « 6 log a” D, bY log «® Dib log a 0) 0 99.82713 99.40521 99.58965 99.40710 1 99.43729 99.55773 99.48545 2 98.97666 99.33815 99.53741 98.86245 a log b) log « D, 0 log a” D2 ui) log a D3 of log «* DE oP 0 0.31845 99.25392 99.39795 99.42037 99.76081 1 99.61363 99.66642 99.26108 99.49930 99.73501 2 99.07914 99.41038 99.52418 99.45459 99.78515 3 98.58895 99.08750 99.44224 99.63073 99.78068 t log a p log oe D, uD log oe Dt a log oe Be 0 0.04554 99.93601 0.25676 99.88463 1 99.78454 0.00572 0.21206 2 99.46034 99.87898 0.21846 99.55725 36 ASTEROID SUPPLEMENT. . IRENE AND MARS. SSS || a log oP log « D, bp log oe Dt ) log & D a) log ot Dt oD 0 0.34611 99. 74747 0.08528 0.53411 1.18604 1 99.83799 99.97707 0.04783 0.55280 1,18554 2 99.49127 99.87563 0.16232 0.55565 1,19855 3 _ 99.18653 99.72402 0.17580 0.61910 1,21121 t log « o) log a” D,, bY log a° D2 log a7 o) 0 0.47908 0.84017 1.47147 0.83806 1 0.36834 0.84950 1.46291 2 0.21387 0.80625 1.45360 0.72688 a log 0 log « D, 0°? log a? D2 oP log o® D3 0 log a* Di vf) OFS 0.33127 99.53026 99.76808 0.03237 0.53507 1 99.74162 99.83400 99.69679 0.06939 0.52887 2 99.31812 99.67316 99.86811 0.05998 0.55256 3 98.93785 99.45365 99.85160 0.16371 0.56372 4 98.5774 99.21003 99.74951 0.20167 0.63164 5 98.22933 98.95316 99.60049 a log a Oe log a” D, Ne log a® De Be) log a sD 0 0.27002 0.42582 0.90701 0.37801 1 0.10187 0.45273 0.88862 2 99.88013 0.38098 0.88085 0.19307 3 99.63572 0.25165 0.83824 a log 0) log « D, 0) “log a? D2 oP log «® D8 of) log a* Dé oD 0 0.30927 98.90322 98.97430 98.67559 98.86403 1 99.44537 - 99.47022 98.72017 98.84395 98.78063 2 98.75482 99.06985 99.12426 98.71546 98.89649 3 98.10934 98.59632 98.92205 99.01469 98.83633 4 97.4847 98.09446 98.58699 98.92633 a log a 0) log a” D, bY log a? D? w) log a” 0) 0 99.80824 99.35663 99.53097 99.36628 1 99.40535 99.51870 99.41935 2 98.93116 99.28887 99.47753 98.79856 3 98.42904 98.94343 99.33210 a log 6) log « D, b') log a* D? of) log a® DB 0 log a* Dé oD 0 0.30302 98.26809 98.28579 97.37518 97.42749 1 99.13255 99.13852 97.75747 97.78971 97.13741 2 98.13752 98.44187 98.45509 97.41944 97.46913 3 97.18807 97.66752 97.97439 97.99736 97.20145 a log « 6D log of D, up log a? D ey log of oD 0 99.44849 98.36782 98.41530 98.60942 1 98.75119 98.78034 98.08513 2 97.97668 98.29156 98.34419 97.49015 ASTEROID SUPPLEMENT. IRENE AND NEPTUNE. 37 a log 0 log « D, 0) log « D2 uf) log «® D3 ot) log a* DE 0) 0 0.30184 97.87332 97.88055 96.57989 96.60181 1 98.93606 98.93848 97.16345 97.17674 96.13978 2 97.74610 98.04848 98.05385 96 .62504 96.64579 3 96.60183 97.07990 97.38329 97.39266 9620552 a log a 6 log a” D, 0 log o® D? UD log a” o 0 99.24314 97.76887 97.78866 98.19082 n 98.35287 98.36386 97.28333 2 97.38422 97.69089 97.71296 96.69354 EUNOMIA AND MERCURY. The inclination of Eunomia is 11° 44’, and its eccentricity 0.188; both too large to make it necessary to give the coefficients for this Asteroid. They may, however, be readily found from the corresponding ones for Fides, if needed. PSYCHE AND MERCURY. (2) a log by log « D, op? log Dt ot) log a Ds OH log a* Dt SY 0 0.30295 98.25276 98.26984 97.34418 97.39479 1 99.12493 99.13070 97.73436 97.76552 97.09846 2 98.12237 98.42662 98.43936 97.38849 97.43655 3 97.16541 97.64478 97.95175 97.97364 96.16257 t log « 0) log a” D, BD log a D2 6 log a” BD 0 99.44036 98.34443 98.39034 | 98.59272 1 98.73565 98.76382 98.05375 2 97.95366 98.26807 98.31899 97.45908 t log @ log a D, OS log ea Dt Oe log of D3 ue log fe Dt Bp 0 0.30787 98.81799 98.87734 98.49838 98.65929 1 99.40383 99.4244] 98.59005 98.69438 98.55527 2 98.67361 98.98621 99.03141 98.53920 98.69335 3 97.98857 98.47384 98.79526 98.87255 98.61273 a log a ® log D, a log a® De “ log o” uD 0 99.75613 — 99.22064 99.36887 99.25426 1 99.31581 99.41109 99.23463 2 98.80289 99.15105 99.31219 98.61945 38 ASTEROID SUPPLEMENT. PSYCHE AND THE EARTH. ; log of) log a D, v') log a” D2 ol) log a D3 o) log at Dé of) 0 0.31444 99.12915 99.24203 99.15200 99.43116 1 99.55435 99.59491 99.06740 9925804 99.38966 2 98.96591 99.29000 99.37802 99.18858 99.45855 3 98.42211 98.91553 99.25742 99.40491 99.43943 z log « Oe log Pa D, uO log & De uD log oe ul 0 99.95604 99.72552 99.98672 99.68802 1 99.64724 99.82327 99 92298 2 99.27174 -99.66403 99.94282 99.28248 a log ? log « D, b? log a D oy log oe Db ul) log a* De Oe 0 0.33479 99.58823 99.85044 0.16436 0.70524 1 99.76775 99.87110 99.78965 0.19541 _ 0.70115 2 99.36575 99.72755 99.94441 0.19038 0.72134 3 99.00677 99.52742 99.93775 0.28196 0.73712 1 log « 0) log «? D, 0 log o® D2 log a” 6) 0 0.32273 0.53358 1.05301 0.49637 1 0.17131 0.55461 1.03793 2 99.96888 0.49161 1.02920 0.33182 a log up log « D, oD log ae Dt oY log of? Ds uD log ca Dt op? 0 0.34122 99.68285 99.98849 0.38278 0.98865 1 99.80979 99.93332 99.94248 0.40585 0.98699 2 99.44132 99.81576 0.07239 0.40613 1.00257 3 99.11525 99.64533 0.07888 0.48012 1.01536 4 98.80890 99.45264 0.01628 0.52360 1.06225 5 98.51342 99.24752 _ 99.91285 0.51961 1.11040 a log « Be) log a D, BY) log a De o) log oe Be) 0 0.41352 0.71382 1.29801 0.69526 1 0.28722 0.72720 1.28828 Q 0.11416 0.67662 1.27844 0.56417 3 99.92031 0.58249 1.24791 t log 6) log « D,, bP log a? Dz oP log a® D3 o log a* DED 0 0.31167 99.02060 99.11126 98.92175 99.15408 1 99.50222 99.53433 98.90009 99.05566 99.09470 2 98.86534 99.18454 99.25456 98.96007 99.18400 3 98.27333 98.76327 99.09642 - 99.21473 99.14757 4 97.70216 98.31415 98.81136 99.16226 t log « of) log a” D, v) log a? D? 0) log a” 0 99.88306 99.54657 99.76272 99.52848 1 99.53011 99.67313 99.67819 2 99.10799 99.48179 99.71410 99.04811 Siete 9865852 99.18380 99.59624 ASTEROID SUPPLEMENT. 39 ood io S04 GEE ACN De UEReANOUES: Z log 6) log « D, bP log a” D2 6D log a? D2 of? log a* DE oD 0 0.30358 98.37714 98.39973 97.59598 97.66205 1 99.18665 99.19430 97 92193 97.96291 97.41507 2 98.24498 98.55028 98.56720 97.63984 97. 70266 3 97.34884 97.82896 98.13748 98.16683 97.47828 a log « 6 log & D, 6 log a? D? a log 2 B® t= } t= “5 t—} a} f=} ¥ 0 99.50678 98.53461 98.59469 98.72964 1 98.86192 98.89903 98.30900 2 98.14040 98.45915 98.52557 97.71162 z log 0 log « D, 0 | log « D2 Uo log a? DB utp log «* DE oP 0 0.30206 97.98087 97.99011 96.79608 96.82394 1 98.98966 98.99276 97.32512 97.34208 96.41069 2 97.85300 98.15576 98.16263 96.84106 96.86746 3 96.76202 97.24035 97.54440 97.55638 96.47609 t log « oD log oe 1D». 2 log oe D log Po oD 0 99.29842 97.93148 97.95667 98.30294 1 98.46109 98.47639 97.50077 2 97.54559 97.85383 97.88189 96.90995 a log oP log « D,, oP log ae Dt a) log a D3 Be log a* Dt © 0 0.30372 98.40145 98.42531 97.64531 97.71487 1 99.19870 99.20678 97.95863 98.00185 97.47715 2 98.26888 98.57442 98.59230 97.68906 97.75522 3 97.38460 97.86488 98.17383 98.20482 97.54016 . i 2 i i PG z log « o log a” D, o log «® D2 o log a” 6D 0 99.51991 98.57191 98.63520 98.75682 1 98.88673 97.92582 98.35811 2 98.17691 98.49666 98.56658 97.76053 D log « D, 0) log «* D? o{)) log «° D3 ()) log o* Dt 0) 0 0.31069 98.97601 99.05871 98.82788 99.04273 1 99.48067 99.50982 98.83161 98.97439 98.97480 2 98.82354 99.14103 99.20469 98.86683 99.07365 3 98.21137 98.70009 99.03019 99.13808 99.02881 a log « BY log a” D, bY log o® D2 0) log a7 oD 0 99.85417 99.47400 99.67344 99.46567 1 99.48248 99.61353 99.57917 2 99.04077 99.40801 99.62294 98.95285 40 ASTEROID SUPPLEMENT. TEE ESAS ND eens; BAU ey ae ete i log 0 log « D, v'? log a” D2 ul) log «? D3 v')) log a* Dt 0) 0 0.32021 99.30064 99.45802 99.52200 99.88739 1 99.63561 99.69379 99.33403 99.59215 99.86625 2 99.12077 99.45520 99.58023 99.55524 99.91057 3 98.65009 99.15092 99.51140 99.71749 99.91024 t log « } log a D, uo? log eu D uw log a vu? 0 0.08060 0.01634 0.36151 99.96229 1 99.83678 0.07699 0.32269 2 99.53107 99.96116 0.32532 99.66183 Z log o log « D, vf) log a” D2 up) log a® D3 uff) log a* Dé oP 0 0.35134 99.81057 0.18183 0.68376 1.38199 1 99.86517 0.02183 0.15150 0.69894 1.38214 2 99.53874 99.93377 0.25220 0.70342 1.39317 3 99.25382 99.80933 0.27091 0.75781 1.40521 * i t OFAG 2k Z log « of) log a” D, bP log a® D2 log a” uP 0 0.54601 0.96623 1.64449 0.98321 1 0.44917 0.97256 1.63759 2 0.31164 0.93550 1.62875 0.88905 a log 0) log « D, bP log «? D? of) log «® D3 oD log a* Dt o) 0 0.32838 99.47825 99.69561 99.91508 0,38466 1 99.71793 99.80133 99.61395 99.95821 0.37607 2 99.27459 99.62414 99,80096 99.94406 0.40342 3 98.87471 99.38649 99.7444 0.05960 0.41309 4 98.49535 99.12421 99.65701 0.09357 0.48965 5 98.12722 98.84841 99.49083 7 log « 0 log a D, 0) log «? Dz of) log a? 0 0 0.22450 0.33073 0.77890 0.28010 1 0.04049 0.36377 0.75696 2 99.80089 0.28339 0.75054 0.06970 3 99.53778 0.13992 0.70297 t log o) log « D, bY log a? D? o log «® D3 o log a* Df of) 0 0.30855 98.86125 98.92631 98.58817 98.76257 1 99.42493 98.44759 98.65604 98.76988 98.66939 2 98.71491 99.02870 99.07837 98.62853 98.79589 3 98.05003 98.53612 98.85962 98.94428 98.72599 4 97.40607 98.01508 99.67889 97.84208 a log « oe log oe D, o) log a D wD log & ) 0 99.78237 99.28948 99.45053 99.31056 1 99.36116 99.46526 99.32807 2 98.86798 99.22078 99.39547 98.71015 3 98.34669 98.85780 99.23913 ASTEROID SUPPLEMENT. 