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The To ay orn eocirtes rie is . 4h. il 7 a ¢ 7 Od 24s She ‘se ? ht ’ . he ' ” ; ? $ oy, 4 .. “phe Tyrie i : 7” ~ tote? 7 Frisys: i Fine duit, tet wiegpr y, oi * , 4 4 , ¢ % o_ we. , — “4 4 oi > ‘. ~¥ A - : Py Ay > = . e a > « ’ 4 = a >> s kh . Ps 7 : ‘ oa TRANSACTIONS OF THE AMERICAN PHILOSOPHICAL SOCIETY. HELD AT PHILADELPHIA, FOR PROMOTING USEFUL KNOWLEDGE. VOL. VIII.—NEW SERIES. IL29 oy, fF. be ee PUBLISHED BY THE SOCIETY. PDhilavelphta: PRINTED BY WILLIAM S, YOUNG,—NO. 88, NORTH SIXTH STREET. 1843. EXTRACT FROM THE LAWS OF THE SOCIETY RELATING TO THE TRANSACTIONS. 1. The Transactions shall be published in numbers, at short intervals, under the direction of the Committee of Publication. 2. Every communication to the Society, which may be considered as intended for a place in the Transactions, shall immediately be referred to a committee to consider and report thereon. 3. If the committee shall report in favour of publishing the communication, they shall make such corrections therein, as they may judge necessary to fit it for the press; or if they shall judge the publication of an abstract or extracts from the paper to be most eligible, they shall accompany their report with such abstract or extracts. But if the author do not approve of the corrections, abstract, or extracts, reported by the committee, he shall be at liberty to withdraw his paper. 4, The order in which papers are read before the Society shall determine their places in the Transactions, priority of date giving priority of location. COMMITTEE OF PUBLICATION. Isaac Lea. Isaac Hays, M. D. J. Francis Fisher. a® ‘ ri ‘ ' ie i ' abl , _ ari) ’ i a : > i os ' ny ; . gait . : ’ Vee =| . ey Fay 1 + 7 | i civebua Panga i aay ; a Ls “a : oe i , f a int aot a - 3 - : a a . eet ex: x 8 ’ Ans y a Libey d : ae A me H igani ny ales enuedd) Ea ii vipat ti 7 adh Nii fon t-yowe’d @ SJ /umlivsiiiis Tale in igeway ; vo te ( inl, oAorieieg ell TEE Piha, ive ita Wi Dee a Vn, est 1h iinet (ag thy . - bl ‘ - : om ibis gum pola vas, occa Paonia ' id P - ‘ a. TE ‘4 i ir j lube He Hie mealigi't 7 _Y Abt T) i ‘ , ‘ i \ 7 % oe 7 = Shere ne oo OFFICERS OF THE AMERICAN PHILOSOPHICAL SOCIETY, FOR THE YEAR 1843. Patron, His Excellency the Governor of Pennsylvania. PRESIDENT, Peter S. Du Ponceau. Nathaniel Chapman, Robert M. Patterson, Franklin Bache. Vicr-PRESIDENTS, John K. Kane, Alexander D. Bache, Robley Dunglison, Joshua Francis Fisher. SECRETARIES, Robert Hare, William Hembel, Charles D. Meigs, Henry Vethake. CounseE.tors elected for three years. In1841, Clement C, Biddle, William Short, Joseph Henry, Philip H. Nicklin. Thomas Biddle, In 1843, Gouverneur Emerson, Isaac Lea, Hartman Kuhn. Covnse.tor for two years in the place of Philip H. Nicklin, deceased, Benjamin Dorr, Isaac Hays, In 1842, Curators, Franklin Peale, John Price Wetherill, TRreaAsuRER and Liprarian, George Ord, vil.—b LIST OF MEMBERS OF THE AMERICAN PHILOSOPHICAL © O16 LE Tay, Elected since the Publication of the Seventh Volume. Col. Edward Sabine, F. R.-S., of London. Robert Christison, M. D., F. R. S., of Edinburgh. A. P. De Candolle, of Geneva, Switzerland. Isaac R. Jackson, of Philadelphia. Roswell Park, of Philadelphia. William Peter, H. B. M. Consul, Philadelphia. Edward Hitchcock, of Massachusetts. George Bancroft, of Boston. Alexis De Tocqueville, of Paris. Baron De Ladoucette, of France. Edward William Brayley, F. R. S., of London. Baron De Roenne, H. P. M. Minister, Washington. Charles Lyell, F. R. S., London. Joseph Nicholas Nicollet, of Baltimore. John F. Frazer, of Philadelphia. E. Otis Kendall, of Philadelphia. Stephen Endlicher, of Vienna. D. Humphreys Storer, M. D., of Boston. Simeon Borden, of Massachusetts. Petty Vaughan, of London. Frederick Fraley, of Philadelphia. Rev. George Peacock, F. R. 8., Cambridge, England. Benjamin Peirce, of Harvard University. J. 1. Clark Hare, of Philadelphia. LIST OF NEWLY ELECTED MEMBERS. vii His Imperial and Royal Highness Leopold the Second, Grand Duke of Tuscany. Louis Agassiz, F. M. R. S., of Neufchatel. W. W. Gerhard, M. D., of Philadelphia. Lieut. Col. William Reid, F. R. S., Governor of Bermuda. Thomas P. Cope, of Philadelphia. John Lenthall, of Philadelphia. Solomon W. Roberts, of Philadelphia. Ellwood Morris, of Philadelphia. Charles Ellett, of Philadelphia. Charles B. Trego, of Philadelphia. Cavaliere Mustoxidi, of Corfu. OBITUARY NOTICE. Since the publication of the last volume of these Transactions, the following members have been reported as deceased :— Count Minot de Melito. Thomas L. Winthrop, of Boston. Samuel Colhoun, M. D., of Philadelphia. William P. Dewees, M. D., of Philadelphia. Joseph P. Norris, of Philadelphia. Rev. James Abercrombie, D. D. of Philadelphia. William J. Macneven, M. D. of New York. Joshua Gilpin, of Delaware. Thomas Cadwalader, of Philadelphia. John Vaughan, of Philadelphia. Julien W. Niemcewicz, of Poland. José da Silva Lisboa, of Rio Janeiro. William Baker, of England. A. P. de Candolle, of Geneva. Joseph Hopkinson, of Philadelphia. Philip H. Nicklin, of Philadelphia. Condy Raguet, of Philadelphia. Samuel L. Southard, of New Jersey. Baron Larrey, of Paris. Isaac R. Jackson, of Philadelphia. John P. Emmet, of the University of Virginia. William R. Fisher, M. D., of Philadelphia. CONTENTS. Laws of the Society relating to the Transactions. - - - : = = mh ale Officers of the Society for the Year 1843. = - - - - - : = = 2 List of the Members of the Society elected since the Publication of the Seventh Volume. - Obituary Notice. - - - - - = = = = Z 2 - - : ARTICLE I. Contributions to Electricity and Magnetism. By Joseph Henry, LL. D. &c., Professor of Natural Philosophy in the College of New Jersey, Princeton. - =e c= - . ARTICLE II. Description of an entire Head and various other Bones of the Mastodon. By William E. Horner, M. D., and Isaac Hays, M. D. _ - - - - - = z = - ARTICLE II. On the Cecidomyia Destructor, or Hessian Fly. By Miss M. H. Morris. — - - = ARTICLE IV. Remarks on the Dental System of the Mastodon, with an Account of some Lower Jaws in Mr, Koch’s Collection, St. Louis, Missouri, where there is a solitary Tusk on the right Side. By William E. Horner, M. D., Professor of Anatomy in the University of Pennsylvania. - - . - - - - - - - - - - - Viall_—c 37 49 53 x CONTENTS. ARTICLE V. Observations to determine the Magnetic Intensity at several Places in the United States, with some additional Observations of the Magnetic Dip. By Elias Loomis, Professor of Mathematics and Natural Philosophy in Western Reserve College. — - - - - ARTICLE VI. On the Perchlorate of the Oxide of Ethule or Perchloric Ether. By Clark Hare and Martin H. Boye. - ais - - - = ss - : : - - ARTICLE VII. Observations on the Storm of December 15, 1839. By William C. Redfield, A. M. - ARTICLE VIII. On the Perturbations of Meteors approaching near the Earth. By Benjamin Pierce, A. A., Hollis Professor of Mathematics and Natural Philosophy in Harvard University ; in a Letter to S. C. Walker, Esq. - - - - - - - - - - ARTICLE IX, Researches concerning the Periodical Meteors of August and November. By Sears C. Walker, A.P.S. - - - 2 = E = = ¢ E Z . E ARTICLE X. Astronomical Observations made at Hudson Observatory, Latitude 41° 14’ 40” North, and Longitude 5h. 25m. 45s. West. By Elias Loomis, Professor of Mathematics and Natural Philosophy in Western Reserve College. - - - - - - = = g ARTICLE XI. Expansion of F (x + h). By Pike Powers, of the University of Virginia. = - - ARTICLE XII. Description of New Fresh Water and Land Shells. By Isaac Lea. - - - - 61 77 83 87 163 CONTENTS. ARTICLE XIIl. Description and Notices of new or rare Plants in the natural Orders Lobeliacew, Campanu- lacew, Vacciniex, Ericacezx, collected in a Journey over the Continent of North America, and during a Visit te the Sandwich Islands, and Upper California. By Thomas Nuttall. ARTICLE XIV. Observations on the Geology of the Western Peninsula of Upper Canada, and the Western part of Ohio. By William B. Rogers, Professor of Natural Philosophy in the University of Virginia and Henry D. Rogers, Professor of Geology in the University of Pennsylvania. ARTICLE XV. Observations of the Magnetie Dip in the United States. Fourth Series. By Elias Loomis, Professor of Mathematics and Natural Philosophy in Western Reserve College. - - ARTICLE XVI. Supplementary Observations on the Storm which was Experienced throughout the United States about the 20th of December, 1836. By Elias Loomis, Professor of Mathematics and Natural Philosophy in Western Reserve College, Ohio. - - - - - ARTICLE XVII. Astronomical Observations, made at several Places in the United States. By J. N. Nicollet. ARTICLE XVIIi. Observations of Encke’s Comet, at the High School Observatory, Philadelphia, March and April, 1842, with the Fraunhofer Equatorial. By Sears C. Walker, and E. Otis Kendall. ARTICLE XIX. Observations of the Magnetic Dip, made in the United States, in 1841. By J. N. Nicollet. Donations for the Library'and Cabinet.- - =) -°9 = =) = see 4) ef xi 251 273 285 307 317 am 4 . ; a Fig 2 ioe as SES TEE ict i ap WEEN ese . Sager = Nidded seuee TRANSACTIONS OF THE AMERICAN PHILOSOPHICAL SOCIETY. ARTICLE I. Contributions to Electricity and Magnetism. By Joseph Henry, LL. D. Pro- fessor of Natural Philosophy in the College of New Jersey, Princeton. Read June 19, 1840. No. IV.—On Electro-Dynamic Induction. ( Continued.) INTRODUCTION. 1. In the course of my last paper, it was stated that the investigations which it detailed were not as complete in some parts as I could wish, and that I hoped to develope them more fully in another communication. After considerable delay, occasioned by alterations in the rooms of the physical department of the college, I was enabled to resume my researches, and since then I have been so fortunate as to discover a series of new facts belonging to different parts of the general subject of my contributions. These I have announced to the Society at different times, as they were discovered, and I now purpose to select from the whole such portions as relate particularly to the principal VIII.—A 2 CONTRIBUTIONS TO ELECTRICITY AND MAGNETISM. subject of my last paper, namely, the induction at the beginning and ending of a galvanic current, and to present them as a continuation, and, in a measure, as the completion, of this part of my researches. The other results of my labours in this line will be arranged for publication as soon as my duties will permit me to give them a more careful examination. 2. In the course of the experiments I am about to describe, I have had occa- sion to repeat and vary those given in my last paper, and I am happy to be able to state, in reference to the results, that, except in some minor particulars, which will be noticed in the course of this paper, I have found no cause to desire a change in the accounts before published. My views, however, of the connexion of the phenomena have been considerably modified, and I think rendered much more definite by the additional light which the new facts have afforded. 3. The principal articles of apparatus used in these experiments are nearly the same as those described in my last paper, namely, several flat coils and a number of long wire helices. (III. 6, 7, 8.*) I have, however, added to these a constant battery, on Professor Daniell’s plan, the performance of which has fully answered my expectations, and confirmed the accounts given of this form of the instrument by its author. It consists of thirty elements, formed of as many copper cylinders, open at the bottom, each five inches and a half in height, three inches and a half in diameter, and placed in earthen cups. A zine rod is suspended in each of these, of the same length as the cylinders, and about one inch in diameter. The several elements are connected by a thick copper wire, soldered to the copper cylinder of one element, and dipping into a cup of mercury on the zinc of the next. The copper and zinc as usual are separated by a membrane, on both sides of which is placed a solution of one part of sulphuric acid in ten parts of water; and to this is added, on the side next the copper, as much sulphate of copper, as will saturate the solution. The battery was sometimes used as a single series, with all its elements placed consecutively, and at others in two or three series, arranged collaterally, so as to vary the quantity and intensity of the electricity as the occasion might require. 4. The galvanometers mentioned in this paper, and referred to in the last, are of two kinds; one, which is used with a helix, to indicate the action of an * When the numerals II. or III. are included in the parenthesis, reference is made to the corre- sponding Nos. of my contributions. ON ELECTRO-DYNAMIC INDUCTION. 3 induced current of intensity, consists of about five hundred turns of fine copper wire, covered with cotton thread, and more effectually insulated by steeping the instrument in melted cement, which was drawn into the spaces between the spires by capillary attraction. The other galvanometer is formed of about forty turns of a shorter and thicker wire, and is always used to indicate an induced current, of considerable quantity, but of feeble intensity. The needle of both these instruments is suspended by a single fibre of raw silk. 5. I should also state, that in all cases where a magnetizing spiral is mentioned in connexion with a helix, the article is formed of a long, fine wire, making about one hundred turns around the axis of a hollow piece of straw, of about two inches and a half long: also the spiral mentioned in connexion with a coil, is formed of a short wire, which makes about twenty turns around a similar piece of straw. The reason of the use of the two instruments in, these two cases is the same as that for the galvanometers, under similar circumstances, namely, the helix gives a current of intensity, but of small quantity, while the coil produces one of considerable quantity, but of feeble intensity. Section I. Onthe Induction produced at the moment of the Beginning of a Galvanic Current, &. 6. It will be recollected that the arrangement of apparatus employed in my last series of experiments gave a powerful induction at the moment of breaking the galvanic circuit, but the effect at making the same was so feeble as scarcely to be perceptible. I was unable in any case to get indications of currents of the third or fourth orders from the beginning induction, and its action was therefore supposed to be so feeble as not materially to affect the results ob- tained. 7. Subsequent reflection, however, led me to conclude, that in order to com- plete this part of my investigations, a more careful study of the mduction at the beginning of the current would be desirable, and accordingly, on resuming the experiments, my attention was first directed to the discovery of some means by which the intensity of this induction might be increased. After some pre- liminary experiments, it appeared probable that the desired result could be ob- tained by using a compound galvanic battery, instead of the single one before employed. In reference to this conjecture the constant battery before men- tioned (3) was constructed, and a series of experiments instituted with it, the results of which agreed with my anticipation. 4 CONTRIBUTIONS TO ELECTRICITY AND MAGNETISM. 8. In the first experiment, coil No. 2, which it will be remembered (III. 7) consists of a copper riband of about sixty feet long, and coiled on itself like the main spring of a watch, was connected with the compound battery and helix No. 1, (III. 8,) formed of one thousand six hundred and sixty yards of fine copper wire, and was placed on the coil to receive the induction, as is shown in figure 3, which is again inserted here for the convenience of the reader. Fig. 3. This arrangement being made, amd currents of increasing intensity ¢ were passed through the coil by constantly retaining one of its $=). SSS by ’}?§. SS ends in the cup of mercury form- = = ZZ) = ing one extremity of the battery, a represents coil No. 1, b helix No. 1, and ¢, d, handles aq successively plunging the vaclmiaitinh canasy gies: other end into the cups which served to form the connexions of the several elements of the battery. With the current from one element, the shock at breaking the circuit was quite severe, but at making the same it was very feeble, and could be perceived in the fingers only or through the tongue. With two elements in the circuit, the shock at beginning was slightly increased; with three elements the increase was more decided, while the shock at breaking the circuit remained nearly of the same intensity as at first, or was comparatively but little increased. When the number of elements was increased to ten, the shock at making contact was found fully equal to that at breaking, and by employing a still greater number, the former was decidedly greater than the latter, the difference continually increasing until all the thirty elements were introduced into the circuit. 9. In my last paper, a few experiments are mentioned as being made with a compound battery of Cruickshank’s construction; but from the smallness of the plates of this, and the rapidity with which its power declined, I was led into the error of supposing that the induction at the ending of the current, in the case of a short coil, was diminished by increasing the intensity of the bat- tery, (see paragraph 19, of No. 3,) but by employing the more perfect instru- ment of Professor Daniell in the arrangement of the last experiment, I am enabled to correct this error, and to. state that the induction at the ending re- mains nearly the same, when the intensity of the battery is increased. If the induction depends in any degree on the quantity of current electricity in the ON ELECTRO-DYNAMIC INDUCTION. 5 conductor, then a slight increase in the induction should take place, since, according to theory, the current is somewhat increased in quantity, in the case of a long coil, by the increase of the intensity of the battery. Although very little, if any, difference could be observed in the intensity of the shock from the secondary current, yet the snap and deflagration of the murcury appeared to be greater from the primary current, when ten elements of the battery were included in the circuit, than with a single one. The other results which are mentioned in my last paper in reference to the compound battery are, I believe, correctly given. 10. The intensity of the different shocks in the foregoing experiments was compared by gradually raising the helix from the coil, (see Fig. 3,) until, on account of the distance of the conductors, the shock in one case would be so much reduced as to be scarcely perceptible through the fingers or the tongue, while the shock from another arrangement, but with the same distance of the conductors, would be evident, perhaps, in the hands. ‘The same method was generally employed in the experiments in which shocks are mentioned as being compared, in the other parts of this paper. 