4] ae — HETIS AND URANUS. 4 74 7(2) log «* D, oY a log iO log « D, wo) log a Dt oD log & Dp oD 0 0.30285 98.22863 98.24482 97.29542 1 99.11235 99.11841 97.69801 97.72754 2 98.09854 98.40261 98.41472 97.33981 3 97.12973 97.60898 97.91535 97.93636 + a log « sD log a” D, o} log «® D2 oe log a oD 0 99.42720 98.30786 98.35121 98.56653 1 98.71121 98.73791 98.00443 2 97.91744 98.23136 98.27947 97.41020 97.34346 97.03721 97.58542 97,10147 THETIS AND NEPTUNE. i log 0) log « D, 0) log a” D? of) log o° D3 log «* DE wD 0 0.30177 97.83428 97.84093 96.50155 96.52162 1 98.91661 98.91882 97.10483 97.11700 96.04164 2 97.70729 98.00955 98.01446 96,54674 96.56573 3 96.54367 97.02165 97.32484 97,33342 96.10747 Z log « Bp log Pa D, 0) log oo D? &@ log a oD 0 99.22317 97.71096 97.72809 98.15041 1 98.31366 98.32461 97,20460 2 97.32570 97.63188 _ 97.6521 96.61516 MELPOMENE AND MERCURY. The inclination of Melpomene is 10°, and its eccentricity is 0.215; both large. We can readily find, however, the coefficients for Melpomene ioe Mercury, from those for Clio and Mercury ; G ‘ Venus, ce sc Themis and The Earth ; & ‘* The Earth, “ § Harmonia and Jupiter ; 6 ce Mars, “ce (73 66 Mars ;: ; fh * Jupiter, oS £f ee “ The Earth ; ae « Saturn, se se & “Saturn ; (13 “cc Uranus, 6c cc ce * Uranus ; ae * Neptune, “ as se “© Neptune. z log 6) log « D, b) log a” D2 ot) log a® D3 vi) log a* Dt vo 0 0.30387 98.42489 98.45003 97.69290 97.76598 1 99.21031 99.21885 97.99402 98.03951 97.53706 2 98.29190 98.59769 98.61653 97.73654 97.80607 3 97.41902 97.89948 98.20886 98.24151 97.59987 i log a log a” D,, log o® D2 6) log ob) 0 99.53262 98.60791 98.67443 98.78318 1 98.91055 98.95176 98.40750 2 98.21211 4 98.53286 98.60632 97.80889 42 ASTEROID SUPPLEMENT. ——- a log vf) log « D, 0) log o” D? ui) log o® D3 uf) log «* DE oP 0 0.31123 99.00123 99.08836 98.88095 99.10556 1 99.49288 99.52366 98.87034 99.02024 9904255 2 98.84723 99.16566 99.23285 98.91954 99.13591 3 98.24648 98.73588 99.06766 99.18135 99.09592 a log a oD log a Dy ae log a DA us) log a uD 0 99.87044 99.51499 99.72377 99.50102 1 99.50938 99.7471] 99.63509 2 99.07880 99.44968 99.67432 99.00667 a log oP log a D, Be log oe Le up log oe D wD log at Dt wD 0 0.32133 99.32855 99.49437 99.58305 99.96385 1 99.64868 99.71031 99.37773 99.64829 99.94520 2 99.14542 99.48190 99.61409 99.61567 99.98633 3 98.68623 99.18854 99.55273 99.76993 99.98815 z log « 09 log a” D, UD log a® D2 vo) log «7 0 0 0.10212 0.06477 0.42507 0.00981 1 99.86824 0.12036 0.38946 2 99.57338 0.01074 0.39014 99.72480 5 k i i : i a log 0) log « D, 0) log 7 D? of) log a? D3 of) log «* Dt of) 0 0.35476 99.84940 0.24217 0.77669 1.50395 1 99.88167 0.04827 0.21570 0.79002 1.50442 2 99.56725 99.96944 0.30851 0.79524 1.51436 3 99.29409 99.84496 0.32976 0.84456 1.52594 a log « 0) log a” Db log a° D? vo log «? 0 az 0 0.58865 1.04517 1.75290 1.07526 1 0.49975 1.05000 1.74688 2 0.37206 1.01636 1.73837 0.99057 a log 0"? log « D, bP log ? D2 o log « D3 oP log «* Dé a 0 0.32682 99.44832 99.65452 99.84805 0.29908 1 99.70421 99.78279 99.56646 99.89506 0.28889 2 99.24920 99.59584 99.76286 99.87780 0.31858 3 98.83779 99.34746 99.73008 0.00051 0.32713 4 98.44669 99.07415 99.60341 0.03166 0.40903 5 98.06738 98.78720 99.42701 a log « oY log a* D, wD log a D } log of ee 0 0.19904 0.27667 0.70639 0.22391 1 0.00554 0.31362 0.68216 2 99.75531 0.22793 0.67675 99.99972 3 0.07613 0.62610 9948121 ASTEROID SUPPLEMENT. FORTUNA AND SATURN. 43 G log op log « D, o) log oe D2 op log oe De ) log at Dt } 0 0.30815 98.83668 98.89844 98.53714 98.70372 1 99.41295 99.43442 98.61856 98.72691 98.60452 2 98.69148 99.00457 99.05166 98.57777 98.73752 3 98.01517 98.50078 98.82308 98.90352 98.66 162 4 97.35981 97.96844 98.45880 98.79280 t log « Be log a D, ed log a® De De log a } 0 99.76742 99.25034 99.40400 99.27845 1 99.33538 99.43439 99.27493 2 98.83101 99.18113 99.34802 98.65860 3 98.29844 98.80774 99.18505 a log log « D, 0) log a” D? log o° D3 uf) log at DE v0) 0 0.30275 98.20543 98.22080 97.24857 97.29425 1 99.10142 99.10660 97.66306 97.69111 96.97837 2 98.07561 98.37952 98.39099 97.29303 97.33638 3 97.09540 97.57455 97.88063 97.90058 97.04277 a log « } log ae D, WY log oe D BY log a ee 0 99.41538 98.27231 98.31372 98.54146 1 98.68774 98.71312 97.95707 2 97.88262 98.19567 98.24163 97.36324 Z log 0) log « D, b>? log «” Dz uf) log «? D3 6 log a* DE uf) 0 0.30173 97.81137 97.81765 96.45547 96.47454 1 98.90516 98.90726 97.07035 97.08191 95.98393 2 97.68445 97.98665 97.99131 96.50070 96.51876 — 3 96.50944 96.98738 97.29046 97.29860 96.04982 a log a BY log o” D, bY log «® D2 0 log a 6) 0 99.21144 97.67533 97.69255 98.12670 1 98.29060 98.30101 97.15832 2 97.29127 97.59719 97.61640 96 .56896 1 log op log « D, op? log oe Dt ay log a De a) log at Dt SY 0 0.30387 98.42530 98.45047 97.69374 97.76688 1 99.21052 99.21905 97.99465 98.04017 97.53812 2 98.29231 98.59810 98.61696 97.73738 97.80697 3 97.41962 97.90008 98.20947 98.24216 97.60092 a log « wD log Pa D, oD log oe D bo) log oe ? 0 99.53284 98.60854 98.67513 98.78364 1 98.91098 98.95222 98.40835 2 98.21273 98.53350 98.60702 97.80973 tt ASTEROID SUPPLEMENT. a logo") log « D, 0) log «” D2 o{)) log a® D8 ul) log a* Dt Uf) 0 0.31124 99.00168 99.08889 98.88188 99.10667 1 99.49309 99.52391 98.87103 99.02103 99.04374 2 98.84764 99.16610 99.23334 98.92047 99.13702 3 98.24709 98.73651 99.06833 99.18211 99.09711 | | 5 Pe F 2 . z log « 09) log a” D, 6) log «° D2 0 log a” o) 0 99.87072 99.51572 99.72468 99.50165 1 99.50986 99.64770 99.63691 | 2 99.07947 99,45041 99.67523 99.00762 a log 0? log « D, v') log a” Di 0) log «° DB o') log a* Dé of) 0 ~ 0.32135 99.32904 99.49502 99.96571 99.96521 1 99.64891 99.71060 99.37851 99.2672 99.94660 2 99.14586 99.48237 99.61469 99.99831 99.98767 3 98.68686 99.18920 99.55345 99.38930 99.98953 a log « vf) log a” D, UY log a? D? of) log 07 6 0 0.10251 0.06563 0.42620 0.01066 1 99.86880 0.12113 0.39064 2 99.57412 0.01162 0.39129 99.72592 a log bP log « D, 0) log «” D? of) log a® D3 a) log a* Dt oP 0 0.35482 99.84976 0.24258 0.77736 1.50481 1 99.88196 0.04843 0.21619 0.79066 1.50528 2 99.56776 99.96974 0.30886 0.79589 1.51519 3 99.29480 99.84544 0.33015 0.84512 1.52678 } log « 0) log o” D, v) log a? D2 log a” 6) 0 0.58875 1.04559 1.75352 1.07560 1 0.49999 1.05036 1.74751 2 0.37247 1.01682 1.73902 0.99107 z log 09) log « D, vf) log a” D? 0) log a® D3 of) log a* Dé oP 0 0.32680 99.4479 99.65380 99.84689 0.29754 1 99.70397 99.78247 99.56564 99.89396 0.28737 2 99.24876 99.59534 99.76219 99.87664 0.31716 3 98.83715 99.34677 99.72930 99.99949 0.32563 4 98.44585 99.07327 99.60248 0.03058 0.40763 5 98.06633 98.78613 99.42589 a log a ne log a Dz wD log of De Ne log of o 0 0.19860 0.27573 0.70514 0.22293 1 0.00494 0.31279 0.68086 2 99.75452 0.22696 0.67547 99.99850 3 99.48022 0.07502 0.62477 ASTEROID SUPPLEMENT. 