11. Experiments were next made to determine the influence of a variation in the length of the coil, the intensity of the battery remaining the same. For this purpose, the battery consisting of a'single element, and the arrangement of the apparatus as represented in Fig. 3, the coil was diminished in length from sixty feet to forty-five, then to thirty, and so on. With the first men- tioned length the shock, at making contact with the battery, was, of course, very feeble, and could be felt only in the tongue; with the next shorter length it was more perceptible, and increased in intensity with each diminution of the coil, until a length of about fifteen feet appeared to give 2 maximum result. 12. The diminution of the intensity of the shock in the last experiment, after the length of the coil was diminished below fifteen feet, was due to the diminu- tion of the number of spires of the coil, each of which, by acting on the helix, tends to increase the intensity of the secondary current, unless the combined length of the whole is too great for the intensity of the battery. That this is the fact is shown by the following experiment: the helix was placed on a single spire or turn of the coil, and the length of the other part of the copper riband, which did not act on the helix, was continually shortened, until the whole of it was excluded from the circuit; in this case the intensity of the shock at the Vilr—s 6 CONTRIBUTIONS TO ELECTRICITY AND MAGNETISM. beginning was constantly increased. We may therefore state generally, that, at the beginning of the battery current, the induction of a unit of its length is increased by every diminution of the length of the conductor. 13. In the experiment given in paragraph 11, the intensity of the shock at the ending of the battery current diminishes with each diminution of the length of the coil; and this is also due to the decrease of the number of the spires of the coil, as is evident from an experiment similar to the last, in which the helix was placed ona coil consisting of only two turns or spires of copper riband; the shock at the ending, with this arrangement, was comparatively feeble, but could be felt in the hands. Different lengths of coil No. 2 were now intro- duced into the same circuit, but not so as to act on the helix; but although these were varied from four or five feet to the whole length of the coil, (sixty feet,) not the least difference in the intensity of the shock could be perceived. We have, therefore, the remarkable result, that the intensity of the ending in- duction of each unit of length of the battery current is not materially altered, at least within certain limits, by changing the length of the whole conductor. From this we would infer that the shock depends more on the intensity of the action than on the quantity of the current, since we know that the latter is di- minished in a given unit of the conductor by increasing the length of the whole. 14. We have seen (8) that with a circuit composed of ten elements of the compound battery and the coil No. 2, the shock, at the beginning of the cur- rent, was fully equal to that at the ending. It was, however, found that if, in this case, the length of the coil was increased, this shock was diminished; and we may state, as an inference from several experiments, that however great may be the intensity of the electricity from the battery, the shock at the be- ginning may be rendered scarcely perceptible by a sufficient increase of the length of the primary circuit. 15. It was also found that when the thickness of the coil was increased, the length and intensity of the circuit remaining the same, the shock at the beginning of the battery current was somewhat increased. This result was produced by using a double coil; the electricity was made to pass through one strand, and immediately afterwards through both: the shock from the helix in the latter case was apparently the greater. 16. By the foregoing results we are evidently furnished with two methods ON ELECTRO-DYNAMIC INDUCTION. 7 of increasing, at pleasure, the intensity of the induction at the beginning of a battery current, the one consisting in increasing the intensity of the source of the electricity, and the other in diminishing the resistance to conduction of the circuit while its intensity remains the same. 17. The explanation of the effects which we have given, relative to the in- duction at the beginning, is apparently not difficult. The resistance to con- duction in the case of a long conductor and a battery of a single element is so great that the full development of the primary current may be supposed not to take place with sufficient rapidity to produce the instantaneous action on which the shock from the secondary current would seem to depend. But when a battery of a number of elements is employed, the poles of this, previous to the moment of completing the circuit, are in a state of electrical tension; and there- fore the discharge through the conductor may be supposed to be more sudden, and hence an induction of more intensity is produced. 18. That the shock at both making and breaking the circuit in some way depends on the rapidity of formation and diminution of the current is shown by the following experiment, in which the tension just mentioned does not take place, and in which, also, the current appears to diminish more slowly. The two ends of the coil were placed in the two cups which formed the poles of the battery, and permanently retained there during the experiment; also, at the distance of about six inches from, say the right hand end of the coil, a loop was made in the riband, which could be plunged into the cup containing the left hand end. With this arrangement, and while only the two extreme ends of the coil were in connexion with the cups of mercury, of course the current passed through the entire length of the riband of the coil, but by plunging the loop into the left hand cup, the whole length of the coil, except the six inches before mentioned, was excluded from the battery circuit. And again, when the loop was lifted out of the cup, the whole length was included. In this way the current in the coil could be suddenly formed and interrupted, while the poles of the battery were continually joined by a conductor, but no shock with either a single or a compound battery could be obtained by this method of operation. 19. The feebleness of the shock at the beginning of the current, with a sin- gle battery and a long coil, is not entirely owing to the cause we have stated, (17,) namely, the resistance to conduction offered by the long conductor, but 8 CONTRIBUTIONS TO ELECTRICITY AND MAGNETISM. also depends, in a considerable degree, if not principally, on the adverse in- fluence of the secondary current, induced in the primary conductor itself, as is shown by the result of the following experiment. Helix No. 1 was placed on a coil consisting of only three spires or turns of copper riband; with this, the shock both at making and breaking the circuit with a single battery could be felt in the hands. A compound coil was then formed of the copper ribands of coils No. 3 and 4 rolled together so that the several spires of the two alternated with each other, and when this was introduced into the circuit so as not to act on the helix by its induction, and the battery current passed through, for example, coil No. 3, the shock at making contact with the pole of the battery was so much reduced as to be imperceptible in the hands, while the shock at breaking the contact was about the same as before this addition was made to the length of the circuit. ‘The ends of coil No. 4 were now joined so as to pro- duce a closed circuit, the induced current in which would neutralize the se- condary current in the battery conductor itself; and now the shock at making the contact was nearly as powerful as in the case where the short conductor alone formed the circuit with the battery. Hence, the principal cause of the feebleness of the effect at the beginning of the battery current is the adverse action on the helix of the secondary current produced in the conductor of the battery circuit itself. ‘The shock at the breaking of the circuit, in this experi- ment, did not appear affected by joining or separating the ends of coil No. 4. 20. Having investigated the conditions on which the inductive action at the beginning of a battery current depends, experiments were next instituted to determine the nature of the effects produced by this induction: and first the coils were arranged in the manner described in my last paper, (III. 79,) for producing currents of the different orders. The result with this was similar to that which I have described in reference to the ending induction, namely, currents of the third, fourth, and fifth orders were readily obtained. 21. Also, when an arrangement of apparatus was made similar to that de- scribed in paragraph 87 of my last paper, it was found that a current of in- tensity could be induced from one of quantity and the converse. 22. Likewise, the same screening or rather neutralizing effect was produced, when a plate of metal was interposed between two consecutive conductors of the series of currents, as was described (III. section IV.) in reference to the ending induction. In short, the series of induced currents produced at the be- ON ELECTRO-DYNAMIC INDUCTION. &) ginning of the primary current appeared to possess all the properties belonging to those of the induction at the ending of the same current. 23. I may mention, in this place, that I have found, in the course of these experiments, that the neutralizing power of a plate of metal depends, in some measure, on its superficial extent. ‘Thus a broad plate which extends, in every direction, beyond the helix and coil, produces a more perfect screening than one of the same metal and of the same thickness, but of a diameter only a little greater than that of the coil. 24. The next step in the investigation was to determine the direction of the currents of the different orders produced by the beginning induction, and for this purpose the magnetizing spirals (5) were used, and the results obtained by these verified by the indications of the galvanometer. It should be stated here, as a fact which was afterward found of some importance, that although the needle of the galvanometer was powerfully deflected when the instrument was placed in the circuit of the secondary current, yet a very feeble effect was produced on it by the action of a current of the third, fourth, or fifth order. The directions, however, of these currents, as indicated by the feeble motion of the needle, were the same as those given by the magnetizing spiral. 25. The direction of the different currents produced at the making of the battery current, as determined by these instruments, is as follows, namely : the direction of the secondary current is, as stated by Dr. Faraday, adverse to that of the primary current, and, also, the direction of each succeeding current is opposite to that of the one which produced it. We have, therefore, from these results, and those formerly obtained, (III. 92,) the following series of di- rections of currents, one produced at the moment of beginning, and the other at that of ending of the battery current. At the Beginning. At the Ending. Primary. current, 5. = tp. vnae + TAA ae + Secondary current, . .. . — a ig crcta Gs + Current of the third order, . . of gta Oe: — Current of the fourth order, —. — sist @ + Current of the fifth order, . . ap Nee ht = 26. These two series, at first sight, may appear very different, but, with a little attention, they will be seen to be of the same nature. If we allow that VIII.—Cc 10 CONTRIBUTIONS TO ELECTRICITY AND MAGNETISM. the induction at the ending of a galvanic battery should be opposite to that at the beginning of the same, then the sign at the top of the second column may be called minus instead of plus, and we shall have the second series — + — + alternating precisely like the first. 27. In connexion with the results given in the last two paragraphs, it is due to Mr. Sturgeon that I should state that, in a letter addressed to me, and pub- lished in the Annals of Electricity, he has predicted, from his theory, that I would find, on examination, the series of alternation of currents for the begin- ning induction which I have here given. I may, however, add, that it appears to me that this result might have been predicted without reference to any the- ory. There was no reason to suppose the induction at the beginning would be different in its nature from that at the ending, and therefore the series which would be produced from the former might be immediately inferred from that belonging to the latter, by recollecting that the direction of the induction at the beginning should be opposite to that at the ending. I do not wish it to be supposed, however, from this remark, that I had, myself, drawn any infe- rence from my experiments as to the alternations of currents which might be produced by the beginning induction; the truth is, that this action was so feeble with the arrangement of apparatus I employed, that I supposed it could not produce a series of currents of the different orders. 28. In the course of the experiments given in this section, I have found that a shock can be produced without using a coil, by arranging about ten elements of the battery in the form of a circle, and placing the helix within this. The shock was felt in the hands at the moment of closing the circuit, but the effect at opening the same was scarcely perceptible through the tongue. An attempt was also made to get indications of induction by placing the helix within a cir- cle of dilute acid, connected with a battery instead of a coil, but the effect, if any, was very feeble. 29. I have shown, in the second number of my contributions, that if the body be introduced into a circuit with a battery of one hundred and twenty elements, without a coil, a thrilling sensation will be felt durimg the continu- ON ELECTRO-DYNAMIC INDUCTION. 11 ance of the current, and a shock will be experienced at the moment of inter- rupting the current by breaking the circuit at any point. This result is evi- dently due to the induction of a secondary current in the battery itself, and on this principle the remarkable physiological effects produced by Dr. Ure, on the body of a malefactor, may be explained. ‘The body, in these experiments, was made to form a part of the circuit, with a compound galvanic apparatus in which a series of interruptions was rapidly made by drawing the end of a con- ductor over the edges of the plates of the battery. By this operation a series of induced currents must have been produced in the battery itself, the intensity of which would be greater than that of the primary current. 30. In this connexion I may mention that the idea has occurred to me that the intense shocks given by the electrical fish may possibly be from a secondary current, and that the great amount of nervous organization found in these animals may serve the purpose of a long conductor.* It appears to me, that in the present state of knowledge, this is the only way in which we can con- ceive of such intense electricity being produced in organs imperfectly insulated and immersed in a conducting medium. But we have seen that an original current of feeble intensity can induce, in a long wire, a secondary current capable of giving intense shocks, although the several strands of the wire are separated from each other only by a covering of cotton thread. Whatever may be the worth of this suggestion, on which I place but little value, the secondary current affords the means of imitating the phenomena of the shock from the electrical eel, as described by Dr. Faraday. By immersing the apparatus (Fig. 3) in a shallow vessel of water, the handles being placed at the two ex- tremities of the diameter of the helix, and the hands plunged into the water parallel to a line joining the two poles, a shock is felt through the arms; but when the contact with the water is made in a line at right angles to the last, only a slight sensation is felt in each hand, but no shock. 31. Since the publication of my last paper, I have exhibited to my class the experiment (No. III. Sec. 3d) relative to the induction at a distance on a much larger scale. All my coils were united so as to form a single length of conductor of about four hundred feet, and this was rolled into a ring of five and a half feet in diameter, and suspended vertically against the inside of the large folding * Since writing the above, I have found that M. Masson has suggested the same idea, in an interesting thesis lately published. 12 CONTRIBUTIONS TO ELECTRICITY AND MAGNETISM. doors which separate the laboratory from the lecture room. On the other side of the doors, in the lecture room, and directly opposite the coil, was placed a helix, formed of upwards of a mile of copper wire, one sixteenth of an inch in thickness, and wound into a hoop of four feet in diameter. With this arrange- ment, and a battery of one hundred and forty-seven square feet of zinc surface divided into eight elements, shocks were perceptible in the tongue, when the two conductors were separated, to the distance of nearly seven feet; at the distance of between three and four feet, the shocks were quite severe. ‘The exhibition was rendered more interesting by causing the induction to take place through a number of persons standing in a row between the two conductors. Section IT. On apparently two kinds of Electro-dynamic Induction. 32. The investigations arranged under this head had their origin in the following circumstances. After the publication of my last paper, I received, through the kindness of Dr. Faraday, a copy of the fourteenth series of his researches, and in this I was surprised to find a statement which appeared in direct opposition to one of the principal facts of my communication. In para- graph 59, I state, in substance, that when a plate of metal is interposed between the coil transmitting a galvanic current, and the helix placed above it to receive the induction, the shock from the secondary current is almost perfectly neutral- ized. Dr. Faraday, in the extension of his new and ingenious views of the agency of the intermediate particles in transmitting induction, was led to make an experiment on the same point, and apparently, under the same circumstances, he found that it ‘makes not the least difference, whether the intervening space between the two conductors is occupied by such insulating bodies as air, sulphur, and shell-lac, or such conducting bodies as copper and other non-magnetic metals.” 33. As the investigation of the fact mentioned above forms an important part of my paper, and is intimately connected with almost all the phenomena sub- sequently described in the communication, I was, of course, anxious to discover the cause of so remarkable a discrepancy. ‘There could be no doubt of the truth of my results, since a shock from a secondary current which would para- lyze the arms was so much reduced by the interposition of plates of metal as scarcely to be felt through the tongue. 34. After some reflection, however, the thought occurred to me that induction ON ELECTRO-DYNAMIC INDUCTION, 13 might be produced in such a way as not to be affected by the interposition of a plate of metal. ‘To understand this, suppose the end of a magnetic bar placed perpendicularly under the middle of a plate of copper, and a helix suddenly brought down on this; an induced current would be produced in the helix by its motion towards the plate, since the copper, in this case, could not screen the magnetic influence. Now, if we substitute for the magnet a coil through which a galvanic current is passing, the effect should be the same. The experiment was tried by attaching the ends of the helix to a galvanometer,* and the result was, as I expected: when the coil was suddenly brought down on the plate the needle swung in one direction and when lifted up, in the other; the amount of deflection being the same, whether the plate was interposed or not. 35. It must be observed in this experiment, that the plate was at rest, and consequently did not partake of the induction produced by the motion of the helix. From my previous investigations, I was led to conclude that a different result would follow, were a current also generated in the plate by simultaneously moving it up and down with the helix. This conclusion, however, was not correct, for on making the experiment, I found that the needle was just as much affected when the plate was put in motion with the helix as when the latter alone was moved. 36. This result was so unexpected and remarkable, that it was considered necessary to repeat and vary the experiment in several ways. First, a coil was interposed instead of the plate, but whether the coil was at rest or in motion with the helix, with its ends separated or joined, the effect on the gal- vanometer was still the same; not the least screening influence could be observed. In reference to the use of the coil in this experiment, it will be recollected that I have found this article to produce more perfect neutralization than a plate. 37. Next, the apparatus remaining the same, and the helix at rest during the experiment, currents were induced in it by moving the battery attached to the coil up and down in the acid. But in this case, as in the others, the effect on the galvanometer was the same, whether the plate or the coil was interposed or not. 38. The experiment was also tried with magneto-electricity. For this pur- pose, about forty feet of copper wire, covered with silk, were wound around a * The arrangement will be readily understood by supposing in Fig. 8, the handles removed, and the ends of the helix joined to the ends of the wire of a galvanometer; also, by a plate of metal interposed between the helix and the coil. VIII.—-D 14 CONTRIBUTIONS TO ELECTRICITY AND MAGNETISM. short cylinder of stiff paper, and into this was inserted a hollow cylinder of sheet copper, and into this again, a short rod ot’ soft iron; when the latter was rendered magnetic, by suddenly bringing in contact with its two ends the different poles of two magnets, a current, of course, was generated in the wire, and this, as before, was found to affect the galvanometer to the same degree, when the copper cylinder was interposed, as when nothing but the paper intervened. 39. The last experiment was also varied by wrapping two copper wires of equal length around the middle of the keeper of a horse-shoe magnet, leaving the ends of the inner one projecting, and those of the outer attached to a galva- nometer. A current was generated in each by moving the keeper on the ends of the magnet, but the effect on the galvanometer was not in the least dimi- nished by joining the ends of the inner wire. 40. At first sight, it might appear that all these results are at variance with those detailed in my last paper, relative to the effect of interposed coils and plates of metal. But it will be observed that in all the experiments just given, the induced currents are not the same as those described in my last commu- nication. They are all produced by motion, and have an appreciable duration, which continues as long as the motion exists. ‘They are also of low intensity, and thus far I have not been able to get shocks by any arrangement of appa- ratus from currents of this kind. On the other hand, the currents produced at the moment of suddenly making or breaking a galvanic current, are of con- siderable intensity, and exist but for an instant. From these, and other facts presently to be mentioned, I was led to suppose that there are two kinds of electro-dynamic induction; one of which can be neutralized by the interposition of a metallic plate between the conductors and the other not. 41. In reference to this surmise, it became important to examine again all the phenomena of induction at suddenly making and breaking a galvanic current. And in connexion with this part of the subject, I will first mention a fact which was observed in the course of the experiments given in the last section, on the direction of the induced currents of different orders. It was found that though the indications of the galvanometer were the same as those of the spiral, in reference to the direction of the induced currents, yet they were very dif- ferent in regard to the intensity of the action. Thus, when the arrangement of the apparatus was such that the induction at making the battery circuit was so feeble as not to give the least magnetism to the needle, and so powerful ON ELECTRO-DYNAMIC INDUCTION. 15 at the ending as to magnetize it to saturation, the indication of the galvanometer was the same in both cases. 42. Also, similar results were obtained in comparing the shock and the de- flection of the galvanometer. In one experiment, for example, the shock was so feeble at making contact that it could scarcely be perceived in the fingers, but so powerful at the breaking of the circuit as to be felt in the breast; yet the galvanometer was deflected about thirty-five degrees to the right, at the begin- ning of the current, and only an equal number of degrees to the left, at the ending of the same. 43. In another experiment, the apparatus being the same as before, the mag- netizing spiral and the galvanometer were both at once introduced into the cir- cuit of the helix. A sewing needle being placed in the spiral, and the contact with the battery made, the needle showed no signs of magnetism, although the galvanometer was deflected thirty degrees. The needle being replaced, and the battery circuit broken, it was now found strongly magnetized, while the valvanometer was only moved about as much as before in the opposite direc- tion. 44. Also, effects similar to those described in the last two paragraphs were produced when the apparatus was so arranged as to cause the induction at the beginning of the battery current to predominate. In this case the galvanome- ter was still nearly equally affected at making and breaking battery contact, or any difference which was observed could be referred to a variation in the power of the battery during the experiment. 45. Another fact of importance belonging to the same class has been men- tioned before, (24,) namely, that the actions of the currents of the third, fourth, and fifth orders produced a very small effect on the galvanometer, compared with that of the secondary current; and this is not alone on account of the di- minishing power of the successive inductions, as will be evident from the fol- lowing experiment. By raising the helix from the coil, in the arrangement of apparatus for the secondary current, the shock was so diminished as to be in- ferior to one produced by the arrangement for a tertiary current, yet, while with the secondary current the needle was deflected twenty-five degrees, with the tertiary it scarcely moved more than one degree; and with the currents of the fourth and fifth orders the deflections were still less, resembling the effect of a slight impulse given to the end of the needle. 46. With the light obtained from the foregoing experiments, I was led to 16 CONTRIBUTIONS TO ELECTRICITY AND MAGNETISM. suppose that some new and interesting results might be obtained by a re-exa- mination of my former experiments, on the phenomena of the interposed plate of metal, in the case where the induction was produced by making and break- ing the circuit with a cup of mercury; and in this I was not disappointed. The coil (Fig. 3) being connected with a battery of ten elements, the shocks, both at making and breaking the circuit, were very severe; and these, as usual, were almost entirely neutralized by the interposition of the zinc plate. But when the galvanometer was introduced into the circuit instead of the body, its indications were the same whether the plate was interposed or not; or, in other words, the galvanometer indicated no screening, while, under the same circum- stances, the shocks were neutralized. 47. A similar effect was observed when the galvanometer and the magnet- izing spiral were together introduced into the circuit. The interposition of the plate entirely neutralized the magnetizing power of the spiral, in reference to tempered steel, while the deflections of the galvanometer were unaffected. 48. In order to increase the number of facts belonging to this class, the last experiments were varied in several ways; and first, instead of the hard steel needle, one of soft iron wire was placed in the spiral, with a small quantity of iron filings almost in contact with one of itsends. The plate being interposed, the small particles of iron were attracted by the end of the needle, indicating a feeble, temporary development of magnetism. Hence the current which moves the needle, and is not neutralized by the interposed plate, also feebly magnetizes soft iron, but not hard steel. 49. Again, the arrangement of apparatus being as in paragraph 46, instead of a plate of zinc, one of cast iron, of about the same superficial dimensions, but nearly half an inch thick, was interposed; with this the magnetizing power of the spiral, in reference to tempered steel, was neutralized ; and, also, the action of the galvanometer was much diminished. 50. Another result was obtained by placing in the circuit of the helix, (Fig. 3d,) at the same time, the galvanometer, the spiral, and a drop of distilled water; with these the magnetizing power of the spiral was the same as with- out the water, but the deflection of the galvanometer was reduced from ten to about four degrees. In addition to these, the body was also introduced into the same circuit; the shocks were found very severe, the spiral magnetized needles strongly, but the galvanometer was still less moved than before. The current of low intensity, which deflects the needle of the galvanometer in ON ELECTRO-DYNAMIC INDUCTION. U7 these instances was partially intercepted by the imperfect conduction of the water and the body. 51. To exhibit the results of these experiments with still more precision, an arrangement of apparatus was adopted similar to that used by Dr. Faraday, and described in the fourteenth series of his researches, namely, a double gal- vanometer was formed of two separate wires of equal length and thickness, and wound together on the same frame; and, also, a double magnetizing spiral was prepared by winding two equal wires around the same piece of hollow straw- Coil No. 1, connected with the battery, was supported perpendicularly on a table, and coils Nos. 3 and 4 were placed parallel to this, one on each side, to receive the induction, the ends of these being so joined with those of the gal- vanometer and the spiral that the induced current from the one coil would pass through the two instruments, in an opposite direction to that of the cur- rent from the other coil. The two outside coils were then so adjusted, by moving them to and from the middle coil, that the induced currents perfectly neutralized each other in the two instruments, and the needle of the galvano- meter and that in the spiral were both unaffected when the circuit of the bat- tery was made and broken. With this delicate arrangement the slightest dif- ference in the action of the two currents would be rendered perceptible; but when a zinc plate was introduced so as to screen one of the coils, the needle of the galvanometer still remained perfectly stationary, indicating not the least action of the plate, while the needle in the spiral became powerfully magnetic. When, however, a plate of iron was interposed instead of the one of zinc, the needle of the galvanometer was also affected. 52. From the foregoing results it would seem that the secondary current, produced at the moment of suddenly beginning or ending of a galvanic cur- rent, by making and breaking contact with a cup of mercury, consists of two parts, which possess different properties. One of these is of low intensity, can be interrupted by a drop of water, does not magnetize hardened steel needles, and is not screened by the interposition of a plate of any metal, except iron, between the conductors. The other part is of considerable intensity, is not intercepted by a drop of water, develops the magnetism of hardened steel, gives shocks, and is screened or neutralized by a closed coil, or a plate of any kind of metal. Also, the induced current produced by moving a conductor towards VIII. —E 18 CONTRIBUTIONS TO ELECTRICITY AND MAGNETISM. or from a battery current, and that produced by the movement up and down of a battery in the acid, are of the nature of the first mentioned part, while the currents of the third, fourth, and fifth orders partake almost exclusively of the properties of the second part. 53. The principal facts and conclusions of this section were announced to the Society in October, 1839, and again presented in the form in which they are here detailed in June last. Since then, however, I have had leisure to ex- amine the subject more attentively, and after a careful comparison of these re- sults with those before given, I have obtained the more definite views of the phenomena which are given in the next section. Section III. Theoretical Considerations relating to the Phenomena described in this and the preceding Communications. Read November 20, 1840. 54. The experiments given in the last No. of my contributions were merely arranged under different heads, and only such inferences drawn from them as could be immediately deduced without reference to a general explanation. The addition, however, which I have since made to the number of facts, affords the means of a wider generalization; and after an attentive consideration of all the results given in this and the preceding papers, I have come to the conclusion that they can all be referred to the simple laws of the induction at the begin- ning and the ending of a galvanic current. 55. In the course of these investigations the limited hypotheses which I have adopted have been continually modified by the development of new facts, and therefore my present views, with the farther extension of the subject, may also require important corrections. But I am induced to believe, from its exact ac- cordance with all the facts, so far as they have been compared, that if the ex- planation I now venture to give be not absolutely true, it is so, at least, in ap- proximation, and will therefore be of some importance in the way of suggesting ON ELECTRO-DYNAMIC INDUCTION. 19 new forms of experiment, or as a first step towards a more perfect generali- zation. 56. To render the laws of induction at the beginning and the ending of a galvanic current more readily applicable to the explanation of the phenomena, they may be stated as follows:—1. During the time a galvanic current is in- creasing in quantity in a conductor, it induces, or tends to induce, a current in an adjoiming parallel conductor in an opposite direction to itself. 2. During the continuance of the primary current in full quantity, no inductive action is exerted. 3. But when the same current begins to decline in quantity, and during the whole time of its diminishing, an induced current is produced in an opposite direction to the induced current at the beginning of the primary current. 57. In addition to these laws, I must frequently refer to the fact, that when the same quantity of electricity in a current of short duration is passed through a galvanometer, the deflecting force on the needle is the same, whatever be the in- tensity of the electricity. By intensity is here understood the numerical ratio of a given quantity of force to the time in which it is expended; and according to this view, the proposition stated is an evident inference from dynamic prin- ciples. But it does not rest alone on considerations of this kind, since it has been proved experimentally by Dr. Faraday, in the third series of his re- searches. 58. In order to form a definite conception of the several conditions of the complex phenomena which we are about to investigate, I have adopted the method often employed in physical inquiries, of representing the varying ele- ments of action by the different parts of a curve. This artifice has been of much assistance to me in studying the subject, and without the use of it at present, I could scarcely hope to present my views in an intelligible manner to the Society. 59. After making these preliminary statements, we will now proceed to con- sider the several phenomena; and, first, let us take the case in which the in- duction is most obviously produced in accordance with the laws as above stated, (56,) namely, by immersing a battery into the acid, and also by with- drawing it from the same. During the time of the descent of the battery into the liquid, the conductor connected with it is constantly receiving additional quantities of current electricity, and each of these additions produces an induc- 20 CONTRIBUTIONS TO ELECTRICITY AND MAGNETISM. tive action on the adjoining secondary conductor. The amount, therefore, of induced current produced during any moment of time will be just in propor- tion to the corresponding increase in the current of the battery during the same moment. Also, the amount of induction during any moment while the cur- rent of the battery is diminishing in quantity will be in proportion to the de- crease during the same moment. 60. The several conditions of this experiment may be represented by the different parts of the curve, A, B, C, D, Fig. 17, in which the distances, Aa, Ab, Ac, represent the times during which the battery is descending to differ- ent depths into the acid; and the corresponding ordinates, ag, bh, eB, repre- sent the amount of current electricity in the battery conductor corresponding to these times. The differences of the ordinates, namely, ag, mh, nB, express the increase in the quantity of the battery current during the corresponding moments of time represented by Aa, ab, be; and since the inductive actions (59) are just in proportion to these increases, the same differences will also re- present the amount of induced action exerted on the secondary conductor during the same moment of time. 61. When the battery is fully immersed in the acid, or when the current in the conductor has reached its state of maximum quantity, and during the time of its remaining constant, no induction is exerted; and this condition is ex- pressed by the constant ordinates of the part of the curve BC, parallel to the axis. Also, the inductive action produced by each diminution of the battery current, while the apparatus is in the progress of being drawn from the acid, will, in a like manner, be represented by the differences of the ordinates at the other end, CD, of the curve. 