45 a log 6) log « D, 6) log a” De ut) log a® D3 of log a* DE oP 0 0.30815 98.83625 98.89797 98.53625 98.70269 1 99.41275 99.43418 98.61790 98.72615 98.60340 2 98.69107 99.00415 99.05120 98.57688 98.73650 3 98.01456 98.50016 98.82243 98.90280 98.66050 4 97.35900 97.96761 98.45796 97.79192 a log « 6) log a” D, log a D2 6) log «7 0 0 99.76716 99.24966 99.40319 99.27792 1 99.33493 99.43388 99.27401 2 98.83063 99.18044 99.34719 98.65769 3 98.29758 98.80686 99.18412 a log OP log « D, b log a” D2 vo’ log a? D3 of) log a* DE uD 0 0.30275 98.20502 98.22037 97.24775 97.29338 1 99.10122 99.10639 97.66245 97.69047 96.9734 2. 98.07522 98.37913 98.39057 97.29221 97.33552 3 97.09480 97.57394 97.88002 97.89995 97.04173 a log a 0 log o# D, oD log a Dt 6D log a Oey 0 99.41516 98.27167 98.31306 98.54102 1 98.68732 98.71265 97.95624 2 97.88201 98.19504 98.24096 97.36242 a log 0) log « D, b) log &? D2 uf) log «® D3 o') log «* DE UD” 0 0.30173 97.81097 97.81724 96.45465 96.47371 1 98.90496 98.90706 97.06975 97.08159 95.98291 2 97.68405 97.98625 97.99091 96.49989 96.51792 3 96.50884 96.98678 97.28985 97.29798 96.04881 O log « o log D, } log & Dt ao log oe ee 0 99.21124 97.67472 97.69192 98.12624 1 98.29019 98.30060 97.15751 2 97.29066 97.59658 97.61577 9656815 t log 6 log « D, 6 log o” D2 ol) log o* D8 if) log «* DE oP 0 0.30381 98.41546 98.44007 97.67373 97.74538 1 99.20564 99.21398 97.97977 98.02433 97.51293 2 98.28264 98.58832 98.60677 97.71742 97.78558 3 97.40516 97.88555 98.19475 98.22673 97.57582 ) log « oD log at D, oe log oe Dt Be) log oe ae 0 99.52749 98.59341 98.65861 98.77255 1 98.90094 98.94130 98.38801 2 98.19794 98.51828 98.59029 97.78965 ASTEROID SUPPLEMENT. LUTETIA AND VENUS. (2) log a ee 2 (i) log a” D, bY 1 log diy log « D, uo log a D ot) log & Db o) log at Dt u 0 0.31101 98.99107 99.07638 98.85954 99.08017 1 99.48796 99.51807 98.85472 99.00171 99.01521 2 98.83769 99.15574 99.22147 98.89828 99.10846 3 98.23234 98.72 146 99.05256 99.16387 99.06883 a log a ee log a D, a log a De oe log a ee 0 99.86386 99.49845 99.70341 99.48671 1 99.49852 99.63353 99.61251 e 2 99.06347 99.45286 99.65354 98.98495 log oP log « D, oP log & Le oD) log & D up log at Dt aD 0.32087 99.31727 99.47965 99.55838 99.93290 99.64341 99.70362 99.36007 99.62556 99.91527 99.13549 99.47112 98.60025 99.59124 99.95566 98.67167 99.17337 99.53303 99.74869 99.95663 a log a - log a D, BQ log ae D Be log ae BY 0 0.09338 0.04517 0.39931 99.99052 1 99.85551 0.10177 0.36243 2 99.55629 99.99067 0.36387 99.69932 LUTETIA AND MARS. log b) log « D, b log a” D? ol) log a® D3 ol) log a* Dé 6) 0.35335 99.83361 0.21754 0.73881 1.45422 99.87498 0.03706 0.18955 0.75287 1.45457 99.55572 99.95494 0.28551 0.75781 1.46494 99.27783 99.82647 0.30579 0.80915 1.47671 log of De Bey 2 4 log « Dy 0.10166 0.65681 0.57117 1.01294 1.70863 1.03757 0.47909 1.01833 1.70226 0.37446 0.98335 1.69361 0.94912 a log UP log « D, 6) log o? D? oP log «® DB 0) log a Dv 0 0.32744 99.46030 99.67093 99.87486 0.33328 1 99.70971 99.79019 99.58547 99.92028 0.32375 2 99 .25940 99.60718 99.77807 99.90430 0.35247 3 98.85263 99.36313 99.74784 0.02411 0.36150 4 98.46614 99.09426 99.62491 0.05643 0.44123 5 98.09144 98.81181 99.45263 log o so log oe D, oD log a D2 BQ log oe oD 0.20918 0.29827 0.73533 0.24628 0.01951 0.33362 0.71204 99.77381 0.25009 0.70621 0.02768 99.50389 ASTEROID SUPPLEMENT. 47 LUTETIA AND SATURN. a log bY log a D, oY) log a? D? o( log a? D2 oY “dog «* DE bY 0 0.30831 98.84656 98.90957 98.55764 98.72733 1 99.41777 99.43970 98.63362 98.74415 98.63057 2 98.70091 99.01429 99.06238 98.59817 98.76094 3 98.02919 98.51500 98.83777 98.91992 98.68747 4 97.37842 97.98720 98.47787 98.81261 a log a BO) log a D, ID) log oe Dt } log a oY 0 99.77341 99.26606 99.42266 99.29131 1 99.34573 99.44677 99 .29627 2 98.84587 99.19705 99.36704 98.67930 3 98.31784 98.82786 99.20676 a log 0 log « D, b) log a” D2 v'P log «® D2 ot log «* Dé vf) 0 0.30279 98.21476 98.23046 97.26742 97.31403 1 99.10606 99.11135 97.67712 97.70576 97.00204 2 98.08483 98.38881 98.40052 97.31185 97.35610 3 97.10922 97.58840 97.89460 97.91497 97.06638 a log « oD log a D, ee log oe D oD log oa D 0 99.42029 98.28652 98.32878 98.55153 1 98.69718 98.72306 97.97612 2 97.89663 98.20993 98.25683 97.38213 a log 6) log « D, b? log ? D? uf) log «® D3 log «* DE o 0 0.30174 97 82061 97.82702 96.47401 96.49348 1 98.90977 98.91191 97.08423 97.09603 96.00715 2 97.69364 97.99587 98.00063 96.51923 - 96.53766 3 96.52321 97.00117 97.39560 97.31261 96.07302 t log « Uf) log o D, b log «® D? log a W 0 99.21616 97.68927 97.70684 98.13624 1 98.29987 98.31051 97.17695 2 97.30512 97.61115 97.63076 96 .58752 CALLIOPE AND MERCURY. The coefficients for this Asteroid may readily be obtained from the corre- sponding ones for Psyche, if needed. THALIA AND MERCURY. The coefficients for this Asteroid may be obtained from the corresponding ones for Fides. 48 ASTEROID SUPPLEMENT. THEMIS AND MERCURY. a log log « D, 0 log «” D2 vi) log «? D3 log a* DE 0 0 0.30266 98.18224 98.19702 97.20176 97.24519 1 99.08989 99.09480 97.62814 | 97.65478 96.91960 2 98.05267 98.35643 98.36731 97.24629 97.28750 3 97.06106 97.54010 97.84593 97.86485 96.98412 a log a ey log a” D, se) log a® D? oD log a” w? 0 99.40318 98.23701 9827637 98.51648 1 98.66428 98.68835 97.90977 2 97.84781 98.16024 98,20394 97.31633 a log a) log « D, 0) log o? D? 6) log o® D3 o') log a* Dt vp 0 0.30683 98.74407 98.79475 98.34563 98.48522 1 99.36766 99.38512 98.47756 98.56724 98.36147 2 98.60265 98.91349 98.95191 98.38717 98.52074 3 97 .88292 98.36693 99.68522 98,75115 98.42026 Z log « UY) log a” D, bP log a® D2 log a” 6 0 99.71223 99.10383 99.23213 99.16053 1 99.23876 99.32044 99.07634 2 98.69174 99.03288 98.17289 98.46534 a log wf? log « D, o log om D Bee log a Db WD) log at pt uD 0 0.31237 99.05051 99.14687 98.97592 99.22955 1 99.51663 99.55089 98.94609 99.11076 99.17551 2 98.89322 99.21366 99.28826 99.02279 99.25878 3 98.31463 98.80544 99.14079 99.26659 99.22756 t log a oD log oe D, BD log of De wi) log of ? 0 99 .90277 99.59552 99.82347 99.57145 1 99.56218 99.71575 99.74507 2 99.15308 99.53160 99.77612 99,11268 a log op log a D, OM log a De Oy log a? D3 up log a* pt ot) 0 0.32918 99.49315 99.71623 99.94857 0.42753 1 99.72474 99.81063 99.63763 99.98988 0.41967 2 99.28715 99.63820 99.82007 99.9716 0.44571 3 98.89293 99.40582 99.79651 0.08923 0.45607 a log a vo log ae Ds oD log a® D oe) log oe bP 0 0.75784 0.35782 0.81532 0.30849 1 0.57845 0.38902 0.79446 2 0.34407 0.31119 0.78760 0.10475 ASTEROID SUPPLEMENT. 49 AD IED 1S MDILISy Za INID) Ue IEE a Jee a log op log a D, sO log a Dt iO log oe De ase log at Dt iQ 0 0.34976 99.79196 0.15316 0.63944 1.32391 1 99.85720 0.00781 0.12083 0.65560 1.32388 P) _ 99.52489 99.91664 0.22547 0.65964 1.33548 3 " 99.23425 99.77726 0.24278 0.71661 1.34770 4 98.96310 99.61714 0.20307 0.75930 1.38308 5 98.70334 99.44530 0.12746 0.76859 1.42451 Z log « log a” D, oY log a? Dz oY log « BD 0 0.52597 0.92876. 1.59306 1.93983 1 0.42514 0.93592 1.58569 2 0.28275 0.89710 1.57670 0.84085 3 0.12127 0.82388 1.55293 THEMIS AND SATURN. a log b") log « D, bY? log «” D2 oD log a? D3 of) log a* DE of) 0 0.31360 99.09862 99.20482 99.08696 99.35234 1 99.53974 99.5773 99.02024 99.20044 99.30623 2 98.93781 99.26050 99.34297 99.12406 99.38045 3 98.38058 98.87294 99.21216 99.25087 99.35691 4 97.84412 98.45810 98.95908 99.31946 Z log « 0 log a D, 0) log a? D2 oY log a” bf) 0 99.93510 99.67483 99.92273 99.64213 1 99.61410 99.78027 99.85355 2 99.22566 99.61250 99.87748 99.21618 3 98.81031 99.34442 99.77560 } log 0) log « D, 0 log a? D2 o( log a® D3 op) log «* DE LD 0 0.30398 98.44835 98.47468 97. 74054 97.81643 1 99.22187 99.23090 98.02949 98.07685 97.59698 2 98.31487 98.62103 98.64078 97.78410 97.85633 3 97.45339 97.93416 98.24405 98.27813 97.65963 1 log « BY log a” D, 0? log o® D? oD) log a” 0 99.54536 98.64401 98.71313 98.80936 1 98.93453 98.9747 98.45592 2 98.24741 98.56912 98.64539 97.85684 i) log } log « D, o log oe Dt Be) log oe Dt wD log at Dt a? 0 0.30224 98.05009 98.06173 96.93703 96.96957 1 99.02454 99.02818 97.43046 97.45032 96.58642 2 97.92253 98.22559 98.23365 96.98187 97.01273 3 96.86618 97.34474 97.64920 97.66335 96.65256 z log a ae log oe D, a log a D ) log oe ee 0 99.33466 98.03757 98.06701 98.37653 1 98.53167 98.54951 97.64268 2 97.65070 97.96017 97.99295 97.05111 50 ASTEROID SUPPLEMENT. PHOCAHA AND MERCURY. The inclination and eccentricity of this Asteroid are both very large; but the coefficients may be obtained from the corresponding ones for Massalia. PROSERPINE AND MERCURY. a log 0) log « D,, 0 log a” D? oi) log «® D3 o) log a* DE b) 0 0.30336 98.33777 98.35846 97.51618 97.57694 1 99.16713 99.17413 97.86253 97.90012 97.31468 2 98.20622 98.51115 98.52663 97.56020 97.61794 3 97.29088 97.77073 98.07860 98.10547 97.37820 D log « D log a D, a log a? D# op log a” oD 0 99.48563 98.47429 98.52950 98.68592 1 98.82189 98.85591 98.22801 2 98.08128 98.39853 98.45962 97.63156 a log of log a D, SY log a” Dt ot) log a® D3 o? log a* Dt op 0 0.30936 98.90791 98 97969 98.68537 98.87543 1 99.44765 99.47276 98.72733 98.85229 98.79308 2 98.75926 99.07444 99.12941 98.72519 98.90780 3 98.11594 98.60303 98.92902 99.02258 98.84869 a log a oe log a D, log a Dt oo log oe o) 0 99.81115 99.36416 99.54003 99.37257 1 99.41030 99.52472 99.42959 : 2 98.93822 99.29649 99.48678 98.80846 a log oD log « D, oP log a” D2 o{) log a? D3 ul? log a* Dt oP 0 0.31747 99.22610 99.36263 99.36016 99 68626 1 99.60048 99.65029 99.21767 99.44468 ~99 65738 2 99.05414 99.38363 99.49116 99.39494 99.71129 3 99.55219 99.04947 99.40106 99.57966 99.70401 a log « wo} log a D, oe log a BD ey log oe uP 0 0.02492 99.88859 0.19534 99.83947 1 99.75365 99.96407 0.14683 2 99.41824 99.83050 0.15579 99.49544 ASTEROID SUPPLEMENT. Ei@ Ss) Rakwe Il N Ee eA NED MVAGE 51 z log 6 log « D,, UP log a” D? v')) log a D3 uf) log «* DE’? 0 0.34330 99.71090 0.03027 0.44827 1.07398 1 99.82209 99.95219 99.98811 0.46935 1.07285 2 99.46318 99.84178 0.11118 0.47081 1.08729 3 99.14649 99.67967 0.12088 0.54009 1.10004 a log « ee log Pa D, oe log a Dt De log Pa Be 0 0.44162 0.76832 1.37316 0.75656 1 0.32223 0.77986 1.36335 2 0.15738 0.73256 1.35401 0.63437 a log 0) log « D, bP log a” D? of log a D3 of) log a DE ui) 0 0.33318 99.56245 99.81361 0.10550 0.62934 i 99.75617 99.85451 99.74829 0.13910 0.62428 2 99.34469 99.70339 99.91029 0.13223 0.64596 3 " 98.97638 99.49476 99.89942 0.22909 0.65777 4 98.62796 99.26238 99.80636 0.26895 0.72073 5 98.29131 99.01691 99.66757 0.24412 0.77390 z log « log a? D, oY log a® Dz vo log a” 6) 0 0.29903 0.48542 0.98767 0.44428 1 0.14029 0.50893 0.97119 2 99.92943 0.44217 0.96283 0.26965 3 99.69610 0.32061 0.92306 PROSERPINE AND SATURN. a log 6") log « D, 0? log «? D? 6) log a® D3 of) log a DE vp 0 0.30975 98.92873 99.00370 98.72885 98.92624 1 99.45776 99.48404 98.75918 98.88936 98.84848 2 98.77897 99.09482 99.15232 98.76841 98.95817 3 98.14521 98.63278 98.95996 99.05770 98.90361 4 97.53235 98.14250 98.63594 98.9754 Z log « 0 log a” D, 0 log a® D2 bf) log a” 6) 0 99.82417 99.39762 99.58046 99.40069 1 99.43230 99.55160 99.475 12 2 98.96956 99.33045 99.52803 98.85247 3 98.47900 98.99554 99.38895 t log oP log « D, 6) log ce Dt BY log a D oD log at Dt K 0 0.30313 98.29196 98.31063 97.42344 97.47852 1 99.14440 99.15070 97.79344 97.82743 97.19808 2 98.16106 98.46561 98.47956 97.46763 97.51995 3 97.22331 97.70290 98.01009 98.03433 97.26193 0 log « oD log a D, o? log o® Dt aw log a” oe) 0 99.46117 98.40425 98.45426 - 98.63551 1 98.77539 98.80613 98.13400 2 98.01251 98.32816 98.38355 97.53855 52 ASTEROID SUPPLEMENT. PROSERPINE AND NEPTUNE. a log 0) log « D, bP log a” D? ut) log «® D2 ov’? log o* DIU) 0 0.30189 97.89689 97.90452 96.62724 96 .65035 1 98.94790 98.95036 97.19887 97.21289 96.19910 2 97.76964 98.07199 98.07766 96.67236 96.69423 3 96.63706 97.11507 97.41859 97.42849 96.26477 o) log « Be log oe D, 3D log oo Dt uD log oe Bo) 0 99.25522 97.80447 97.82535 98.21530 I 1 98.37657 98.38922 97.33093 2 9741958 97.72656 97.74983 96.74091 a log a) log « D, 0 log a” D2 ul) log a® D3 of) log «* Dé oP 0 0.30393 98.43455 98.46023 97.71251 97.78709 1 99.21508 99.22381 98.00860 98.05505 97.56177 2 98.30140 98.60728 98.62653 97.75611 97.82707 3 97.43322 97.91372 98.22329 98.25665 97.62448 1 log « &D log a* Dv? log o® D* D log ae 0 99.53787 98.62275 98.69065 98.79407 1 98.92040 98.96249 98.42745 2 98.22661 98.54779 98.62279 97.82858 a log vip) log « D, 0 log a” D2 v()) log «® D3 uf) log «* Dt oP 0 0.31145 99.01166 99. 10068 98.90290 99.13165 1 99.49791 99.52940 98.88635 99.03927 99.07061 2 98.85697 99.17583 99.24452 98.94135 99.16187 3 98.26095 98.75063 99.08314 99.19930 99.12371 9 i 2 6 a i 1 log « 6) log a” D, v) log o® D2 of log a” of) 0 99.87722 99.53198 99.74470 99.51575 1 99.52052 99.66109 99.65827 2 99.09451 99.46695 99.69570 99.02897 a log wo log a D, up log Pa D wp log a D> o log at bt wo 0 0.32181 99.34012 98.41956 99.60847 99.99576 1 99.65409 99.71720 99.30590 99.67174 99.97908 2 99.15560 99.49296 99.53823 99.64081 0.01795 3 98.70114 99.20408 99.47986 99.79183 0.02059 t log « BY log a” D, oY log o® Do log a” 0D 0 0.02116 0.08497 0.45167 0.02979 1 99.79135 0.13854 0.41732 2 99.50094 0.03142 0.41725 99.75104 ASTEROID SUPPLEMENT. 53 EUTERPE AND MARS. a log oP log « D, op log ee Db Dy log & D3 By log a pt oD 0 0.35624 99.86581 0.26840 0.81612 1.55585 1 99.88858 0.05999 0.24290 0.82874 1.55633 2 99.57913 99.98446 0.33251 0.83420 1.56584 3 - 99.31079 99.86404 0.35468 0.88150 1.57721 a log « o log D, ) log & Dt t@ log OS 0 0.60698 1.07881 1.79911 1.11474 1 0.52129 1.08303 1.79342 2 0.39762 1.05080 1.78508 1.03382 Z log 0) log « D, 0? log « D? oP log a® D3 o') log «* Dt oD 0 0.32621 99.43613 99.63791 99.82086 0.26446 1 99.69861 99.77529 99.54649 99.86952 0.25355 2 99.23881 99.58429 99.47446 99.85091 0.28424 3 98.82265 99.33148 99.71202 99.7464 0.29229 4 98.42683 99.05363 99.58152 0.00652 0.37644 5 98.04281 98.76209 99.40089 1 log « oD log oe D, a log a De bo log oe Ne 0 0.18705 0.25480 0.67714 0.20035 1 99.99018 0.29462 0.65191 2 99..3676 0.20548 0.64696 99.97138 3 99.45815 0.05023 0.59501 EUTERPE AND SATURN. 7 log 6) log « D, b log a” D? oP log «® DB oP log «* DE oP 0 0.30800 98.82660 98.88705 98.51623 98 67968 1 99.40803 99.42902 98.60318 98.70935 98.57795 2 98.68185 98.99467 99.04073 98.55697 98 71367 3 98.00083 98.48626 98.80807 98.88680 98.63524 4 97.34078 97.94926 98.43933 98.77258 a log a oD log a D, oD log & Dt } log a oD 0 99.76132 99.23431 99.38501 99.26538 1 9932482 99.42181 99.25318 2 98.81584 99.16490 99.32867 98.63747 3 98.27862 98.78722 99.16293 ) log 6) log « D, bP log a” Di? b'? log o® D3 6) log «* Dé 0 0.30270 98.19589 98.20193 97.22931 97.27405 1 99.09668 99.10174 97.64863 97.67615 96.95419 2 98.06617 98.37001 98.38124 97.27380 97.31625 3 97.08128 97.56038 97 86626 97.88587 97.01863 a log a } log oe D, oD log a D 5) log a” Be 0 99.41036 98.25778 98.29833 98.53117 1 98.67808 98.70290 97.93760 2 97.86830 98.18114 98.22610 97.34394 54 ASTEROID SUPPLEMENT. EUTERPE AND NEPTUNE. Z log uo) log « D, OY log oe Db uo log oe DS oD log at iD OS 0 0.30171 97.80193 97.80807 96.43651 96.45518 1 98.90045 98.90251 97.05617 97.06748 95.96019 2 97.67505 97.97723 97.98179 96.48175 96.49943 3 96.49535 96.97327 97.27631 97.28427 96.02611 t log a Be) log Pi D, oD log a D oy log of ee 0 99.20662 97.66108 97.67793 98.11695° 1 98.28111 98.29130 97.13928 Q 97.27710 97.58292 97.60173 96.54999 z log of log « D, bY log a” D2) | log a® D3 2) log «* Dé of) 0 0.30314 98.29689 98.31576 97.43342 97.48908 1 99.14685 99.15322 97.80080 97.83523 97.21061 Q 98.16593 98.42061 98.48462 97.47759 97.53046 3 97.23059 97.71020 98.01746 98.04187 97.27443 a log « ey log a D, oD log Pi Dt a log o? s? 0 99.46379 98.41178 98.46232 