62. The sum of the several increasements of the battery current, up to its full development, will be expressed by the ordinate cB, and this will, there- fore, also represent the whole amount of inductive action exerted in one direc- tion at the beginning of the primary current; and, for the same reason, the ON ELECTRO-DYNAMIC INDUCTION. Q1 equal ordinate, Cd, will represent the whole induction in the other direction at the ending of the same current. Also, the whole time of continuance of the inductive action at the beginning and ending will be represented by Ac and dD. 63. If we suppose the battery to be plunged into the acid to the same depth, but more rapidly than before, then the time represented by Ac will be dimi- nished, while the whole amount of inductive force expended remains the same; hence, since the same quantity of force is exerted in a less time, a greater in- tensity of action will be produced, (57,) and consequently a current of more in- tensity, but of less duration, will be generated in the secondary conductor. The relative intensity of the induced currents will, therefore, evidently be ex- pressed by the ratio of the ordinate cB to the abscissa Ac. Or, in more gene- ral and definite terms, the intensity of the inductive action at any moment of time will be represented by the ratio of the rate of increase of the ordinate to that of the abscissa for that moment.* 64. It is evident from the last paragraph, that the greater or less intensity of the inductive action will be immediately presented to the eye, by the greater or less obliquity of the several parts of the curve to the axis. Thus, if the battery be suddenly plunged into the acid for a short distance, and then gradu- ally immersed through the remainder of the depth, the varying action will be exhibited at once by the form cf AB, the first part of the curve, Fig. 17. The steepness of the part Ag will indicate an intense action for a short time Aq, while the part gB denotes a more feeble induction during the time represented by ac. In the same way, by drawing up the battery suddenly at first, and afterwards slowly, we may produce an inductive action such as would be re- presented by the parts between C and D of the ending of the curve. 65. Having thus obtained representations of the different elements of action, we are now prepared to apply these to the phenomena. And, first, however varied may be the intensity of the induction expressed by the different parts of the two ends of the curve, we may immediately infer that a oalvanometer, * According to the differential notation, the intensity will be expressed by wv - Insome cases the dx effect may be proportional to the intensity multiplied by the quantity, and this will be expressed by 2 . = x and y representing, as usual, the variable abscissa and ordinate. Ei Vilt.==F 22 CONTRIBUTIONS TO ELECTRICITY AND MAGNETISM. placed in the circuit of the secondary conductor, will be equally affected at the beginning and ending of the primary current; for, since the deflection of this instrument is due to the whole amount of a current, whatever may be its intensity, (57,) and since the ordinates cB and Cd are equal, which represent the quantity of induction in the two directions, and, consequently, the amount of the secondary current, therefore the deflection at the begin- ning and ending of the battery current will, in all cases, be equal. This inference is in strict accordance with the results of experiment; for, however rapidly or slowly we may plunge the battery into the acid, and however irregular may be the rate at which it is drawn out, still, if the whole effect be produced within the time of one swing of the needle, the galvanometer is deflected to an equal degree. 66. Again, the intensity of one part of the inductive action, for example that represented by Ag, may be supposed to be so great as to produce a secondary current capable of penetrating the body, and of thus producing a shock * while the other parts of the action, represented by gB and CD, are so feeble as to affect the galvanometer only. We would then have a result the same as one of those given in the last section, (42,) and which was supposed to be produced by two kinds of induction; for if the shock were referred to as the test of the existence of an induced current, one would be found at the beginning only of the battery current, while, if the galvanometer were consulted, we would per- ceive the effects of a current as powerful at the ending as at the beginning. 67. The results mentioned in the last paragraph cannot be obtained by plunging a battery into the acid; the formation of the current in this way is not sufficiently rapid to produce a shock. The example was given to illustrate the manner in which the same effect is supposed to be produced, in the case of the more sudden formation of a current, by plunging one end of the con- ductor into a cup of mercury permanently attached to a battery already in the acid, and in full operation. The current, in this case, rapid as may be its de- velopment, cannot be supposed to assume per saltum its maximum state of quantity; on the contrary, from the general law of continuity we would infer, that it passes through all the intermediate states of quantity, from that of no current, if the expression may be allowed, to one of full development; there are, however, considerations of an experimental nature which would lead us * The shock depends more on the intensity than on the quantity. See paragraph 13. ON ELECTRO-DYNAMIC INDUCTION. 23 to the same conclusion, (18,) (90,) and also to the farther inference that the decline of the current is not instantaneous. According to this view, therefore, the induc- tive actions at the beginning and the ending of a primary current, of which the formation and interruption is effected by means of the contact with a cup of mercury, may also be represented by the several parts of the curve, Fig. 17. 68. We have now to consider how the rate of increase or diminution of the current, in the case in question, can be altered by a change in the different parts of the apparatus; and, first, let us take the example of a single battery and a short conductor, making only one or two turns around the helix; with this arrangement a feeble shock, as we have seen, (11,) will be felt at the making, and also at the breaking of the circuit. In this case it would seem that almost the only impediment to the most rapid development of the current would be the resistance to conduction of the metal; and this we might sup- pose would be more rapidly overcome by increasing the tension of the electri- city ; and, accordingly, we find that if the number of elements of the battery be increased, the shock at making the circuit will also be increased, while that at breaking the circuit will remain nearly the same. To explain, however, this effect more minutely, we must call to mind the fact before referred to, (17,) that when the poles of a compound battery are not connected, the apparatus acquires an accumulation of electricity, which is discharged at the first mo- ment of contact, and which, in this case, would more rapidly develope the full current, and hence produce the more intense action on the helix at making the circuit. 69. The shock, and also the deflection of the needle, at breaking the circuit with a compound battery and a short coil, (9,) appears nearly the same as with a battery of a single element, because the accumulation just mentioned, in the compound battery, is discharged almost instantly, and, according to the theory (71) of the galvanic current, leaves the constant current in the conductor nearly in the same state of quantity as that which would be produced by a battery of a single element; and hence the conditions of the ending of the current are the same in both cases. Indeed, in reference to the ending induction, it may be assumed as a fact which is in accordance with all the experiments, (9, 13, 73, 74, 75, 76, &c.,) as well as with theoretical considerations,* that when the cir- * See the theory of Ohm. 24 CONTRIBUTIONS TO ELECTRICITY AND MAGNETISM. cuit is broken by a cup of mercury, the rate of the diminution of the current, nithin certain limits, remains the same, however the intensity of the electricity or the length of the conductor may be varied. i Kigq. 18 e lisa toma ob woh ait ce ol A b c D 70. The several conditions of the foregoing examples are exhibited by the parts of the curves, Figs. 18 and 19. The gradual development of the current in the short conductor, with a single battery, and the gradual decline of the same, are represented by the gentle rise of AB and fall of CD, Fig. 18; while, in the next Fig., (19,) the sudden rise of AB indicates the intensity which produces the increased shock, after the number of elements of the bat- tery has been increased. The accumulation of the electricity, which almost instantly subsides, is represented by the part Bee, Fig. 19, and from this we see, at once, that although the shock is increased by using the compound bat- tery, yet the needle of the galvanometer will be deflected only to the same number of degrees, since the parts Bc and ce give inductive actions in contrary directions, and both within the time of a single swing of the needle, and, con- sequently, will neutralize each other. The resulting deflecting force will, therefore, be represented by ¢ f, which is equal to Ck, or to OB, in Fig. 18. Spe 0 AC: lagage A. baf IK: D The intensity of the shock at the breaking is represented as being the same in the two figures, by the similarity of the rate of descent of the part CD of the curve in each. 71. We have said (69) that the quantity of current electricity in a short conductor and a compound battery, after the first discharge, is nearly the same as with a single battery. The exact quantity, according to the theory of Ohm, in a unit of length of the conductor is given by the formula ON ELECTRO-DYNAMIC INDUCTION. 25 n A rn + RO In this, » represents the number of elements; A, the electromotive force of one element; 7, the resistance to conduction of one element; and R, the length of the conductor, or rather its resistance to conduction in terms of r. Now, when R is very small, in reference to 7m, as is the case with a very short me- tallic conductor, it may be neglected, and then the expression becomes nA A. —— or —; Tn r and since this expresses the quantity of current electricity in a unit of the length of the circuit, with either a single or a compound battery, therefore, with a short conductor, the quantity of current electricity in the two cases is nearly the same. 72. Let us next return to the experiment with a battery of a single element, (68,) and instead of increasing the intensity of the apparatus, as in the last ex- ample, let the length of the conductor be increased; then the intensity of the shock at the beginning of the current, as we have seen, (14,) will be dimi- nished, while that of the one at the ending will be increased. That the shock should be lessened at the beginning, by increasing the length of the conductor, is not surprising, duction would diminish the rapidity of the development of the current. But the secondary current, which is produced in the conductor of the primary cur- rent itself, as we have seen, (19,) is the principal cause which lessens the in- tensity of the shock; and the effect of this, as will be shown hereafter, may also be inferred from the principles we have adopted. since, as we might suppose, the increased resistance to con- 73. The explanation of the increased shock at the moment of breaking the circuit with the long conductor, rests on the assumption before mentioned, (69,) that the velocity of the diminution of a current is nearly the same in the case of a long conductor as in that of a short one. But, to understand the applica- tion of this principle more minutely, we must refer to the changes which take place in the quantity of the current in the conductor by varying its length; and this will be given by another application of the formula before stated, (71.) This, in the case of a single battery, in which 7 equals unity, becomes Ei r+ R’ Vill.—G 26 CONTRIBUTIONS TO ELECTRICITY AND MAGNETISM. and since this, as will be recollected, represents the quantity of current electri- city in a unit of length of the conductor, we readily infer from it that, by in- creasing the length of the conductor, or the value of R, the quantity of current in a unit of the length is lessened. And if the resistance of a unit of the length of the conductor were very great in comparison with that of 7, (the resistance of one element of the battery,) then the formula would become A “R ? or the quantity in a single unit of the conductor would be inversely as its en- tire length, and hence the amount of current electricity in the whole conductor would be a constant quantity, whatever might be its length. This, however, can never be the case in any of our experiments, since in no instance is the resistance of R very great in reference to 7, and therefore, according to the formula, (73,) the whole quantity of current electricity in a long conductor is always somewhat greater than in a short one. 74. Let us, however, in order to simplify the conditions of the induction at the ending of a current, suppose that the quantity in a unit of the conductor is inversely as its whole length, or, in other words, that the quantity of current electricity is the same in a lone conductor as in a short one; and let us also suppose, for an example, that the length of the spiral conductor, Fig. 3, was increased from one spire to twenty spires; then, if the velocity of the diminu- tion of the section of the current is the same (69) in the long conductor as in the short one, the shock which would be received by submitting the helix to the action of one spire of the long coil would be nearly of the same intensity as that from one spire of the short conductor; the quantity of induction, how- ever, as shown by the galvanometer, should be nearly twenty times less; and these inferences I have found in accordance with the results of experiments, (75.) If, however, instead of placing the helix on one spire of the long con- ductor, it be submitted at once to the influence of all the twenty spires, then the intensity of the shock should be twenty times greater, since twenty times the quantity of current electricity collapses, if we may be allowed the expres- sion, in the same time, and exerts at once all its influence on the helix. If, in addition to this, we add the consideration that the whole quantity of current electricity in a long conductor is greater than that in a short one, (73,) we shall ‘ON ELECTRO-DYNAMIC INDUCTION. 27 have a further reason for the increase of the terminal shock, when we increase the length of the battery conductor. 75. 'The inference given in the last paragraph, relative to the change in the quantity of the induction, but not in the intensity of the shock from a single spire, by increasing the whole length of the conductor, is shown to be true by repeating the experiment described in paragraph 13. In this, as we have seen, the intensity of the shock remained the same, although the length of the cir- cuit was increased by the addition of coil No. 2. When, however, the gal- vanometer was employed in the same arrangement, the whole quantity of in- duction, as indicated by the deflection of the needle, was diminished almost in proportion to the increased length of the circuit. I was led to make this addi- tion to the experiment (13) by my present views. 76. The explanation given in paragraph 74 also includes that of the peculiar action of a long conductor, either coiled or extended, in giving shock and sparks from a battery of a single element, discovered by myself in 1831; (see Contrib. No. II.) The induction, in this case, takes place in the conductor of the pri- mary current itself, and the secondary current which is produced is generated by the joint action of each unit of the length of the primary current. Let us suppose, for illustration, that the conductor was at first one foot long, and after- wards increased to twenty feet. In the first case, because the short conductor would transmit a greater quantity of electricity, the secondary current pro- duced by it would be one of considerable quantity, or power to deflect a gal- vanometer; but it would be of feeble intensity, for although the primary cur- rent would collapse with its usual velocity, (69,) yet, acting on only a foot of conducting matter, the effect (74) would be feeble. In the second case, each foot of the twenty feet of the primary current would severally produce an in- ductive action of the same intensity as that of the short conductor, the velocity of collapsion being the same; and as they are all at once exerted on the same conductor, a secondary current would result of twenty times the intensity of the current in the former case. 77. To render this explanation more explicit, it may be proper to mention that a current produced by an induction on one part of a long conductor of uniform diameter, must exist, of the same intensity, in every other part of the conductor; hence, the action of the several units of length of the primary cur- rent must enforce each other, and produce the same effect on its own conductor 28 CONTRIBUTIONS TO ELECTRICITY AND MAGNETISM. that the same current would if it were in a coil, and acting on a helix. I need scarcely add, that in this case, as in that given in paragraph 74, the whole amount of induction is greater with the long conductor than with the short one, because the quantity of current electricity is greater in the former than in the latter. 78. We may next consider the character of the secondary current, in re- ference to its action in producing a tertiary current in a third conductor. The secondary current consists, as we may suppose, in the disturbance, for an in- stant, of the natural electricity of the metal, which, subsiding, leaves the con- ductor again in its natural state; and whether it is produced by the beginning or ending of a primary current, its nature, as we have seen, (22,) is the same. Although the time of continuance of the secondary current is very short, still we must suppose it to have some duration, and that it increases, by degrees, to a state of maximum development, and then diminishes to the normal condition of the metal of the conductor; the velocity of its development, like that of the primary current, will depend on the intensity of the action by which it is gene- rated, and also, perhaps, in some degree, on the resistance of the conductor; while, agreeably to the hypothesis we have assumed, (69,) the velocity of its diminution is nearly a constant quantity, and is not affected by changes in these conditions; hence, if we suppose the induction which produces the se- condary current to be sufficiently intense, the velocity of its development will exceed that of its diminution, as in the example of the primary current from the intense source of the compound battery of many elements. Now this is the case with the inductions which produce currents of the different orders, capable of giving shocks or of magnetizing steel needles; the secondary currents from these are always of considerable intensity, and hence their rate of develop- ment must be greater than that of their diminution, and, consequently, they may be represented by a curve of the form exhibited in Fig. 20, in which there is no constant part, and in which the steep- xg AU ness of A B is greater than that of BC. There a folas aie are, however, other considerations, which will be noticed hereafter, (89,) which may affect the form of the part BC of the curve, Fig. 20, rendering it still more gradual in its descent, or, in other words, which tend to diminish the intensity of the ending induction of the secondary current. ON ELECTRO-DYNAMIC INDUCTION: 29 79. It will be seen at once, by an inspection of the curve, that the effect produced, in a third conductor, and which we have called a tertiary current, is not of the same nature as that of a secondary current. Instead of being a single development in one direction, it consists of two instantaneous currents, one pro- duced by the induction of AB, and the other, by that of BC, in opposite di- rections, of equal quantities, but of different intensities. The whole quantity of induction in the two directions, will each be represented by the ordinate Bb, and hence they will nearly neutralize each other, in reference to their action on the galvanometer, in the circuit of the third conductor. I say, they will nearly neutralize each other, because, although they are equal in quantity, they do not both act in absolutely the same moment of time. The needle will, therefore, be slightly affected; it will be impelled in one direction, say to the right, by the induction of A B, but, before it can get fairly under way, it will be arrested, and turned in the other direction, by the action of BC. This inference is in strict accordance with observation; the needle, as we have seen, (24) starts from a state of rest, with a velocity which, apparently, would send it through a large arc, but before it has reached, perhaps, more than half a degree, it suddenly stops, and turns in the other direction. As the needle is first af- fected by the action of A B, it indicates a current in the adverse direction to the secondary current. 80. Although the two inductions in the tertiary conductor nearly neutralize each other, in reference to the indications of the galvanometer, yet this is far from being the case with regard to the shocks, and the magnetization of steel needles. ‘These effects may be considered as the results alone of the action of AB; the induction of BC being too feeble in intensity to produce a ter- tiary current of sufficient power to penetrate the body, or overcome the co- ercive power of the hardened steel. Hence, in reference to the shock, and magnetization of the steel needle, we may entirely neglect the action of BC, and consider the tertiary excitement as a single current, produced by the action of A B; and, because this is the beginning induction, the tertiary current must be in an opposite direction to the secondary. For a similar reason, a current of the third order should produce in effect a single current of the fourth order, in a direction opposite to that of the current which produced it, and so on: we have here, therefore, a simple explanation of the extraordinary phenomenon VIIIl.—H 30 CONTRIBUTIONS TO ELECTRICITY AND MAGNETISM. of the alternation of the directions of the currents, of the different orders, as given in this and the preceding paper. 81. The operation of the interposed plate, (32, 47, 48, &c.,) in neutralizing the shock, and not affecting the galvanometer, can also be readily referred to the same principles. It is certain, that an induced current is produced in the plate (III. 64,) and that this must react on the secondary, in the helix; but it should not alter the total amount of this current, since, for example, at the ending induction, the same quantity of current is added to the helix, while the current in the plate is decreasing, as is subtracted while the same current is increasing. To make this more clear, let the inductive actions of the inter- posed current be represented by the parts of the curve, Fig 20. The induction represented by A B will react on the current in the helix, and diminish its quantity, by an amount represented by the ordinate 6 B; but the induction represented by B C, will act in the next moment, on the same current, and increase its quantity by an equal amount, as represented by the same ordinate Bb; and since both actions take place within a small part of the time of a single swing of the needle, the whole deflection will not be altered, and consequently, as far as the galvanometer is concerned, the interposition of the plate will have no perceptible effect. 82. But the action of the plate on the shock, and on the magnetization of tem- pered steel, should be very different; for, although the quantity of induction in the helix may not be changed, yet its intensity may be so reduced, by the adverse action of the interposed current, as to fall below that degree which enables it to penetrate the body, or overcome the coercive force of the steel. To under- stand how this may be, let us again refer, for example, to the induction which takes place at the ending of a battery current: this will produce, in both the helix and the plate, a momentary current, in the direction of the pri- mary current, which we have called plus; the current in the plate will react on the helix, and tend to produce in it two inductions, which, as before, may be represented by A B, and B C, of the curve, Fig. 20; the first of these, A B, will be an intense action, (78,) in the mnus direction, and will, therefore, tend to neutralize the intense action of the primary current on the heljx; the second, (B C,) will add to the helix an equal quantity of induced current, but of a much more feeble intensity, and hence the resulting current in the helix ON ELECTRO-DYNAMIC INDUCTION. 31 will not be able to penetrate the body; no shock will be perceived, or at least a very slight one, and the phenomena of screening will be exhibited. 83. When the plate of metal is placed between the conductors of the second and third orders, or between those of the third and fourth, the action is some- what different, although the general principle is the same. Let us suppose the plate interposed between the second and third conductors; then the helix, or third conductor, will be acted on by four inductions, two from the secondary current and two from the current in the plate. The direction and character of these will be as follows, on the supposition that the direction of the secondary current is itself plus: The beginning secondary . . imtenseand . .. . minus. The ending secondary . . . feebleand ... - plus. The beginning interposed . . intenseand . . . - plus. The ending interposed . . . feebleand ... . minus. Now if the action, on the third conductor, of the first and third of the above inductions be equal in intensity and quantity, they will neutralize each other; and the same will also take place with the action of the second and fourth, if they be equal, and hence, in this case, neither shock nor motion of the needle of the galvanometer would be produced. If these inductions are not precisely equal, then, only a partial neutralization will take place, and the shock will only be diminished in power; and, also, perhaps, the needle will be very slightly affected. 84. If, in the foregoing exposition, we throw out of consideration the actions of the feeble currents which cannot pass the body, and, consequently, are not concerned in producing the shock, then the same explanation will still apply which was given in the last paper, (IIL, 94,) namely, in the above example, the helix is acted on by the minus influence of the secondary, and the plus influence of the interposed current. 85. We are now prepared to consider the effect on the helix (Fig. 3) of the induced currents produced in the conductor of the primary current itself. These are true secondary currents, and are almost precisely the same in their action as those in the interposed plate. Let us first examine the induced cur- rent at the beginning of the primary, in the case of a long coil and a battery of a single element; its action on the helix may be represented by the parts of the a 32 CONTRIBUTIONS TO ELECTRICITY AND MAGNETISM. curve, Fig. 20. The first part, AB, will produce an intense induction oppo- site to that of the primary current; and hence the action of the two will tend to neutralize each other, and no shock, or a very feeble one, will be produced. The ending action of the same induced current, which is represented by BD, restores to the helix the same quantity of current electricity (but in a feeble state) which was neutralized by AB, and hence the needle of the galvanometer will be as much affected as if this current did not exist. 'These inferences per- fectly agree with the experiment given in paragraph 19. In this, when the ends of the interposed coil were joined so as to neutralize the induced current in the long conductor, the shock at the beginning of the primary current was nearly as powerful as with a short conductor, while the amount of deflection of the galvanometer was unaffected by joining the ends of the same coil. 86. At first sight it might appear that any change in the apparatus which might tend to increase the induction of the primary current (16) would also tend to increase, in the same degree, the adverse secondary in the same con- ductor; and that hence the neutralization mentioned in the last paragraph would take place in all cases; but we must recollect that if a more full current be suddenly formed in a conductor of a given thickness, the adverse current will not have, as it were, as much space for its development, and, therefore, will have less power in neutralizing the induction of the primary than before. But there is another, and, perhaps, a better reason, in the consideration that in the case of the increase of the number of elements of the battery, although the rapidity of the development of the primary current is greater, yet the increased resistance which the secondary meets with, in its motion against the action of the several elements, will tend to diminish its effect. Also, by diminishing the length of the primary current, we must diminish (76) the intensity of the secondary, so that it will meet with more resistance in passing the acid of the single battery, and thus its effects be diminished. 87. The action of the secondary current, in the long coil at the ending of the primary current, should, also, at first sight, produce the same screening influence as the current in the interposed plate; but, on reflection, it will be perceived that its action in this respect must be much more feeble than that of the similar current at the beginning; the latter is produced at the moment of making contact, and hence it is propagated in a continuous circuit of conduct- ing matter, while the other takes place at the rupture of the circuit, and must ON ELECTRO-DYNAMIC INDUCTION. 33 therefore be rendered comparatively feeble by being obliged to pass through a small portion of heated air; very little effect is therefore produced on the helix by this induction, (19.) The fact that this current is capable of giving intense shocks, when the ends of a long wire, which is transmitting a primary current, are grasped at the time of breaking the circuit, is readily explained, since, in this case, the body forms, with the conductor, a closed circuit, which permits the comparatively free circulation of the induced current. 88. It will be seen that I have given a peculiar form to the beginning and ending of the curves, Figs. 17, 18, &c. These are intended to represent the variations which may be supposed to take place in the rate of increase and de- crease of the quantity of the current, even in the case where the contact is made and broken with mercury. We may suppose, from the existence of analogous phenomena in magnetism, heat, &c., that the development of the current would be more rapid at first than when it approximates what may be called the state of current saturation, or when the current has reached more nearly the limit of capacity of conduction of the metal. Also, the decline of the current may be supposed to be more rapid at the first moment, than after it has lost somewhat of its intensity, or sunk more nearly to its normal state. These variations are indicated by the rapid rise of the curve, Fig. 17, from A to g, and the more gradual increase of the ordinates from h to B; and by the rapid diminution of the ordinates between C and J, and the gradual decrease of those towards the end of the curve. 89. These more minute considerations, relative to the form of the curve, will enable us to conceive, how the time of the ending of the secondary current, as we have suggested, (78,) may be prolonged beyond that of the natural subsi- dence of the disturbance of the electricity of the conductor on which this current depends. If the development of the primary current is produced by equal increments in equal times, as would be the case in plunging the battery (59) into the acid with a uniform velocity; then the part A B of the curve Fig. 17 would be a straight line, and the resulting secondary current, after the first in- stant, would be one of constant quantity during nearly the whole time repre- sented by Ac; but if the rate of the development of the primary current be supposed to vary in accordance with the views we have given in the last para- Vill.—1 34 CONTRIBUTIONS TO ELECTRICITY AND MAGNETISM. graph, then the quantity of the secondary current will begin to decline before the termination of the induction, or as soon as the increments of the primary begin to diminish; and hence the whole time of the subsidence of the second- ary will be prolonged, or the length of 6 C, Fig. 20, will be increased, the descent of BC be more gradual, and the intensity of the ending induction of the second- ary current be diminished: (see last part of paragraph 78.) 90. Besides the considerations we have mentioned, (88,) there are others of a more obvious character, which would also appear to affect the form of particular parts of the curve. And first we might perhaps make a slight correction in the drawing of Figs. 17, 18, &c., at the point A, in consideration of the fact that the very first contact of the end of the conductor with the surface of the mer- cury is formed by a point of the metal, and hence the increment of develop- ment should be a little less rapid at the first moment than after the contact has become larger; or in other words, the curve should perhaps start a little less abruptly from the axis at the point A. Also Dr. Page has stated* that he finds the shock increased by spreading a stratum of oil over the surface of the mer- cury; in this case it is probable that the termination of the current is more sudden, on account of the prevention of the combustion of the metal by means of the oil, and the fact that the end of the conductor is drawn up into a non- conducting medium. 91. The time of the subsidence of the current, when the circuit is broken by means of a surface of mercury, is very small, and probably does not exceed the ten thousandth part of a second, but even this is an appreciable duration, since I find that the spark at the ending presents the appearance of a band of light of considerable length, when viewed in a mirror revolving at the rate of six hundred times in a second; and I think the variations in the time of ending of the current under different conditions may be detected by means of this in- strument. 92. Before concluding this communication, I should state that I have made a number of attempts to verify the suggestion given in my last paper, (III. 127,) that an inverse induction is produced by a galvanic current by a change in the distance of the conductor, but without success. These attempts were made * Silliman’s Journal. ON ELECTRO-DYNAMIC INDUCTION. 35 before I had adopted the views given in this section, and since then I have found (80) a more simple explanation of the alternation of the currents. 93. In this number of my contributions, the phenomena exhibited by the galvanic apparatus have alone been discussed. I have, however, made a series of experiments on the induction from ordinary electricity, and the reaction of soft iron on currents, and I think that the results of these can also be referred to the simple principles adopted in this paper; but they require further exami- nation before being submitted to the public. a Ge nT want yet (yg) ey devivah a cifoas 599 WA sient allt dpauery it oat alt na nies tat peo ih rath bck singe 0s bE 00 Eight athaah i tabi pol c« ’ ai athlig adh of Mall loge guateck: ? hihies oe a rt | (idif> otal aph + angel jh : eam My oe * caw ham Chad: Led, Shae nO 3 eer ee in -.¥ ~iag Gv Sead WY lib adlg- sain Om = 2 7 Pe | on iicr en see ae wee 2 F i. ee ek <4 nig Sulla pA : si fle Where (me Sool? eae foe facie ‘eo Gn: 0 ORE a >. : Cet 400) 1 V0 peeeiiaa iter naa ag thw quer, ca + aw = i, SOhL SE A Ae fee Unie ae =? ibn a i ee <— new + ie = amet eke ONY Ute Ti a or po) Se rae ons! ig “SS sven! t we er py on = 24-3 & : i” i sa tot on ched te ee a - SO” eee uti > lip oes a “ay yng eaten ovation i mf .-6 .