98.64091 1 98.78039 99.81146 98.14411 2 98.01991 98.33572 98.39170 97.54855 a log a) log « D, UY log a” D2 vi) log «® D3 o) log o* Dt 0) 0 0.30860 98.86354 98.93005 98.59501 98.77048 1 99.42654 99.44936 98.66106 98.77565 98.67808 Q 98.71805 99.03189 99.08195 98.63534 98.80373 3 98.05469 98.54085 98.86452 98.94987 98.73462 a log a ue) log a” D, a log a? Dy SS log oe oP 0 99.78437 99.29472 99.45678 99.31487 1 99.36461 99.46941 99.33520 2 98.87293 99.226 10 99.40184 98.71706 BELLONA AND THE EARTH. log a log « D,, OW log D? OW log o® De ae log a* Df 2 0.31594 99.17915 99.30376 99.25904 99.56182 99.57820 99.62331 99.14483 99.35358 99.52720 99.01162 99.33836 99.43601 99.29472 99.58799 98.48956 98.98487 99.33151 99.49443 99.57540 log a } log oe D, Oe log oe Dt oe log a uD? 99.99109 99.80921 0.09327 99.76501 99.70190 99.89526 0.03778 99.34727 99.74942 0.05161 99.39186 ASTEROID SUPPLEMENT. a9) BELLONA AND MARS. = a log b log « D, 0’) log «” D? v!)) log a? D3 a) log a* DE 0 0.33893 99.65064 99.94099 0.30800 0.89139 1 99.79557 99.91190 99.89027 0.33356 0.88903 2 99.41591 99.78564 0.02834 0.33227 0.90604 3 99.07883 99.60556 0.03075 0.41194 0.91877 z log « 0 log o* D, oD log o® D2 oD log a” UP 0 0.38193 0.65184 ¥.21398 0.62619 1 0.24739 0.66756 1.20168 2 0.06461 0.61301 1.19260 0.48432 1 log Bey log « D, aD log a De BQ log a Db BR log at Dt wo} 0 0.33679 99.89114 99.89493 0.23511 0.79682 1 99.78154 99.61906 99.83927 0.26334 0.79364 2 99.39068 99.75636 99.98563 0.26027 0.81220 3 99.04258 99.56619 99.98365 0.34583 0.88472 4 98.71444 99.35294 99.90558 0.38804 0.87966 5 98.39791 99.12689 99.78400 0.37382 0.93088 0D log a Oe log oc D, BO log oe D oD log sD 0 0.35165 0.59170 1.13203 0.55984 1 0.20872 0.60998 1.11849 2 0.01613 0.55127 1.10944 0.40679 3 99.80183 0.44319 1.07428 a log 6 log « D, 0) log o? D? 6 log «® D3 ow log a* Dio") 0 0.31062 | 98.97263 99.05477 98.82083 99.03439 1 99.47904 99.50797 98.82645 98.96829 98.96578 2 98.82038 99.13775 99.20094 98.85982 99.06537 3 98.20667 98.69528 99.02519 99.13233 99.01987 4 97.61383 98.22481 98.71996 99.06587 - z log « oY log «” D, 6) log a® D? of) log a 0) 0 99.85201 99.46854 99.66676 99.46099 1 99.47889 99.60908 99.57173 2 99.03570 99.40249 99.61613 98.94568 3 98.56499 99.08540 99.48751 BELLONA AND URANUS. t log 6) log « D, b log a? D? oP log o° D3 oD log a* DEL 0 0.30333 98.33283 98.35329 97.50618 97.56630 1 99.16468 99.17160 97.85508 97.89226 | 97.30209 2 98.20136 98.50624 98.52155 97.55021 97.60742 3 97.28360 97.76346 98.07122 98.09779 9736565 a log « } : log oe D, wy? log a D oD log a oD 0 99.48298 98.46673 98.52136 98.68046 1 98.81688 98.85052 98.21786 2 98.07387 98.39093 98.45139 97.62152 56 ASTEROID SUPPLEMENT. BELLONA AND NEPTUNE. a log oP log « D, bP log «D2 Uf log a® D8 ot) log a! Dé v) 0 0.30196 97.93721 97.94557 96.70829 96.73357 1 98.96790 98.97069 97.25948 97.27485 96 .30066 2 97.80963 98.11220 98.11844 96.75334 96.77728 3 96.69703 97.17524 97.47900 97.48985 96.36620 4 log « } log oe D, w log oe D Oe log oe wo 0 99.27594 97.86543 97.88828 98.25729 1 98.41714 98.43100 97.41243 2 97.48009 97.78764 97.81215 96 .82204 t log log « D, 0 log a” D2 ol) log a® Do) log «* DE oD 0 0.30355 98.37249 98.39486 97.58656 97.65198 1 99.18435 99.19192 98.11492 97.95549 97.40322 2 98.24041 98.54566 98.56240 97.63044 97 69264 3 97.34201 97.82209 98.13054 98.15958 97.46647 a log a D log a D, Io) log a ioe OY) log a? oD * 0 99.50428 98.52748 98.58697 98.72445 1 98.85720 98.89393 98.29943 2 98.13342 98.45199 98.51779 97.70217 a log Uff) log « D, 0 log a” D2 bl) log a® D8 o) log a* Dt oP 0 0.31006 98.94495 99.02251 98.76280 98.96606 1 99.46563 99.49286 98.78403 98.91842 98.89176 2 98.79430 99.11070 99.17024 98.80216 98.99764 3 98.16797 98.65592 98.98407 99.08520 98.94651 t log a oe log oe D, oD log & D oe log ot oD 0 99.83440 99.42378 99.61219 99.42282 1 99.44949 99.57272 99.51074 Q 98.99400 99.35701 99.56042 98.88687 AMPHITRITE AND THE EARTH. t log oP log « D, v')) log a” D2 o) log a? D3 vl) log a* DE bo) 0 0.31891 99.26652 99.41405 99.44772 99.79478 1 99.61957 99.67377 99.28073 99.52420 99.77029 Q 99.09041 99 42248 99.53922 99.48167 99.81880 3 98.60552 99.10465 99.46090 99.65401 99.81551 a log a ) log Po D, oD log oe D? ey log a” Lu? 0 0.05480 99.95758 0.28480 99.90535 1 99.79858 0.02478 0.24176 2 99.47940 99.90104 0.24708 99.58535 ASTEROID SUPPLEMENT. 57 AMPHILTRITE AND MARS. Z log 0? log « D, 0) log ? D? of) log o® 13 0”) log a* DE 0 0.34748 99.76428 0.11083 0.57383 1.23800 1 99.84528 99.98863 0.07536 0.59153 1.23766 2 99.50406 99.89113 0.18607 0.59483 1.25015 3 99.20471 99.74420 0.20105 0.65579 1.26262 a log a oD log of D, o log oe Dt o@ log & sD 0 0.49662 0.87347 1.51721 0.87621 1 0.38970 0.88198 1.50908 2 0.23985 0.84042 1.49993 0.76972 t log 0 log « D, UP log o? D2 o) ‘log o® D3 oD log o* DE oD 0 0.33045 99.51599 99.74806 0.00008 0.49358 1 99.73515 99.82498 99.67402 0.03807 0.48677 2 99.30625 99.65973 99.84957 0.02807 0.51142 3 98.92065 99.43531 99.83041 0.13497 0.52222 4 98.55524 99.18664 99.72420 0.17240 0.59243 5 98.20156 98.92464 99.57056 Z log « 6 log a” D, 0 log o® D2 0) log «7 0), 0 0.25737 0.39957 0.87159 0.35255 1 0.08494 0.42809 0.85227 2 99.85844 0.35405 0.84483 0.15874 3 99.60889 0.22067 0.80091 t log 6) log « D, bP log 0” D2 log «° D3 of) log o* DE ov 0 0.30907 98.89180 98.96119 98.65176 98.83630 1 99.43981 99.46405 98.70270 98.82371 98.75029 2 98.74398 99.05866 99.11174 98.69178 98.86900 3 98.09323 98.57996 98.90506 98.99549 98.80625 4 97.49668 98.07289 98.56503 98.90339 z log a B@ log a D, Bo log of Dt o log a Ne 0 99.80115 99.33832 99.50895 99.35100 1 99.39330 99.50406 99.39444 2 98.91396 99.27029 99.45506 98.77446 3 98.40663 98.92010 99.30672 Z log oP log « D, 0) log ? D2 oP log a® D3 oP log a* DE of) 0 0.30297 98.25757 98.27465 97.35351 97.40453 1 99.12723 99.13305 97.74132 97.77279 97.11018 2 98.12693 98.43121 98.44411 97.39780 97.44635 3 97.17223 97.65163 97.95835 97.98078 97.17426 t log « KO) log oo D, wy log oe D2 o log oe oD 0 99.44281 98.35146 98.39784 98.59774 1 98.74033 98.76879 98.06319 2 97.96059 98.27513 98.32656 97.46843 8 58 ASTEROID SUPPLEMENT. a log Bp log a D,, Be log ce De BO) log oe D3 Oe log at Dt uD 0 0.30182 97.86273 97.86979 96.55862 96.58002 1 98.93078 98.93314 97.14753 97.16051 96.11315 2 97.73556 98.03791 98.04315 96.60378 96.62404 3 96.58604 97.06408 97.36742 97.37657 96.17891 a log wo log « D, uD log a® D2 Be dog & ed 0 99.23771 97.75287 97.77220 98.17984 1 98.34222 98.35393 97.26195 Q 97.36833 97,67486 97.69640 96.67221 URANIA AND MERCURY. a log 0) log « D, 0 log a” Dz v') log a? DB a) log a* DE vf) 0 0.30398 98.44208 98.46820 97.72782 97 80357 1 99.21882 99.22768 98.01999 98.06720 97.58105 2 98.30877 98.61475 98.63434 97.77138 97.84348 3 97.44424 97.92483 98.23454 98.26848 97.64369 i log « 0 log o? D, 0? log a® D? vo log a? BO 0 99.54197 98.63434 98.70334 98.80260 1 98.92808 98.97087 98.44304 Q 98.23792 98.55946 98.63560 97.84395 a log ff) log « D, 0) log a” D2 v') log o® D3 o') log a* DE uD 0 0.31165 99.01981 99.11032 98.92008 99.15209 1 99.50184 99.53389 98.89887 99.05420 99.09256 2 98.86460 99.18377 99.25366 98.95840, 99.18202 3 98.27224 98.76215 99.09324 99.21336 99.14545 Z log « 0) log a” D, v) log a? D2 bf) log a 6) 0 99.88254 99.54527 99.76112 99.52734 1 99.52924 99.67205 99.67642 2 99.10679 99.48047 99.71246 99.04641 z log wo? log « D, oD log «” D2 ol) log a® De WD log a* Dt of 0 0.32220 99.34919 99.52150 99.62840 0.02083 1 99.65832 99.72262 99.41014 99.69006 0.00388 2 99.16356 99.50162 99.63933 99.66054 0.04279 3 98.71278 99.21623 99.58329 99.80904 0.04605 0) log « } log oe D, oD log os Dt ey log oe oD 0 0.11829 0.10083 0.47258 0.04554 1 99.89165 0.15285 0.43920. 2 99.60470 0.04767 0.43858 99.77165 ASTEROID SUPPLEMENT. 59 a log o) log « D, 0? log ” D2 of) log «® D8 of) log a* Dé 6) 0 0.35744 99.87875 0.28823 0.84736 1.59684 1 99.89403 0.06927 0.26444 0.85945 1.59749 2 99.58845 99.99632 0.35158 0 86509 1.60669 3 99.32389 99.87907 0.37441 0.91083 1.61787 a log a eg log a” 1D. Ne log ae De o log a” op 0 0.62162 1.10552 1.83583 1.14623 1 0.53841 1.10933 1.83039 2 0.41785 1.07815 1.82219 1.06819 a log } log « D, op log a Dt ee log oe De wo} log at Dt OS 0 0.32575 99.42669 99.62509 99.79982 0.24769 1 99.69426 99.76950 99.53223 99.84979 0.22621 2 99.23072 99.57534 99.73556 99.83011 0.25772 3 98.81087 99.31907 99.69803 99.95819 0.26533 4 98.41137 99.03767 99.56452 99.98705 0.35127 5 98.02368 98.74254 99.38057 a log « b log a” D, UD log a? D2 6) log 0” 6 0 0.18096 0.23789 0.65455 0.18398 1 99.98046 0.27785 0.62853 2 99.72240 0 18815 0.62397 99.94947 3 99.44024 0.03017 0.57098 i log 8? log « D, 0? log & D? o log a? D8 00 log «! Dt of? OF 0.30788 98.81875 98.87820 98.49996 98.66100 1 99.40420 99.42482 98.59083 98.69571 98.55728 2 98.67434 98.98696 99.03223 98.54078 98.69515 3 97.98966 98.47494 98.79639 * 98.87381 98.614 /3 4 97.32595 97.93431 98.42415 98.76684 a log a D log oe D, oD log a Dt op log oe Ae 0 99.75659 99.22185 99.37030 99.25525 1 99.31661 99.41204 99.23627 2 98.80403 99.15228 99.31365 98.62104 3 98.26319 98.77105 99.14573 i log 8) log « D, oP log ? D2 oP log o® D8 a) log «* Dé oP 0 0.30269 98.18846 98.20324 97.21430 97.25832 1 99.09298 99.09796 97 63750 97.66450 96.93534 2 98 05881 98.36273 98.37365 97.25881 97.30058 3 97.07027 97.54933 97.85522 97.87442 96.99983 z log « 6) log a” D, oP log o° D? o? log o” 6) 0 99 40645 98.24647 98.28636 98.52316 1 98.67056 98.69497 97.92244 2 97 85714 98.16973 98.21402 97.32889 60 ASTEROID SUPPLEMENT. SSS SS URANIA AND NEPTUNE. a log } log « D, uy? log «* D2 6) log a? Db o) log «* D* op 0 0.30170 97.79457 97.80061 96 .42174 96.44010 1 98.89678 98.89886 97.04511 97.05623 95.94668 2 98.66773 97.96988 97.97437 96.46699 96.48386 3 97.48437 96 .96228 97.26528 97.27311 96.06762 a log « oe log oe D, 6D log oe iDp OY log a oD 0 99.20286 97.64998 97.66655 98.10936 1 98.27372 98.28374 97,12444 2 97.26606 97.57180 97.59029 96.53520 EUPHROSYNE AND MERCURY. Both the inclination and eccentricity of this Asteroid are large ; but if the coefficients are needed, we may find those for Euphrosyne and Mercury, fr 66 ce 66 G6 Venus, The Earth, Mars, Jupiter, Saturn, Uranus, Neptune, om those for Hygeia and Mercury ; cc 6G ee « Themis and The Earth ; Venus ; “Thetis and Jupiter ;_ ce (73 Mars ; «© Themis and Saturn’; Clio and Mercury ; Themis and Neptune. POMONA AND MERCURY. a log up log « D, oD log a Dt uy) log a® De a log a* Dt o? 0 0.30349 98.36221 98.38407 97.56572 97.62972 1 99.17926 99.18665 97.89941 97.93907 97.37699 2 98.23029 98.53545 98.55180 97.60963 97.67049 3 97.32688 97.80689 98.11516 98.14354 97.44032 a log a D log o” D, wD log a? D? op log « BD 0 99.49874 98.51173 98.56991 98.71302 1 98.84674 98.88264 98.27827 2 98.11799 98.43615 98.50050 97.68126 t log oD log « D, o log a Dt o) log oe D3 wD log a pt SY 0 0.30985 98.93397 99.00976 98.73981 98.93908 1 99.46030 99.48688 98.76720 98.89873 98.86244 2 98.78392 99.09995 99.15810 98.77931 98.97090 3 98.15257 98.64025 98.96774 99.06658 98.91746 i log « 6 log a” D, 6) log a® D? 6) log a” 0) 0 99.82747 99.40606 99.59068 99.40782 1 99.43785 99.55841 99.48661 2 98.9745 99.33902 99.53847 98.86357 —_-" s POMONA AND THE EARTH. ASTEROID SUPPLEMENT. 61 o: log 0) log « D, bP log a” D2 log o® Do) log a* DE a 0 0.31847 99.25450 99.39869 99.42163 — 99.76236 1 99 61390 99.66676 99.26198 99.50044 99.73663 2 99.07966 99.41094 99.52486 99.45583 99.78669 3 98.58971 99.08829 99.443 10 99.63180 99.78227 t log a oD log a D, SS) log of Dt Bee log oe ee 0 0 04584 99.93700 0.25804 99.88558 1 99.78518 0.00670 0.21342 2 99.46121 99.87999 0.21976 99.55853 a log Bo) log « D,, eu log a Dt De log oe ve wy log at Dt Od 0 0.34619 99.74824 0.08649 0.53598 1.18851 1 99.83834 99.97761 0.04909 0.55465 1.18795 2 99.49188 99.87632 0.16342 0.55745 1.20100 3 99.18739 99.72493 0.17693 0.62082 1.21358 a log a ee log oe D, 6p log oe Dt &D log of oD 0 0.47989 0.84169 1.47364 0.83986 1 0.36931 0.85105 1.46504 2 0.21504 0.80782 1.45581 0.72846 z log b log « D, 0) log «? D? op log «® D? o()) log a* Dé of) 0 0.33123 99.52960 99.76716 0.03088 0.53315 1 99.74132 99.83358 99.69574 0.06797 0.52692 2 99.31758 99.67254 99.86726 0.05850 0.55066 3 98.93706 . 99.45280 99.85062 0.16238 0.56180 4 98.57671 99.20896 99.74834 0 20030 0.62982 5 98.22806 99.01335 99.59912 t log « BY log a” Db log o® D2 oD log o” 6) 0 0.26943 0.42460 0.90538 0.37914 1 0.10108 0.45159 0.88694 2 99.87923 0.37973 0.87918 0.19109 3 99.63448 0.24989 0.83652 a log 64) log « D, bP log o” D2 b log a® D3 of) log a* DI i) 0.30926 98.90269 98.97369 98.67449 98.86275 1 99.44511 99.46993 98.71936 98. 84302 98.77923 2 98.75432 99.06934 99.12370 98.71473 98.89522 3 98. 10860 98.59557 98.92127 99.01380 98.83495 4 97.48379 98.09347 98.58598° 98.92527 z log « b log «” D, b? log a? D2 of) log a” ui) 0 99.80791 99.35579 99.52996 99.36557 1 99.40479 99.51802 99.41820 2 98.93037 99.28801 99.47650 98.79745 3 98.42801 98.94236 99.33093 ASTEROID SUPPLEMENT. z log oP log « D, v log a” D2 b”? log «® D2 oP log «* DE oP 0 0.30301 9826760 98.28527 97.37418 97.42644 1 99.1323 99.13827 97.75673 97.78893 97.13616 2 98.13703 98.44138 98.45458 97.41844 97.46808 3 97.18734 97.66679 97.97365 97.99660 97.20017 a log a @ log oe D, D> log ob De 6D log of BD 0 99.44823 98.36707 98.41449 98.60888 1 98.75068 98.77980 98.08412 | 2 97.97594. 98.29081 98.34338 97.48916 POMONA AND NEPTUNE. | | a log wo log « D, SY log a D? up log a? D3 5) log at Dt BR 0 0.30184 97.87284 97.88006 96.57891 96.60080 1 98.9358] 98.93823 97.16272 97.17600 96.13855 2 97.74561 98.04799 98.05336 96.62406 96.64479 3 96.60110 97.07917 97.38256 97.39192 96.20429 a log « a log oe D, SY log a D? Bey log oe a 0 99.24289 97.76814 97.78790 98.19032 1 98.35238 98.36436 97.28235 2 97.38349 97.69015 97.71220 96.69253 This Asteroid has a large eccentricity; but if the coefficients are needed, they may be found from the corresponding ones for Euterpe. CIRCE AND MERCURY. z log log « D, 0 log a” D? 4) log a® D3 {)) log a* Dé BD 0 0.30331 98.32692 98.34711 97.49421 97.55358 1 98.32009 99.16857 97.84608 97.88321 97.28705 2 97.35388 98.50037 98.51547 97.53827 97.59468 3 96.43323 97.75468 98.06208 98.08861 97.35065 a log « Oe) log at D, u) log oe Dt Oe log «2 D 0 99.47982 98.45770 98.51163 98.67394 1 98.81088 98.84409 98.20572 2 98.06499 98.38185 98.44155 97.60953 ASTEROID SUPPLEMENT. 63 Z log of) log « D,, 4) log a” D? oi) log «° D3 uf) log o* DE o¢? 0 0.30926 98.89638 98.96644 98.66132 98.84741 1 99.44204 99.46652 98.70970 98.83182 98.76246 2 98.74833 99.06315 99.11676 98.70127 98.88001 3 98.09969 98.58652 98.91187 99.00318 98.81831 D log a o} log oo D, } log a D> oe log ae 6 0 99.80399 99.34566 99.51778 99.35709 1 99.39823 99.50992 99.40443 2 98.92086 99.2774 99.46407 98.87412 a log 0 log « D, oP log «” D2 o) log o® D3 ul) log «* Dé of) 0 0.31705 99.21358 99.34684 99.33314 99.65290 1 99.59455 99.64306 99.19829 9942025 99.62257 2 99.04284 99.37157 99.47638 99.36816 99.67824 3 98.53555 99.03230 99.38251 99.55682 99.66962 t log a ? log oe D, oD log oe De oy log oe Me 0 0.01550 99.86734 0.06792 99.81940 1 99.73981 99.94551 0.11762 2 99.39931 99.80879 0.12781 99.46773 Z log b) log a D, 0? log a” D vi) log o® D3 uly) log a* Dt 0 0 0.34208 99.69466 0.00602 0.41031 1.02450 1 99.81498 99.94124 99.96167 0.43252 1.02307 2 99.45056 99.82672 0.08867 0.43332 1.03816 3 99.12845 99 .65982 0.09655 0.50530 1.05094 t log «a oD log o” Dz ee log a? Dt D log Pa D 0 0.42528 0.73670 1.32990 0.72093 1 0.30192 0.74929 1.31951 2 0.13234 0.70010 1.31016 0.59365 O log 0 log « D, v) log «” D2 of) log « D3 oP log «* DE oP 0 0.33410 99.57726 99.83473 0.13928 0.67284 1 99.76283 99.86402 99.77203 0.17139 0.66839 2 99.35681 99.71727 99.92985 0.16560 0.68918 3 98.99378 99.51355 99.92143 0.25940 0.70125 4 98.65082 99.28626 99.83240 0 30001 0.76202 5 98.31949 99.04594 