% he 1 orn’ Perec Se fenced = Seek oF gn - SO ft ‘ 1s oh » 6) Gita Netra whlig, at Ua nal Te . mip tenes : ” a» | § (F@GE hve Maaatie in Ojo tue of aading som | bate we Sd De celky te heen) fig ion ot Ula fae @ - a ; | ‘ te , 1. eo ie) ely a : och ngewe Vine angen OU, (A agaee <_ ee eR ae! i" ® @tee Dies Ces (19) eal “; - 7 \@ ad + _ ; ; « - Le / ARTICLE II. Description of an entire Head and various other Bones of the Mastodon. By William E. Horner, M. D., and Isaac Hays, M.D. Read October 2, 1840. Tue undersigned, a committee appointed by the Society, January 3d, 1840, to report a description of the collection of Mastodon bones recently presented to the Society by some of its members, have the honour to submit the follow- ing account: According to the statement of Mr. D. Wood, from whom these bones were purchased, they were discovered two years since about seven feet below the surface of the ground, in digging a mill-race on the estate of Abraham Halm, three-fourths of a mile east of Bucyrus, Crawford County, Ohio, on the dividing ridge between the Sandusky and Sciota valleys. This ridge, consisting of table land, is one of the highest elevations in Ohio, is well cultivated, and abounds in never-failing springs, which constitute the sources of the Sandusky and Sciota rivers. The waters of the former flow into Lake Erie by a course almost due North, and those of the latter, into the Ohio, by a course nearly due South. The soil in which the bones were buried is entirely alluvial. The collection contains portions of the skeletons of two animals, one larger than the other. The bones of the larger of these animals are lighter, more worn, more decomposed, and larger in their specific measurements than the other, and are of a different colour. All these bones were sold as common to one skeleton, but that they appertained to different individuals is sufficiently substantiated from what is alleged; and, moreover, by some of the carpal bones of the right side being in duplicate. Whether or not all were really exhumed. from the same spot cannot now be ascertained by the committee. Vill. —k 38 DESCRIPTION OF AN ENTIRE HEAD Though both skeletons have been inhumed, they do not seem to be fossil- ized. The first set has a much lighter specific gravity than corresponding re- cent bones would have, and the second set has about the same specific gravity as the latter, or perhaps a somewhat greater, but yet with a freshness of sur- face and of texture which would seem to indicate that either no very long interval could have elapsed since the death of the animal, or that the soil in which they were deposited possessed unusual preservative powers. Of the skeleton of the larger animal there are the following pieces: A fragment of the pelvis, containing the right acetabulum. Inferior end of right scapula. Inferior end of left scapula, a small fragment. Upper end of right radius and ulna, with olecranon process, the latter de- tached. Lunare—Trapezium—Trapezoides of right carpus. Head of a rib. Ten fragments of vertebre, &c., and a number of undetermined fragments, much comminuted. The long diameter of the glenoid cavity of the scapula measures nine and a half inches. The diameter of the acetabulum is seven and a half inches. The lunare is three and three-eighths of an inch in thickness. Upon the preceding data, this animal was from a thirteenth to a tenth larger than the Mastodon of the Philadelphia Museum, whose scapula has a glenoid cavity of eight and three-fourths of an inch in its long diameter, and an aceta- bulum of six and three-fourths of an inch in diameter. The bones of the second, or smaller animal, are in a state of fine preserva- tion, and consist of A complete head. Six anterior cervical vertebre. Six vertebra of thorax and loins, complete, and some fragments of same class of bones. Sacrum complete, and seven succeeding caudal bones. The left innominatum complete; the right ischium and pubes, with some fragments of right ilium. Thirteen ribs of right side. Eighteen ribs of left side. AND VARIOUS OTHER BONES OF THE MASTODON, 39 Os humeri of right side. Scaphoides, lunare, cuneiform and unciform of right carpus. Os femoris, tibia, and os calcis of right side. Radius and ulna of left side. Tibia, fibula, and patella of left side. Os calcis, astragalus, scaphoides and cuboides of left tarsus Conformation of Head. The occipital bone (see Plate I., fig. 1,) forms a plane, looking backwards and upwards, roughened by the insertion of muscles: its superior semicircular ridge is extremely scabrous, and makes a well defined angle with the top of the head. There is no hemispherical protuberance on each side of it, as in the Asiatic Elephant, (see Plate IV., fig. 2, e;) on the contrary, the plane of the occipital bone is slightly depressed near the centre of each side. ‘The insertion of the ligamentum nuche is somewhat depressed and very scabrous, and makes a triangular area, the base of which, being the line of the occipital ridge, is five inches wide; from this it extends downwards eight and a half inches to- wards the foramen magnum; it is divided symmetrically by a well-marked vertical ridge. The occipital condyles rise immediately from the surface of the bone, instead of standing out on a high base, as in the Elephant; they form one-third of a circle, and measure nearly six and three-fourths inches in length, by two and three-fourths in breadth. The plane of the occiput and the cuneiform process form, in their relation to each other, a right angle, upon which is placed the condyles. The cranium (see Plate II., fig. 1,) presents, in front, a flattened, or slightly raised convexity, from the occipital ridge to the anterior nares, and exhibits there an area of one foot eight inches long, by one foot two and a half inches wide, between the temporal fosse. The plane of the occiput and the upper front part of the cranium make, at their line of junction, a well defined angle of ninety-five degrees, (see Plate III.) In an Elephant belonging to the Wistar Museum, the corresponding portion is rounded, but if designated by supposititious planes, the latter would meet at an angle of eighty-five degrees. The incisive fossa (see Plate IV., fig. 1, a,) of upper maxilla is distinguished 40 DESCRIPTION OF AN ENTIRE HEAD by great depth, and terminates above in a narrow, profound pit, which pene- trates two inches under the anterior nares. Besides the ordinary infra-orbitary foramen, there is a second, much smaller one, a branch from the former, and placed three inches within and above it. This second infra-orbitary foramen has four superficial sulci, two within and two without, radiating from it, and indicating the direction of nerves and blood-vessels. The malar bone is much broader than in the Elephant. The conformation of the orbit is like that of the latter animal, but it is a section of a more regular circle, and is six and a half inches in diameter. ‘Two and a half inches poste- rior to the spine of bone, at the internal margin of the orbit, near its middle, there is a small canal, which leads to the infra-orbitar canal, and which, in the Elephant, is merely a groove. ‘The orbit has the same relative position as in the Elephant, in which respect Cuvier* has been led into error by the de- claration of Mr. Peale,t that there was no trace of orbit at the anterior part of the arch, (zygomatic;) for we find this arch continued into the orbit of the Mastodon, just as in the Elephant, the greater breadth of the malar bone in the former making the chief difference. ‘The zygomatic suture is nearly the same as in the Elephant. The meatus auditorius externus (see Plate I., fig. 1,) is a compressed oval orifice, the distance of which, from the anterior margin of the orbit, is seventeen and a half inches. The temporal fossa is broad, deep, and nearly uniformly concave, with very little of that convexity near its posterior part which exists in the Elephant. The pterygoid processes of the sphenoid bone, said by Cuvier to be larger than in any other quadruped, are eight inches in length, have a well-marked fossa, and present no inconsiderable resemblance to those in the human subject, which is not the case in the Elephant. ‘The tuber of the upper maxillary bone is not so full as in the latter. The hard palate is destitute of a notch behind, which exists in the Elephant, being flush; it is, in its whole length, nearly a plane, instead of curving down abruptly at its anterior portion, as in the Elephant. It measures, from its pos- terlor margin to its anterior, at a central point between the edges of the alveoli of the tusks, two feet two inches. The temporal bone presents the articular surface for the lower jaw exclu- * Recherches sur les Ossemens Fossiles, Vol. II., p. 301. Paris, 1840. t Historical Disquisition on the Mammoth, p. 41. London, 1803. AND VARIOUS OTHER BONES OF THE MASTODON. Al sively on the tubercle at the root of the zygomatic process. This surface re- sembles, in shape, that on the trapezium of the human hand for the thumb, except that it is proportionately more oblong, as it measures five inches by two and a half; its margin is sharp, elevated, and well defined. There is behind the tubercle a depression corresponding with the glenoid cavity of the Elephant, but it is narrow, deep, and rough; it appears not to have had a coating of carti- lage, and, from its constricted condition, could not have entered into the con- tour of the temporo-maxillary joint. The upper maxilla has a tooth on each side which measures seven and a fourth by four and a half inches. These teeth converge behind and were placed four inches in advance of the pterygoid process: they are furnished with five denticules, which are much worn. The left alveolus for tusk in the incisive bone is very complete, the right one is slightly mutilated at the margin. Their depth is nineteen inches— transverse diameter, four and three-fourths of an inch—and vertical diameter five and a half inches. The following supplementary measurements may be of some value : From end of alveoli of tusks to occipital condyles three feet two inches. From inferior margin of foramen magnum to vertex one foot five inches. Transverse diameter of occiput two feet two inches. From vertex to spine of bone, between anterior nares, one foot nine inches. From orbit to orbit one foot nine inches. Incisive fossa four inches deep. From posterior margin of pterygoid process of sphenoid bone, to anterior edge of alveoli for tusks, two feet four inches. From anterior edge of foramen magnum to posterior nares five inches. Depth of temporal fossa, from bottom to the crown of the zygomatic arch, nine inches. From superior margin of temporal fossa, to inferior margin of pterygoid pro- cess, one foot ten inches. Diameter of orbit six and a half inches. Across alveoli for tusks, and immediately below infra orbitary foramen, six- teen inches. Across alveoli for tusks, at their inferior end, eighteen inches and a half. VIIL.—L 42 DESCRIPTION OF AN ENTIRE HEAD Breadth of malar bone just at orbit six inches. From posterior margin of tooth, to posterior margin of os palati, six inches. Lower Jav.—The conformation of this is similar to that of the jaw belonging to the Baltimore Museum, and described by one of the members of the Com- mittee.* Its body is semicylindrical; on the external face there is a deep round groove, just above the symphysis, and which presents a rough foliated margin on each side, considerably expanded. The chin presents no alveoli for tusks, as in the Titracaulodon of Godman;} neither are there traces of such alveoli ever having existed. The jaw contains one tooth on each side, with five denticules, each with two points, all worn, and most so at their outer edge. In front of these teeth are re- mains of the alveoli of the deciduous teeth preceding them, The teeth are parallel; the left measures eight inches by four and a half—the right eight and a quarter, by four and three-quarters of an inch. The length of this jaw is two feet six inches. The height of ramus fifteen inches, and its breadth ten inches. The condyle is nearly transverse in its long diameter, with a slight inclination of the latter inwards and backwards; it has no groove dividing its articular surface into an inner and outer portion, as in the specimen in the Baltimore Museum, though there is a faint indication of one. -The coronoid process rises an inch and a half higher than the condyle; the latter measures five and a half inches in its long diameter. The angle of the bone is rather well defined and obtuse. VERTEBRE. The vertebra, of which there are, as stated, specimens of each class, have a conformation analagous to those of the Elephant. The first cervical vertebra (see Plate I., Fig. 2) measures fourteen inches between the tips of the transverse processes, and ten inches from the anterior to the posterior margin: immediately behind the superior oblique process there is also a perfect canal for conveying the vertebral artery into the foramen mag- num occipitis. * Description of Inferior Jaws of Mastodon, &c. By Isaac Hays, M.D. ‘Transactions of the American Philosophical Society, Vol. [V., New Series. t Transactions of the American Philosophical Society, Vol. III., New Series. AND VARIOUS OTHER BONES OF THE MASTODON. 43 The second cervical vertebra (see Plate I., Fig. 3) exhibits in its processus dentatus a broad regular cone, elevated one and a half inches, and whose sum- mit reaches to the level of the internal margin of the superior oblique processes of the first vertebra. Its spinous process is more robust than in the Elephant, and comes in contact with that of the first by a broad well-marked surface. This vertebra in the specimen before us, is anchylosed with the third in almost the whole length of the long bridge between the oblique processes inclusive. Its transverse diameter in the body is seven and a half inches—and the antero- posterior diameter, from the front of the body to the tip of the spinous process, measures ten inches. The spinous process of the third, fourth, fifth, and sixth vertebre is very small and short. ‘These vertebre are nearly circular, (see Plate II. Fig. 2) and measure nearly six inches in diameter, and nearly two and a half inches in thickness, in their bodies. They shoot up from the anterior root of the trans- verse process, a conical spine, sixteen or eighteen inches in height, which sets close against the body of the vertebra above, and assists materially in prevent- ing its dislocation. A vertebra of this description, when inverted, resembles a table standing on four legs; the two front legs being these conical spines, and the two hind ones the upper oblique processes. ‘There is an arrangement in the Elephant tending to this, but by no means so finished, as the conical spine is much shorter, and does not touch, by a considerable space, the vertebra above it. The first six thoracic vertebre have very long spinous processes ; that of the foremost measures twelve inches, of the second thirteen and a half, and of the third about the same; they then diminish in length. The lumbar vertebra, sacrum, and the caudal vertebre, are similar to those of the Elephant. The sacro iliac junction is anchylosed. PELVIS. Its conformation presents the same type as in the Elephant, but the measure- ments are much more considerable. The innominata join also from the top of the pubes to the anterior part of the tuber of ischia by a synchondrosis ar- ticulation ; there is, therefore, no pubic arch as in the human subject. The distance from the anterior superior spinous process to the centre of the sacrum is two feet nine inches. From the same process to the posterior ex- tremity of the symphysis of ischia measures three feet two inches. 44 DESCRIPTION OF AN ENTIRE HEAD From the superior extremity of the tuberosity of the ischium of one side, to the corresponding point of the other, one foot six inches. Transverse diameter of sacrum, at base, eleven inches; length, one foot five and a half inches. Antero-posterior diameter of pelvis, at superior strait, one foot six inches.— Transverse diameter of same strait, one foot nine inches. From anterior point of symphysis pubis to posterior of symphysis ischii, one foot five inches. From anterior superior spinous process of ilium to symphysis pubis, two feet four inches. From one anterior superior spinous process to the other, four feet eight inches, and little further back four feet ten inches for the extreme breadth of the pelvis. From the middle of crista of ilium to inferior point of tuber of ischium, three feet six inches. Diameters of thyroid foramen eight and five inches. Diameter of acetabulum six and a half inches. RIBS. The ribs resemble those of the Elephant: their length appears to be the same, but their size is greater in about the same proportion with the other bones. The first rib measures in length nineteen and a half inches, and has very dis- tinct processes marking the insertion of the scalenus anticus and medius mus- cles, and depressions also well marked for the subclavian artery and subcla- vian vein. The longest rib in the collection measures three feet seven inches along its outer convex edge. EXTREMITIES. The conformation of the bones of the anterior and posterior extremities is analagous to those of the Elephant, but they are shorter, thicker, and more strongly marked by the muscles. The os humeri is two feet five inches long—transverse diameter at condyles eight and a half inches, and at upper end eleven inches. Circumference just above insertion of deltoid two feet, and at middle, one foot four and a half inches. AND VARIOUS OTHER BONES OF THE MASTODON. 45 Ulna, length two feet one and a half inches; circumference in middle, one foot. Radius, one foot eleven inches long. Lunare, two and seven-eighths of an inch thick. Os femoris, two feet eleven inches long; circumference in middle, one foot four inches; diameter of head, six and a half inches; transverse diameter at condyles, eight and a half inches. Tibia, one foot ten inches in length, and eleven inches in circumference at middle. Fibula, one foot nine inches long. SIZE OF THE MASTODON. The following admeasurements of the bones of the extremities of the Mas- todon and Elephant, afford some data for determining the probable size of the former animal. Mastodon. Elephant. Os Humeri, length 2 feet 5 inches, 2 feet 8 inches. Ulna cas ita a OC A’ Radius age Opt 5 2: att Os Femoris “ Fae fal) Lee Sire Sen Tibia Fi SSRs OP eae 1 pee bd ies The skeleton of the specimen affording the above standard of comparison belongs to a young Elephas Indicus, and measures nine feet from the tips of the spinous processes, of the first two dorsal vertebre, to the ground. But it has been seen that the ribs of the Mastodon are nearly of the same length as those of the Elephant, and that the extremities are about six inches shorter in the fore-legs and five inches in the hind-legs: the greatest height of the ani- mal described would, consequently, be short of nine feet at the shoulders.* * Cuvier limited the stature to twelve feet. Oss. Foss. Vol. II. p. 24. A portion of the head, and some other bones of a Mastodon, in Mr Koch’s Museum, at St. Louis, Missouri, afford ground to think that the individual was about thirteen feet high. See Bullet. American Philosophical Society, for 1840, paper by W. E. Horner, M.D, Of the two existing species of Elephants, the Elephas Africanus reaches a stature of from VItIl.—™M 46 DESCRIPTION OF AN ENTIRE HEAD The cervical vertebre of this Mastodon are from an eighth to a fifth thicker than they are in the Elephant. The latter measures eleven feet from the anterior nares to the end of the ischia: the Mastodon was probably twelve and a half feet in the same line. Measurements and estimates thereon give, in the Mastodon, supposing the feet to be of the same vertical height as in the Elephant, the following results: Mastodon. Elephant. From tips of spinous processes of Ist and 2nd dorsal vertebre to ground, 8 feet 9 inches. 