99.69822 0.27809 0.81477 a log a } log oe D, oo) log oo De Bo log oe wo 0 0.31259 0.51304 1.02512 0.47410 1 0.15806 0.53511 1.00947 2 99.95209 0.47052 1.00088 0.30531 3 99.72381 0.35258 0.96236 64 ASTEROID SUPPLEMENT. a log bY log « D,, v6) log a? D2 wo) log o® D3 uD log a* DE vo 0 0.30997 98.94033 99.01713 98.75312 98.95469 1 99.46239- 99.49034 98.77694 98.91012 _98.87941 2 98.78993 99,10617 99.16513 98.79253 98.98637 3 98.16149 98.64933 98.97720 99.07735 98.93428 4 97,55394 © 98.16430 98.65817 99.00085 ) log « He log oe D, @ log & Dt Oe log a oP 0 99.83148 99.41631 99.60324 99.41649 1 99.44459 99 .56669 99.50058 2 98.98704 99.34951 99.51116 98.87706 3 98,50171 99.01927 99.41491 a log 0) log a D, 0) log a” D2 b log o® D3 vo) log a* Df b) 0 0.30318 98.30278 98.32191 97.44535 97.50172 1 99.14977 99.15623 97.80977 97.84457 97 22561 2 98.17174 98.47638 98.49067 97.48949 97.54305 3 97.23929 97.71894 98.02628 98.05112 97.28939 Z log « 0 log «” D, b%) log o® D2 of log a? 09 0 99.46693 98.42079 98.47198 98.64738 1 98.78637 98.81786 98.15619 2 98.02876 98.34477 98.40147 97.56052 a log 0") log « D, 0 log o? D2 uD log o° DB o log a* DE oP 0 0.30192 97.90758 97.91539 96.64872 96.67238 1 98.95313 98.95575 97.21493 97.22930 96.22601 2 97.78016 98.08265 98.08846 96.69381 96.61622 3 96.65288 97.13102 97.43461 97.44475 96.29165 a log a se log a” D, o log a ide Oe log of BY 0 99.26071 97.82063 97.84201 98.22641 1 98.38732 98.40028 97.35253 2 97.43562 97.74274 97.76655 96.76240 If the coefficients for this Asteroid are ever needed, they may be found for Leucothea and Mercury, from those for Psyche and Mercury ; 6 “¢ Venus, ec “© Clio and Saturn ; @ “ The Earth, “« «Themis and Saturn ; ce “Mars, ce “« Proserpine and Jupiter ; 6c 66 Jupiter, 74 6c 66 66 Mars ; BD “: Saturn, ce ‘¢ Clio and Venus ; oA “ Uranus, cc “¢ Psyche and Uranus ; a “ Neptune, ce ce “© Neptune. ATALANTA AND MERCURY. ASTEROID SUPPLEMENT. 65 Both the inclination and eccentricity of this Asteroid are large. efficients may, however, be found for Atalanta and Mercury, from those for Ceres and Mercury ; (73 sc Venus, « The Earth, “Mars, ‘© Jupiter, « Saturn, “ Uranus, “« Neptune, 6c oe ce 15 ce (t5 «Venus ; “ The Earth « | Veda and Mars ; (73 (75 (x3 5 “ Jupiter ; “ Saturn ; “ Uranus ; “© Neptune. The co- FIDES AND MERCURY. a log oD log a D,, wp log oe Dt Oe log a? DS wD) log a* Dt wo 0 0.30334 98.34233 98.36336 97 52564 97.58703 1 99.16943 99.17652 97.86957 97.90756 97.32659 2 98.21079 98.51579 98.53145 97.56964 , 97.62798 3 97.2971 97.77762 98.08559 98.11276 97.39007 t log a Dee log a D, a) log Oa Dt ey log B® 0 99.48815 98.48146 98.53724 98.69114 1 98.82665 98.86104 98.23762 2 98.08829 98.40572 98.46745 97.64108 D logo) log a D, 0) log «” D? o{)) log «® D3 oi) log a* Dé o'? 0 0.31112 98.91285 98.98537 98.69568 98.88746 1 99.45256 99.47543 98.73489 98.86 106 98.80622 2 98.76674 99.07928 99.13484 98.73544 98.91973 3 98.12584 98.61009 98.93636 99.03090 98.86171 z log a BY log a” D, bY log a D? oo log a” 6) 0 99.81423 99.37209 99.54960 99.37922 1 99.41551 99.53108 99.44038 2 98.94566 99.30455 99.49654 98.81889 a log B log « D, bY log a” D2 oi) log a? D3 vi) log o* DE ov) 0 0.31766 99.23148 99.36942 99.37177 99.70061 1 99.60302 99.65339 99.22612 99.45519 99.67234 2 99.05898 99.38880 99.49751 99.40644 99.72550 3 98.55931 99.07683 99.40905 99.58949 99.71879 a log « 6) log oD, bY log o® D2 wo) log 0” 6) 0 0.02885 99.89772 0.20714 99.84813 1 99.75960 99.97207 0.15939 2 99.42637 | 99.83983 0.16783 99.50735 ASTEROID SUPPLEMENT. FIDES AND MARS. log b log « D, of) log a” D® ol) log a® D8 of) log a* Dt Uf) 0.34383 99.71781 0.04076 0.46468 1.09540 99.82515 99.95693 99.99953 0.48529 1.09438 99.46861 99.84827 0.12093 0.48702 1.10854 99.15423 99.67820 0.13138 0.55517 1.12127 log a Oe log oe D, oe log a D? op log a B® 0.44879 0.78202 1.39191 0.77204 0.33102 0.79313 1.38234 0.16818 0.74551 1.37301 0.65201 a log uo? log a D,, B® log o Dt OW log a® p® wo log «* Dt oD 0 0.33280 99.55616 99.80467 0.09118 0.61078 1 99.75333 99.85048 99.73821 0.12542 0.60559 2 99.33952 99 69749 99.90201 0.11808 0 62784 3 98.96881 99.48675 99.89007 0.21629 0.63934 4 98.61821 99.25220 99.79527 0.25578 0.70325 5 98.27928 99.00452 99.65455 0.22968 0.75658 a log « log a” D, bY log «® D? of log a7 0 0 0.29331 0.47363 0.97183 0.43169 1 0.13276 0.59789 0.95499 2 99.91981 0.43016 0.94673 0.25455 3 99.68431 0.30704 0.90642 = z log 64) log « D, b'? log a” D? 0? log a? D3 0) log a* DE vf) 0 0.30965 98.92377 98.99797 98.41847 98.91412 1 99.45535 99.48135 98.75160 98.58051 98.83528 2 98.77429 99.08997 99.14686 98.45802 98.94615 3 98.13859 98.62570 98.95259 98.74932 98.89052 4 97.52312 98.13318 98.62644 98.66759 a log a 0 log a” D, bY log a® D2 v) log ao) 0 99.82106 99.08964 99.57082 99.39397 1 99.42706 99.54518 99.46429 2 98.96210 99.02236 99.51818 98.84199 3 98.46930 98.68541 99.37805 FIDES AND URANUS. log at Dt BO log 0 log « D, bY log a” D2 b) log o® D3 uP 0.30311 98.28733 98.30581 97.41408 99.14210 99.14834 97.78647 97.82010 98.15650 98.46101 98.47481 97.45828 97.21648 97.69604 98.00317 98.02676 log a 0 log a” D, d%) log o® D2 o) log a” 1 99.45755 98.39718 98.44669 98.63044 98.7060 98.80112 98.12452 98.00556 98.32105 98.37590 97.52916 97.4686 1 97.18630 97.51008 97.25019 ASTEROID SUPPLEMENT. — FIDES AND NEPTUNE. a log 0? log « D, 0’) log a” Dz 0“) log «° D3 o) log o* DE oP 0 0.30187 97.89232 97.89987 96.61807 96 .64093 1 98.94553 98.94806 97.19200 97.20588 96.18760 2 97.76499 98.06743 98.07304 96.66318 96.68484 3 96.63015 97.10825 97.41175 97.42154 9625328 z log « oD log o? D, 0) log a D2 0 log a? 0 0 99.25288 97.79757 97.81823 98.21055 1 98.37197 98.38449 97.32170 2 97.41273 97.71964 97.74267 96.73171 a log O° log « D, log o” D2 ol) log «* D3 vl) log a* Dt 0) 0 0.30321 98.30996 98.32940 97.54988 97.51713 1 99.15334 99.15990 97.82059 97.85595 97.24387 2 98. 17882 98.48351 98.49804 97.50399 97.55839 3 97.24988 97.72957 98.03702 98.06226 97.30760 i log « UY log o” D, 0 log o° D? vt log «7 0 99 47076 98.43176 98.48375 98.65526 1 98.79366 98.82564 98.17092 2 98.03953 98.35579 98.41337 97.57509 a log 0) log « D, bP log a” D? bi)) log «® D3 of) log a* Dé of) 0 0.30884 98.87839 98.94584 98.62383 98.80385 1 99.43328 99.45681 98.68221 98.80002 98.71474 2 98.73123 99.04551 99.09706 98.66399 98.83683 3 98.07428 98.56073 98.885 12 98.97302 98.77098 ° i 2 i i } 2 (i a log a } log « D, SO log a? D2 iD) log @ B? 0 99.79288 99.31685 99.48322 99.33317 1 99.37918 98.48697 99.36527 2 98.89377 99.24853 99.42882 98.74620 a log 0) log « D, bP log a” D? oi) log «® D3 of) log a* DEO) 0 0.31641 99.19410 99.32240 99.29117 99.60125 1 99.58531 99.63186 99.16803 99.38243 99.56853 2 99.02520 99.35279 99.45349 99.32657 99.62706 3 98.50957 99.00549 99.35366 99.52144 99.61624 a log « D log oc D, Ue) log oe Dt uy log oe 0 0.00176 99.83439 0.12555 99.78848 1 99.71833 99.04133 0.07236 2 99.36986 99.7514 0.04856 99.42474 68 ASTEROID SUPPLEMENT. LEDA AND MARS. a log oP log a D, o log a” D? 0) log o® D3 of) log a* Dt 0) 0 0.34027 99.66964 99 96894 0.35205 0.94865 1 99.80397 99.92450 99.92104 0.37612 0.94670 2 99.33094 99.80348 0.05426 0.37578 0.96287 3 99.10038 99 62906 0.05913 0.45206 0.97565 a log « up log oe D, sD log ae Dt oD log of op 0 0.40047 0.68831 1.26376 0.66675 1 0.27017 0.70263 1.25242 2 0.09382 0.65044 1.24310 0.53132 a log 0 log « D, vf) log a” D2 vf) log a® D8 0) log a* Dt of) 0 0.33558 99.60071 9.86839 0.19296 0.74223 1 99.77334 99.87918 99.80972 0.22257 0.73855 2 99.37588 99.73922 99.96105 0.21863 0.75804 3 99.02127 99.54316 99.95623 0.30774 0.77039 4 98.68667 99.32380 99.87352 0.34933 0.82783 5 98.36370 99.09154 99.74648 0.33183 0.87978 a log « Be) log a D, oD log a De oD log a o? 0 0.33437 0.55705 1.08489 0.52192 1 0.18642 0.57693 1.07046 2 99.98800 0.51570 1.06158 0.36209 3 99.76762 0.40336 1.02498 a log of) log « D, bP log a? D? of? log a® D3 of) log a* DE b) 0 0.31033 98.95854 99.03831 98.79126 98.99952 1 99.47222 99.50027 98.80483 98.94285 98.92805 2 98.80711 99.12397 99.18529 98.83044 99 .03082 3 98.18698 98.67527 99.00425 99.10829 98.98248 4 97.58773 98.19844 98.69302 99.03744 a log « 0) log a” D, 0 log a® D? vo log a 0) 0 99.84301 99.44572 99.63890 99.44148 1 99.46391 99.59151 99.54063 2 99.01446 99.37929 99.58768 98.91570 3 98.53734 99.05653 99.45577 a log oP log a D, oy log & ins SY log a® D> oY log at Dt 20 0 0.30326 98.31974 98.33981 97.47967 97.53813 1 99.15819 99.16490 97.83533 97.87146 97 26876 2 98.18846 98.49323 98.50809 97.52375 97.57930 3 97.26430 97.74404 98.05154 98.07744 97.33242 a log « oD log oe D, oq) log of D De log oe oP 0 99.47598 98.44671 98.49981 98.65602 1 98.80358 98.83627 98.19098 2 98.05421 98.37081 98.42960 97.59494 ASTEROID SUPPLEMENT. aaa aa aS a eS NE | LEDA AND NEPTUNE. a log 6) log « D, b) log «” D2 uf) log o® D3 o) log a* DEV? | 0 0.30194 97.92430 97.93242 96.68234 96.70690 1 98.96147 98.96419 97.24007 97.25500 96.26814 Q 97.79679 98.09934 98.10538 96.72765 96.75067 3 96.67780 97.15598 97.45966 97.47020 96.33372 a log « oD log Pi D, ae) log & De a log ae op 0 99.26930 97.84591 97.86811 98.24383 1 98.40415 98.81761 97.38633 2 97.46072 97.76808 97.79281 96.79606 LATITIA AND MERCURY. HARMONIA AND MERCURY. The coefficients for this Asteroid may be found from the corresponding ones for Ceres. a log 6) log « D, bY log a” D? ui) log a? D3 of) log a* Dé 0) 0 0.30423 98.47913 98.50749 97.80317 97.88502 1 99.23715 99.24679 98.07597 98.12714 97.67598 2 98.34509 98.65151 98.67280 97.84654 97.92449 3 97.49852 97.97942 98.28990 98.32675 97.73826 a log « sD log a” D, o@ log «® D* a log a oD 0 99.56223 98.69140 98.76601 98.84475 1 98.96591 99.01231 98.51979 2 98.29357 98.61688 98.69913 97.91961 O log wD log « D, o log Po Dt oi) log & Db wy) log at pt 3 0 0.31261 99.06005 ~ 99.15830 99.00511 99.25466 1 99.52122 99.55619 98.96078 99.12844 99.20136 2 98.90209 99.22294 99.29906 99.04283 99.28278 3 98.32775 98.81887 99.15495 9928322 99.25315 a log « oD log oe D, o) log a Dt ed log a oe 0 99.90912 99.61120 99.84300 99.58530 1 99.57245 99.72682 99.76650 2 99.16747 99.54756 99.79606 99.13285 70 ASTEROID SUPPLEMENT. 99.06189 a log 6 log « D, b') log a” D2 bi) log o® D3 U) log «* Dt 0 0 0.32420 99.39428 99.58142 99.72787 0.14640 1 99.67928 99.74976 99.48116 99.78254 0.13282 2 99.20280 99.54456 99.69502 99.75895 0.16724 3 98.77015 99.27627 99.65003 99.89534 0.17322 a log a uD log a D, oD log oe De Be log oe uD 0 0.15436 0.18022 0.57773 0.12521 1 99.94312 0.22497 0.54882 2 99.67314 0.12902 0.54573 99.87470 a log 0 log a D, 0) log a” D? vi) log a® D3 o) log at Dt 0 0 0.36382 99.94485 0.40343 1.00803 1.80630 1 99.92153 0.11744 0.37491 1.01768 1.80924 2 99.63506 0.05673 0.45020 1.02391 1.81695 3 99.38909 99.95480 0.47565 1.06235 1.82715 a log « 6) log a” D, v') log o° Do) log a? 0 0.69826 1.24373 2.02578 1.31181 1 0.62709 1.24574 2.02145 2 0.52146 1.21949 2.01400 1.24595 a log wo log « D, uP log Po D? Os log Pe D3 oe) log at Dt 2) i) 0.32436 99.38092 99.56357 99.69837 0.10903 1 99.67308 99.74168 99.46002 99.75503 0.09450 2 99.19122 99.53185 99.67844 99.72972 0.13020 3 98.75324 99.25855 99.63024 99.86964 0.13543 4 98.33597 98.95969 99.48173 99.89298 5 97.92995 98.64694 99.64224 —_—— a log a uD log Pa D, uD log ae De BO log a Oe 0 0.14354 0.15659 0.54638 0.10136 1 99.92781 0.20343 0.51619 2 9965285 0.10481 0.51378 99.84405 3 99.35330 99.93328 0.45554 0) log oD log « D,, oS log of D uP log oe D oP log at pt BY 0 0.30732 98.78034 98.83510 98.42047 98.57016 1 99.38540 99.40436 98.53271 98.62933 98.45637 2 98.63750 98.94918 98.99080 98.46167 98.60501 3 97.93485 98.41945 98.73921 98.81050 98.52453 4 97.25316 97 86101 98.34978 98.67983 a log « Be log a” D, o) log «° Dt uD log o” ee 0 99.74363 99.16100 99.29879 _ 99.20615 1 99.27650 99.36465 99.15379 2 98.74626 99.09071 99.24077 98.54081 3 98.18760 98.69314 ASTEROID SUPPLEMENT. 71 eee ones for Lutetia. for Iris, if needed. ISIS AND MERCURY. ste log op log « D, op? log ae Dt 3? log a De op log at Dt ae 0 0.30256 98.15197 98.16559 97.14069 97.18134 1 99.07420 99.07942 97.58256 96.60746 96.84293 2 98.02199 98.32629 98.33644 97.18528 97.22385 3 97.01620 97.49511 97.80061 97.81829 96.90761 a log a BO log of D, 6) log oe ip ow) log & @ 0 99.38731 98.19098 98.22863 98.48400 1 98.63368 98.65617 97.84810 2 97,80237 98.11405 98.15496 97.25513 Tae log b) og « D, bY log a” D2 v) log o® D3 oP log o* DE uP 0 0.30165 97.75844 97.76400 | 96.34922 96.36615 1 98.87876 98.88062 96.99083 97.00107 95.85087 2 97.63175 97.93381 97.98794 96.39450 96.41053 3 96.43044 96.90829 97.21113 97.21834 95.91688 a log « oD log oe D, wo log a D? 5D log Pa oD 0 99.18443 97.59547 97.61075 98.07214 1 98.23744 98.24666 97.05163 2 97.21187 97.5172 97.53427 96.46262 The coefficients for Daphne may be obtained from the corresponding ones The coefficients for this Asteroid may be obtained from the corresponding [ee cee eee Dor no Site: rar}: Devel ae Raat ee meat een MIP RNEN ON TAL WA RC RS TS PES ROU PL AD ADI a ears Al’ Wen wy my PL Aa} alien Wht fhe ‘ot ee Oe. a - . Sa AN Ale myely nyc ahi AWW Hoy Ap le Peer w 1! UIA ita uty tostenntrneates aL yebeuaor pestiyn casmrigh aes Te itateu ini ta utah Put i wih’ Ce HES Ara RENT hited ite his 5 ita led ar My CRC eT eS Te A UT RPA a aA i " PONT Moe MT ACTON \ WO arU GA WIAD mick Musil ben but ke ST Ea MTR 7 eae TR A A TORII WERT TITIS SY TCA a EY A Bre WAS Ry og te AE ch be Tac . aes oaks 4h i La a EH wie Ma A ROAWEEET CAMARA REA GACT HAAS AT ARMM ut tht ue kN Ta: CONT MUh edhe beihcde hed hatlec ieee henmicutwrar uty aatitetticlat ste» edt pal if MWe ipcacacieen Hf COC MONTH AT ACM A IE PWM Ii nee MAMIE ewe yg TUONO RAT Ae NO OP A an AA ae ; \e ‘e Mivnicy secu ewes) beatae a , TAN . Bee etme ca aw bomen menial A We MU eC ENCORE yt ot CEEMU ERO T CLI? = p i 04h FRAN mag) ARE ms viele 1 CUNT CLUTCH A Sa SOW wk ol pas tata yd Ay A sy hn 89 se WO PEDO AL ESEALISIOU GON Pik dele debt by SMITHSONIAN INSTITUTION LIBRARIES Tyner) pv Hi ty Slate bin Hit hy Nps hi y t STATA EMBO Hear ecA aleut oui cicu edi f meine knees ie ehstar ay a hla mage fife sen toil wi yc a i TAC a evant a4 i nt PO ee eG Eel Wbasgeebiblisirpusey ev: teak / atari het iy hts lye be trea sonny ‘ iN Puacnumiciee eet NaTa tibetan iy rary yeni tek toe « AN neh i a Wiecaclirveg uunsdtera Aten sbennyeu bent Sivenity wigan ie SVAN a erinccity te %s STitaiuinifh Renalbeien Hdl MOM te Newt Retest win WKN aca * ; Tia atetts NACA Mata Lente MM MAS UMA CNC at has patna tiie tht i i Ue nS Co A rf i iy i iy bebe AMI AS iy hvsan ewes WEN NR tepty TOTNES bays vw AAG) werd Pe WALT ONG bee isbebeb AURA AY ea ng tT VAI VACA SUAQ 4 i SCT Pe NR TCR a POAC CUTS Sct RE MO MT Ta . Wt ae nin aera HY we Wasa Se OW Wn A AW penuubnestaly a nl ST VOR EH RITA MCC ST MUTI DUC CR eI SOT BT Aa ace ceuunnenrenttie i t Ha ita ARAN MR Sr AST ox MrT RAD ORTUCRTO S TuTTT : , INN) it ment ate 7 Renaayaen meat POW NAMEN CTLON MA CNA ENT WTS ORT OAT TB I Pe REAL TCA aPC TT TN Meier Weeds Na iron in epeg eemticsiiNdt Geet eM h HUI D gwen Wee 489N rhe TA fee Cmaps 1) wae Vie CORD ao iy segue Regn 9) 48 fou as ef) Nw 0 ROR AE ET teat a ‘ Wine nen nto iye PUNE NCR a RT CHANT arC ACM TR MS MT AMT een hen 8 wa won D Aibcheorp neylanwesiaeayd Muprnce cht ies Wee Reb my Wy hed Aas oer ote ty geal tite ita Atalatioaataeniemtenen ntact stiverweton dabturtad once A Pecan Nn lantge Moti Mediiiyede jem RajeQ tre) kefien to ety we wm (iH Bo 8) Pei heed SAIN EAGAN OUANIN AC NAMI HACAUHE CRNA ACMA NEU eH Wher nied) Wye te hepa Aen COTM Ca wyewar Heol) Une Haas SED UDUNCA LON EM eye Geu Ue Tige wese gua ALT wet AQAM A AYE ANS fy AH ANCA RV ACC CACO BTEC TU ees Micaela wey" PUORASTENTAT NI WeRTHAC ba ol WANTON ATW praetlve ech ten yah Bethe NAN Lip eee to Henge bn bet Bee CuIW ALN Fh TD Rha neg fuwsied diode thy HIN Ube jyaiee quent. 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