9 feet. From tip of spinous process of last lumbar ver- tebra to ground, 7 feet 10 inches. 8 feet. The Mastodon above described is inferior in the measurements of its several pieces to the one in the Philadelphia Museum; the latter, however, in being articulated at a height of eleven and a half feet, has probably transcended its natural limits at least eighteen inches: its length also exceeds, probably, the proper bounds. The thorax appears to be unnaturally expanded by the undue length of the costal cartilages: the pelvis, also, by the keeping apart the sym- physis of the pubes and ischia, instead of joining it, has an excess in its di- ameter of from eight to ten inches. The head is likewise thrown too much forward. The probability is, that the Mastodon carried his head with the front part almost vertical, as the Elephant, which would ease much the action of the muscles intended for its support. In the collection of Mastodon bones previously in the cabinet of the Society, there is a vertebra dentata eight and three-fourths of an inch broad, by eleven and a half in its antero-posterior diameter, and an os calcis ten and a half inches long: the animal, of which these are the remains, was probably from an eighth to a tenth larger than the subject of this paper. Whether the remains of the largest animals of this race have as yet been brought to light, must continue for some eight to ten feet, and the Elephas Indicus one of from eight to sixteen feet. The Elephas Pri- mogenus, or Fossil Elephant, also called Mammoth or Behemoth, now extinct, and whose re- mains are so abundant in Siberia and the borders and islands of the Frozen Sea, as to justify the expression that the ground is in places strewed with them, appears to have been about, or a little beyond, the stature of the Indian Elephant. Cuvier’s Oss. Foss., Ed. 1812, p. 135, vol. II. AND VARIOUS OTHER BONES OF THE MASTODON. 47 » time a question among scientific men; but the Committee are of opinion that ten or ten and a half feet was the greatest natural height of any one whose remains they have examined. The committee cannot conclude this report without congratulating the So- ciety on the possession of the entire head of this interesting animal. The ac- quisition is indeed a precious one, not only from its being, so far, unique, but as it furnishes materials for determining nearly all the doubtful points relative to the characters of the genus, and for fixing its relations and position in the animal kingdom, &c. All that is now wanting, indeed, to complete the history of the osteology of this animal, is the discovery of a head with the tusks 77 stfu, so as to deter- mine positively the direction of the latter—whether their convexity was up- wards or downwards. NOTE, BY) DR.cHAwS: Read May 21, 1841. Since the preceding paper was read to the Society, I have seen the “ Se- cond annual Report on the Geological Survey of the State of Ohio, by W. W. Mather, principal Geologist, and several assistants,” in which I find a brief notice of the bones which have just been described, and some facts rela- tive to their geological position, of much interest, and which I will therefore subjoin. These bones, according to Mr. Briggs, one of the assistants of Mr. Mather, were found in a bed of fresh-water-shell marl, about four feet thick. This marl is composed of argillaceous matter and fresh-water shells, among which were observed lymniea, planorbis, physa, and some species of cyclas, and is covered by a layer of peat four feet thick. These beds were deposited in a depression in a stratum of yellowish clay, which forms the surface of the coun- try, and contains pebbles of primary and secondary rocks. Beneath this is a stratum of bluish clay, reposing on shale and limestone, containing pebbles of primitive rocks, and of the subjacent shale and water-worn limestone. 48 DESCRIPTION OF AN ENTIRE HEAD, ETC., OF THE MASTODON. Wherever examined, this clay seems to be destitute of organic remains. The > shale is part of the formation which extends from the Ohio river to Lake Erie. The limestone is generally destitute of fossils. The following sketch repre- sents the geological structure of a portion of Crawford county, and exhibits the position in which the bones were found. A, limestone. B,shale. C,sandstone. D, blue clay. E, ’ yellow clay. a, bed of fresh-water-shell marl, in which the R bones were found. b,6, Sandusky river, crossing twice the , above profile, extending from east to west. The fresh-water-shell marl, being deposited in the yellowish clay, is more recent than the latter, and therefore, as Mr. Briggs observes, “the Mastodon has become extinct since the deposite of the materials upon the surface of which are our magnificent forests and beautiful prairies.’ Thus confirming the opinion expressed by the committee, as to the comparatively very recent period at which this animal became extinct. It is proper to state, also, that a brief notice of these bones, with a profile sketch of the head, was communicated to Professor Silliman by Mr. J. W. Foster, and have been published in the American Journal of Science and the Arts, Vol. XXXVI, p. 189. Lil & Ge 7 Y Vee cts A ot CO. Ae & CL Se x CG ton. F CMa. oY ?. a ~ Sr) ~~! 71a i /3 odon. * Ss Ma TervicalVerte bra Se cond t an od ertehTa. ervicalh st © 77 Fr a Fial Head On WEL ESF¢.2. LEP > z. = eet TA Sa on a Fh pe C%ra@7es. ertehrw. rcal | /O l erv wu ~ Ni u S ~ N ™s & Ny Sinclair i o y 7 aie. a efron eS Se wae eo. Cy Vid e.FY x Mastodon. ce. Orhit. if Temporal LPowsa. Drawn by OscarALawson On stone by WS Weaver Lurth. of T. Sinclaa vo GyA snnernarte gta Ed st nda Pts 4 tay 4 Mastodon. ao /ncisivelossa, bit, » © Orbits, LTO ON vied re, AAMntertor Nares. Qa Z / Kona An. Pd i, 24 Ibs VE: le eLlenisphe rical Fratiuh erunces, e€ phant, \ ni T'emp oval Fossa. ARTICLE IIL On the Cecidomyia Destructor, or Hessian Fly. By Miss M. H. Morris. Read Oct. 2, 1840. THE enormous injury to which the wheat crops in the United States have been, for many years, subjected by the Cecidomyia Destructor, or Hessian Fly, induced me to study, minutely, the habits of the insect, with a view to discover some remedy for the evil. Having ascertained that the perfect fly appears in June, and lives but a few day’, and that the larva is only to be found in the young wheat, in the succeeding fall, or spring, I was led to infer that the grain itself was the nidus selected, not the culm, as Mr. Say haa supposed. The fact of the egg being laid in the grain does not, however, rest upon in- ference; I have actually detected the larva in the grain, when peculiar circum- stances had prevented it from leaving its birth-place, in order to ascend the stalk, as it is prone to do. While I admit the correctness of Mr. Say’s description of the Cecidomyia, given in the first volume of the Journal of Natural Sciences, I must beg leave to differ from him respecting the history of the insect. He alleges “the egg to be deposited in the stalk of the wheat, between the vagina and the culm, near the root,” and that, “in this situation, with the body inverted, the head being invariably down, the infant larva passes the winter; here he leaves it, and proceeds to describe its appearance in the flax-seed state, evidently sup- posing that it had not moved from its position from the time of its exclusion from the egg until its change to the pupa. He then states that “the perfect fly appears early in June, lives but a short time, deposites its eggs, and dies.” VIII. —N 50 ON THE CECIDOMYIA DESTRUCTOR, OR HESSIAN FLY. If the larva remains in the same place and position, from the time of its ex- clusion from the egg to the pupa state, how does it get from near the root to the third joint, and sometimes, although rarely, above it, as the facts prove? Again, I would ask, if the perfect fly appears in June, lives only a short time, and in that time the female deposites her eggs, where are those eggs placed? surely not in the old and dying stalk of wheat from whence she has derived her subsistence; and I know of no other plant on which she feeds. Mr. Say continues, “the insects from these eggs,’ deposited in June, “complete the history by preparing for the winter brood;” we are here left in the dark re- specting the home ahd food of this second brood, since there is no wheat grow- ing from June until September, when the grain is again planted. Had the information of Mr. Say, respecting the history of the insect, been as accurate as his knowledge of its appearance, he would not have left room for these doubts. ‘The eggs described by Mr. Say, I am compelled to believe, were those of some other insect, which he has mistaken for those of the Hes- sian Fly, as they appear to have been found where his previous impression led him to search for them. My first observations were made in June, 1836, when the Hessian Fly was making its ravages around us. ‘The insect was then in the pupa, as shown by Mr. Le Sueur’s beautifully correct drawings, in the first volume of the Journal of the Academy of Natural Sciences, illustrating Mr. Say’s description of the insect. The pupe were scattered from the root to the third joint of the straw, and the wheat was beginning to ripen, although still soft. In a few days the flies made their appearance in countless numbers, hovering over and settling on the ears of wheat, where they were, no doubt, depositing their eggs in the grain, thus securing a home and future food for their progeny. In about ten days they had all disappeared, and the impoverished grain ripened for the harvest. In 1837, a field was sown so late that the grain did not vegetate until the following spring. I watched it closely, but could not observe that any injury was sustained until the beginning of May. Then I detected the worm in the root, and, in many instances, in the old grain, where it had originally been de- posited, but seldom or ever above the first jomt of the straw. JI am not pre- pared to say positively at what time the worm passed into the pupa, but be- lieve it to be about the beginning of June. From this field I preserved a ON THE CECIDOMYIA DESTRUCTOR, OR HESSIAN FLY. 51 handful of straws, torn up by the roots, and in every instance the pupa was either in the old grain or the root. Within a week from the time of these observations the wheat was reaped, but the pupa in the stubble was not perfected until August. In the spring of 1838 I detected the larva in a field that had been sown early in the previous fall; it was always in the centre of the culm, there being from one to six in the same stalk, at various distances, from the root to the third joint. It had a pale, greenish-white, semitransparent appearance; in form bearing some resemblance to the silk-worm. I regret that I made no drawings or notes at the time; this description, therefore, is from memory. The upward path of the worm was distinctly marked. The perfect fly appeared in June. In the fall of 1837, Mr. Kirk, a farmer of Bucks County, procured Mediter- ranean wheat, which yielded an abundant crop, free from the Hessian Fly. The seed from this wheat was sown in the fall of 1838. In the spring follow- ing he detected the larva thinly scattered in the resulting crop; but the orain of the present year, 1840, from the same stock, has been greatly injured by flies from neighbouring fields, planted with American wheat. From these facts I have been confirmed in my first impression, that the egg is deposited in the grain, remains dormant until the grain vegetates, is then hatched in or near the grain, lives in the centre of the culm, and mounts with the growing stalk. Should the egg be hatched in the fall, the slow growth of the wheat allows the insect to penetrate into every shoot, and rise with the growing straw, but if it be retarded until spring, the uninfected shoots grow rapidly, while those containing the larva become sickly and abortive; hence the difference in the position of those found in the wheat vegetating in the fall, and those not ap- pearing until spring. Various experiments have been tried to destroy the egg in the grain, but the vital principle appears so carefully guarded in insects’ eggs, that whatever de- stroys life injures the grain. The only remedy, then, is to procure seed from an uninfected district. Nore.—In Susquehanna and Bradford counties the Hessian Fly has never yet made its ap- pearance. ~ 18 “ye hésujni leony soot ent foots emia’ od? fifo? ObBN pide dt = * 2 ay’ af iaroniy bers mle oil? tu. wis ott ct — Hing att man 10 'RF bediwd revit i007 ; pb nquc nil . tbc | od eh Qu ittor waite heb Ve pe RG deere daft Teidy ‘blo onl Seotlt Yes oni SP ot Aine sii -aVlecin ‘boqeot ashy (ad ome ot OF «ton regi eb a det aieral oitr Sadoatets DaseE to gate ied 1 al iPM oil to eeitiras oul ot aicitls eames ED Rap ORE bE» hattt ir a oa? aif) stoi) 2aameteily acormy $f ified ontee! wiltil Xie mba 7 natlivesiadfa deormysuhiionta tibia Ship ae gutta OF finns T sas! angst LC nixow-alid of of. vontetdl i fe Aroatsat Muit.et oilorad ? aolkgioush adh; ore Ae heroorpye yt soolsie) olT Dotnet: yfioedibi enw or Gainey yhitio®? aliolk Ww teatidt oi aM reer “ACE celveok? oft mbit doit qovs tanbnude lit hebbeng dotitw) “guts gititega odt ul BRB E16 Link acl ttt dean dave Heady’ ail? trio) Beate’ wiery aift fit :qora gaithiaer ont itt Leraktnse 7fiith arvol deff Homaod i ole © dnoda aootstadk dee Lolmalty ebfoit yains yye oslt deve cote sae een HF beriaitnos iad oon? Loetou ‘oy ai (RMegay Mary od? fine idatimeb aeiwertor nie aif F Pn oO Gili aivony edt "syle sheave af” it ive Woia, orld a adt ii bedotwif ed agh OED yd" gate Quiwovg adr ifiw eaiz bin Jootke-ti074 oft alanieaeiy rine “Bodh atte prlbiwtworg alooie bataataiue’ silt qulnge ~ ba it ot ag ndtotihodh sone (a 7iivota Lite yidole anion & ‘uveted oh A fe ieee’ rt) inie TR ont itt sessiv? with AP Bete toed io eevisiae » j - ed fay st a Tr seritgar tients ee 7 - wierg ott ae edt yotteals of = eed over secanigs Hota Gb wavotadiy Talt mag “Ne rat ire yilitovat ely initaay Ti "devit’ bce giienig of Rr cil “elit wt se a we i We sbinhath hedodlicias i cue ag nhl finies criiew © Gar nb aes ine ae bege’ eae ebome “ee oon iM nuines a milan: Grolherth bem iene! ast pends, eit ar . He © Geom peel tae ggg > sone 7 . - Ve & 1 Prom The Vuh, | jure ARTICLE IV. Remarks on the Dental System of the Mastodon, nith an Account of some Lower Jans in Mr. Koch's Collection, St. Louis, Missourt, where there 1s a solitary Tusk on the right Side. By W. E. Horner, M. D., Professor of Anatomy in the University of Pennsylvania. Read Nov. 6, 1840. THE extinction of an animal having so many claims to our curiosity as sthe Mastodon, from its localities—its conformation, and its colossal magnitude—an extinction so complete and final that its fiat has reached not only all the indi- viduals of that genus, but also extended its fatal influence to cognate genera of every description without exception, is an event in the revolutions of the earth so confounding, that the mind is lost in seeking for a cause, and dwells on the circumstance with astonishment andawe. An insatiable desire exists for further knowledge on the subject; and we are pleased with almost any attempt to explore the probable history and habits of these animals—their peculiarities of structure—the modifications of development, dependent on their species and genera—and, finally, the particular catastrophe which overwhelmed them at once, or, by a sequence of physical changes in atmosphere and food, brought about their ultimate destruction. It is upon this ground that I propose to offer a few remarks on the Dentition of the Mastodon. The data from observations already made, on the phenomena of dentition in these animals, leave the inference that, mechanism and texture excepted, a very close analogy existed between the development of their teeth and those of the Elephant. In the mechanism of the tooth of the Elephant we find vertical, transverse strata of bony matter and of enamel, alternating with one another, and depending for their relation upon an original arrangement of the pulp of the tooth and of its capsule well known to anatomists, and which is partially VIII.—o 54 REMARKS ON THE DENTAL SYSTEM OF THE MASTODON. represented by extending the fingers of the two hands, and thrusting them, point to point, between each other. In the Mastodon, besides the division of the triturating surface into denticules, the mechanism resembles that of the human tooth, by the enamel covering completely the crown or body of the tooth, and not being arranged into those transverse vertical layers. ‘The texture of the Mastodon teeth is also closer, or more compact. In both instances the teeth are formed by excretion, and though chemically of similar materials with bone, to wit, calcareous and animal matter, yet they differ organically from it in their mode of production, in their manner of growth, and in their texture. As the result of an excretion, they are destitute of cancellated structure, are in successive lamine, enclosing one another, and have no blood-vessels penetrating into and diffusing themselves in their texture. They are therefore absolutely inorganic, though porous and filamentous,* and have within themselves neither a power of repair nor of growth. It hence arises that, being of a fixed size, dependent on the size and excretive power of their original germs, such size, which is adequate to the process of mastication in an ungrown animal, is inadequate as the animal increases in magnitude, and a supplementary provision is therefore called for. The shoulders of a Mastodon, at birth, had a diameter not exceeding, proba- bly, sixteen inches, by about twenty, to enable it to pass through the pelvis of the female, but its full grown state is that of the largest Elephant. Allusion is here made chiefly to the living Elephas Indicus. Remains of fossil Elephants have been found near Verona, in Italy, which indicate a stature of fifteen feet high, so far as a correct conclusion can be formed from an examination of the lower jaw, and a metacarpal bone. A tusk was found there twelve feet long, by nine inches in diameter.t There are, as yet, no exhumations of the Mastodon which exhibit such altitude; the tallest of which we have the remains did not exceed thirteen feet; itis probable, however, that the bulk was not inferior, as the Mastodon appears to have been a stouter animal than the elephant in proportion to its height. Remains of fossil Elephants have been found in several other parts of Italy, France, Germany, Holland, and Belgium, under circumstances which leave the persuasion that such animals were once indigenous to Kurope. The largest * See Retzius on Teeth.* t Cuvier Ossen, Fossils, Art. Elephans, page 11. Paris, 1812. REMARKS ON THE DENTAL SYSTEM OF THE MASTODON. 55 skeleton was probably that which was raised near the Castle of Chaumont, in France, about the year 1613. Its thigh bone measured five feet in length, and its tibia four feet. It passed for the remains of Teutobochus, king of the Cim- brians, who had fought against the Roman general Marius, about one hundred years before Christ. Many publications for and against their authenticity as such, appeared at that time. We may infer from the preceding remarks how great must be the changes in a dental system in passing from the calf to the adult, so as to secure at all periods a masticating surface of sufficient extent. ‘The process of nature in providing this surface consists in bringing forward, from the back of the jaw bones, a series of teeth, successively larger and larger; and as these teeth emerge from behind, the smaller teeth advance forwards to near the chin, and their alveolar processes are absorbed. The advanced teeth, having no longer the latter support, then drop out. The teeth, from their inorganic character, suffer less in the influences from time and atmosphere than any other portions of the animal frame; hence they are the last vestiges of individuals. They are also, in many instances, the last traces of races of animals, and our only idea of the latter is furnished upon the analogies of the teeth. The Mastodon, in some of its species, comes under this category : there is no remaining evidence, in certain cases, but the teeth, and in others only the teeth and the lower jaw, the latter seeming to be next to the teeth, in the character of indestructibility. To the naturalist, therefore, it is of consequence to have such a system of dentology as will enable him, on the one hand, to separate different species, and, on the other hand, to avoid the error of multiplying them, contrary to the order of nature. A distinct species may be ascertained by the number of teeth in the jaw of a mature animal, and by their texture and mechanism. But as different periods of time, between birth and the mature or adult state, exhibit different numbers of teeth, a species, it is clear, cannot be determined upon their number alone, until we know the number existing at each age. Age may also have its peculiar concomitants of mechanism and texture; and, likewise, sex may affect the dental system of the Mastodon, as it does in other animals. In fine, with such narrow limits for correct judgment, the naturalist is much exposed to error, and it would perhaps be safer, in the present state of our knowledge in regard to the facts of dentology in the Mastodon, to refrain from admitting the existence 56 REMARKS ON THE DENTAL SYSTEM OF THE MASTODON. of new species except when the most positive evidences of difference in the texture and number of the teeth existed. In regard to the latter, it may be very safely asserted, that it is yet doubtful what was the entire amount of teeth protruded in the Mastodon, from the beginning to the end of its dentition; what were the teeth which were cotemporaneous, the periods of life of their existence, the peculiarities of sex, and, lastly, the irregularities of dentition in individuals. The teeth of the Mastodon are all formed upon one type of configuration, the number of denticules excepted; they, therefore, like those of the elephant, do not admit of the division into incisors, cuspidate, and molars, as in some other animals. ‘The teeth are, in fact, all molars. The lower jaw itself re- sembles somewhat a human lower jaw, cut off in front of the molar teeth, and there joined in the two posterior segments. These teeth invariably succeed each other from behind, as stated; the hindmost ones as they emerge, pushing the others forward, and out of their places, until the latter all drop out, and a large, solitary tooth is finally left on each side of each jaw. The progress of dentition in the elephant is said to be as follows: the first teeth protrude at eight or ten days after birth, and are fully out at three months. The second are completely protruded in two years from birth, and fall out at six years. ‘The third teeth appear at two years, and the fourth at nine years. The entire succession brings forward eight teeth on each side of each jaw, er thirty-two in the whole set. The periods at which the fifth, sixth, seventh, and eighth teeth protrude, are not so well known; it is ascertained, however, that the intervals of succession go on increasing. Such may have been the case exactly with the Mastodon. The early ideas of naturalists on the teeth of the Mastodon were very ex- travagant. Buffon, for example, supposed, from their rectangular form, that they were very numerous; and having only insulated specimens of large teeth to form a judgment on, he concluded that we might infer how enormous would be the size of a head which had twenty-four or even sixteen teeth, each of which weighed ten or eleven pounds, (Epoques de la Nature. Note Justif. 9.) He made the double mistake of supposing that all the teeth were of the same magnitude, and that the entire set was co-existent in the animal. We now know, with some degree of certainty, that the earliest teeth of this animal were not more than an inch and a half square, and that the three immediately suc- REMARKS ON THE DENTAL SYSTEM OF THE MASTODON, 57 cessive teeth were a gradual and successive enlargement upon this and each other’s volume. In the Museum of Mr. Koch at St. Louis, there is a young head, the long diameter of which is eighteen or twenty inches, and where the fact of four co-existent teeth on each side of each jaw, is exhibited. This spe- cimen, with a dozen lower jaws of different ages and sizes, enables us to trace with some accuracy the stages of dentition until it reaches the large solitary grinder of ten inches in length, and on each side. Judging from these phases of dentition, I should infer that the entire amount of teeth was at least twenty- four. M. Cuvier had satisfied himself, that the number was at least twelve, and he had almost reached the conclusion, from a comparison of publications, that. there were sixteen. To our learned colleague, Dr. Isaac Hays, we owe a fur- ther conclusion on this subject, to wit, that the number was twenty-four.* I am, indeed, not satisfied, on viewing the difference of size between the smallest and the largest tooth of the Mastodon, that the number did not approximate still more that of the Elephant, and amount to at least twenty-eight, and, pos- sibly, thirty-two. Among the remarkable observations on the Mastodon, is that of Dr. Godman,+ that there were examples of this animal having a short tusk on each side of the chin, and which he named Tetracaulodon. The existence of these tusks in unquestionably adult specimens, as demonstrated by Dr. I. Hays,t quashed the objection that they belonged to the sucking state, and were lost as the ani- mal advanced to maturity. The naturalist was left therefore with the conclu- sion that either a new species of the animal had been discovered, or that it was merely a sexual peculiarity belonging most probably to the male. The perfect similitude of the other teeth with those of the known Mastodon, embarrasses this question deeply, and it may be safely doubted whether we have the ma- terials to solve it. In examining the specimens of the lower jaw, in Mr. Koch’s Museum in St. Louis, I was struck with some, bearing on this question, and of which there are * Description of the Inferior Maxillary Bones of Mastodons. Transactions of the American Philosophical Society, Vol. LV. New Series. + Transactions of the American Philosophical Society, Vol. III. New Series, p. 478. t Loe. cit. p. 22. VIlI.——P 58 REMARKS ON THE DENTAL SYSTEM OF THE MASTODON. three. The first is a large adult with two of the largest class of molars on each side: it is perfect, with the exception of a small fractured surface of the left ante- rior part of the chin. This specimen has a lower maxillary tusk, twenty lines in diameter and five inches long. It protrudes from the anterior right side of the chin, and is directed horizontally. ‘There is not the smallest indication of there ever having been a similar production from the left side of the chin, the frac- ture of which has not been deep enough to remove such vestiges, had they existed. The second specimen is also an adult lower jaw of the same size, in which the whole of the chin and the left half of the bone remain. In the right side of the chin, there is a horizontal alveolus, the size of the preceding ; the tusk is not in it, but there is a loose one in the cabinet which may have belonged to it. In this jaw there is no corresponding alveolus, or even a ves- tige on the left side. The third specimen is the chin alone, of a very young and small animal, it is three inches in length by one and a half wide, is fossil- ized, and cemented thereby to a fragment of limestone about its own size. Here an alveolus for an inferior maxillary tusk exists also for the right side, but not on the left. The dentition of these three specimens is, by a very curious coincidence, not symmetrical, that is, a tusk exists only on the right side of the chin in each. The questions in regard to the Tetracaulodon of Godman, are rendered still more embarrassing by their existence; for are we to consider them merely as abnormal ty pes of that animal—as known Mastodons—or as still another species, to which, if such, the name of Tricaulodon might be attached? I confess my- self unable to suggest a probable solution of this difficulty. Connected with it is, in fact, another; Mr. Koch has the lower part of the head of a Mastodon of middling size in which, from the intermaxillary bone, as usual, protrudes a tusk ; but the tusk exists only on the left side, there being not even a vestige of alve- olus on the right. We are informed by Tavernier, that some examples of the Elephas Indicus have but one tusk; are we, then, to consider this head as an abnormal instance of the common Mastodon, or is there really an extinct animal, which has an inferior maxillary tusk on the right side, and a superior maxil- lary on the left? Each jaw sacrificing one tusk. The minute anatomy of the teeth, as exhibited by the microscope, has lat- terly been a very favourite object of study. The unquestionable result appears to be, that there are well established differences of texture in different animals, REMARKS ON THE DENTAL SYSTEM OF THE MASTODON. 59 depending upon the osseous filaments entering into their composition, and upon the direction and branching of certain tubes between these filaments.* While we are waiting for the exhumation of more heads of the above animals, possi- bly a microscopic examination of teeth and of tusks may serve to clear away some of the mysteries which obscure these problems in the extinct race, of which we have been treating. These details and difficulties, apparently trivial, will perhaps be excused when we recollect that a single print of the cranium of a fossil Elephant, found in Siberia, and published seventy years before by Messerschmidt,} gave to the great Cuvier his first idea on the Theory of the Earth and of its changes, and caused him to execute the work which stood highest in his own estimation, to say nothing of the approbation which it has received from the scientific world, to wit, the Oss. Fossiles. * See Muller’s Archives for 1837, for an account of the Danish work of Professor Retzius, of Stockholm. The reader may for these, and other investigations on the same subject, consult also with advantage a Compilation called Researches, &c.,on the Teeth, by A. Nasmyth. Lond.: 1839. t Transactions Philosoph. Vol. XI. p. 446. ie i % She ante ase wa neta vo pitted git Ri averted 103 Wi rei tv tial Medi Ueve late ans soisto tls ai al ical SaddioFtt Head ates anit titty al yitin Pod toll il OF Hy) Hab iinet sl. whorintorl tines -qinerae benkedld aly liar ain aged aout ett Te fare aoc ot to qed wild ny arabe rat alll vobemt ofienitie nod aid dt taadghl boots Write Arow-adhonmers OF fides ott moit havianvt: wind $b itsil sect tuoriqya! gilt Yo gawitan olin Dna ail eg w patsy at win 1a str uel ul} “ee a nn “0G Ha TOT peat "et vidi, ail calen alevwtio boo fit itt als uy amteciticeg Gemedl sydd hha ; abaft wit Yate yabusd 9 vf ot: baw Regula 4) INT O71 10 ots sibveornu tt ie sapien ti rom ; Abba dh teF uljooutilt saclrsennegh =6 ea ie > — 2/1 tei iM, Vi! F - ; du 9s 6e mies i - — - yi ’ am tage Why) * oo — ‘ a cetecie, Get. Timedy ew — ——— spun te vel ail Ene i =: © —+-s0., aes apeetm om = a ©9) «= $271) Sfp! 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ARTICLE V.
Observations to determine the Magnetic Intensity at several Places in the United
States, with some additional Observations of the Magnetic Dip. By Elias
Loomis, Professor of Mathematics and Natural Philosophy in Western Re-
serve College. Read Nov. 6, 1840.
Macnetic INTENSITY.
In the autumn of 1839, while engaged upon a series of observations for the
magnetic dip, the results of which are given in the Society’s Transactions, Vol.
VII, pp. 101—111, Professor Renwick of New York kindly offered me the use of
his apparatus for magnetic intensity, The offer was gladly accepted, and
observations made with the needles whenever circumstances would permit.
AsI had not yet learned to observe alone, and it was seldom I could find a
suitable assistant, the observations were few in number; and I should not
think them worthy the attention of the Society, were it not that they furnish
an approximate value of the magnetic intensity at one station somewhat re-
mote from the Atlantic coast, and in a region where such observations have
been seldom attempted.
The apparatus employed in these observations was constructed after the mo-
del of thatof Professor Hansteen. Three needles were used. The first, made un-
der the direction of Professor Hansteen himself, is 2.35 inches in length, and
.16 inch in diameter, mounted in a stirrup of parchment. The second, which
was furnished by Major Sabine, is 2.34 inches long, and .14 inch in diameter,
mounted in a brass stirrup. The third, by Professor Henry, is 2.40 inches
long, .15 inch in diameter, mounted in a silk stirrup. ‘The needles are accor-
VIII.—Q
62 OBSERVATIONS TO DETERMINE THE MAGNETIC INTENSITY
dingly distinguished by the names of Hansteen, Sabine, and Henry. They were
enclosed in a small cylindrical box of wood, supported by levelling screws, and
having a glass tube fitted to the top, from which the needles were suspended by
a few filaments of the silkworm’s thread. At the bottom of the box was a di-
vided circle for the purpose of noting the are of vibration, and the temperature
was shown by an enclosed thermometer. The bottom of the box being ren-
dered horizontal, and the needle properly placed in the stirrup, it was drawn
aside from the magnetic meridian by bringing near it another needle. ‘The
registry of the oscillations was commenced when the half are of vibration was
reduced to 30°, and continued to 320 oscillations, the instant of the comple-
tion of every tenth vibration being noted. The amplitude of the final arc was
generally recorded, being about five degrees. Five intervals of time were thus
obtained, each corresponding to 280 vibrations, namely, the interval between the
Oth, and 280th vibration, between the 10th, and 190th, etc., and between the
40th and 320th; and the mean of these is taken as the result.
At Dorchester, Princeton, and Philadelphia, the times were noted by a chro-
nometer. At the other stations, alever watch was used. At Hudson, the watch
was compared with the Observatory clock, immediately before and after the
observations. At the remaining stations there is a little uncertainty with
regard to the time, yet, it is thought, its influence upon the results will not be
great.
No correction has been applied for the arc of vibration. In order to deter-
mine the correction for temperature, the apparatus was placed upon a large
earthen plate, covered by a bell glass, alternately heated from below by a lamp,
and surrounded by a freezing mixture. The usual mode of observation was
employed, and the results are shown in the following table, the first column of
which indicates the time of commencement of each series of observations.
1839, Dec. 11,
‘“ “c
Date." Needle. Time of 280 Temp. Date. Needle. Time of 280
Vibrations. Vibrations| Temp.
1» 32™ P, M.| Sabine 7325.56 | 30°.8|| 1840, Jan. 4, 1" 28" M. P.| Sabine 7325.06 | 17°.9 >
b 51 088 ‘s 732.10/28.1]) « « 145 « ‘“ 731.79) 17.1
6 2. Al « |Hansteen |859 .36|29.6]} ‘* 2 32 &e Hansteen | 858 .47 19 .9
66 2 59 b6 oe |858 .42| 26.5 oe ce 2 53 an se 859 .14\15.7
“ 3 41 <« |Henry |592.36/34.0]| “ <« 3.47 ‘ | Henry 591 31) 21 27
“ 355 « ‘“ 592 .20|30.4|| “« «& 43 « “ 593.6617 .9 |
“ 444 6 “ 595 .18|89.4|| « «& 445 « “ 597 .26 | 85 .0
bs 4 59 be Ge 595 .64/90 .9)| *§ &6 ayaa | ide oD 598 .38 | 85 .0
“ ca i «© |Hansteen | 869 .93/91.0]} « «© yO 6 Hansteen | 870.10 84 .3
ee Me SBT yaiSs oe S68+.29]90 1 liye “anyts T2Ouras a 870.31 | 88 .8
“ 8 9 s*« | Sabine 745 87/84 .2|| bs 7 fees} 66 Sabine 748 .11| 89 .4
se 8 26 66 sc 747 .31|85 .0 | se se 8 ll 66 *6 746 .83 | 84 .0
AT SEVERAL PLACES IN THE UNITED STATES. 63
The mean of the preceding observations furnish,
Time of Time of
Vibration. Temp. Vibration. aiemp:
Hansteen, 869°.64 88°.8 858°.85 22°.9
Sabine, 747 .08 85 .6 732.18 23 .5
Henry, 596.61 87 .6 592.38 26 .0
T—T to!
Then, by the usual formula a Sra” obtain :—
10.79
teen’ le. 24> ———__——— = 000191.
For Hansteen’s needle, 858.85 x 65.9
Hoe. Sabine's aidedie, qesesttL 149 on wt poogag.
; 732.13 x 62.1
4.23
nry’s needle Sa te 000116.
Hon Ronny » = 592.38 x 61.6
The standard temperature, to which the following results are reduced, is 60°
Fahrenheit. Nocorrection is applied for the diurnal variation of intensity, but
the hours of observation are always stated. To test the permanency of the
magnetism of the needles, I have been furnished, by Prof. Renwick, with two
series of observations, made at New York, besides those made in September,
1839. The results are as follows:
Needle. Date. ree Temp. Correction
Hansteen | 1838, June 22, 0% 6™ P.M. | 8735.60 | 82°.0 8695.94
ae 1839, Sept. 9,1113 A.M. | 869.40 | 86 .0| 865 .09
ee 1840, June 6, 0 4 P.M. | 948 .60 | 80 .2 | 939 .97
Sabine 1838, June 21, 5 23 6s 744.35 |77 .0 | 740 .21
ee 1839, Sept. 9,1048 A.M. | 744.34] 85 .2 | 738 .24
ce 1840, June 6,10 23 oe 740 .00 | 78 .8 | 735 .44
Henry 1838, June 25,10 21 “ 590 .80 | 77 .0 | 589 .64
2 1839, Sept. 9,11 38 se 596 .72 | 86 .2 | 594 .91
a 1840, June 6,11 26 $6 598 .20 | 79 .0 | 596 .88
In Sabine’s needle, the time of vibration continually diminished, and in
Henry’s increased; indicating, in the former case, a slight increase of magnetic
force, and in the latter adiminution. The inequality, however, does not much,
if at all, exceed the irregular fluctuations of intensity which may be observed
at a single station, within a moderate interval; and as the variation indicated
in the two needles are opposite in kind, and will consequently, in part, balance
each other in taking the mean, the magnetism of both is regarded as invariable.
In Hansteen’s needle there is a striking increase in the time of vibration
64 OBSERVATIONS TO DETERMINE THE MAGNETIC INTENSITY
between 1839 and 1840. This is believed to be due to rust contracted in the
As, however, the rust was contracted after the subsequent obser-
vations, the magnetism of the needle throughout the series is regarded as
The stations of observation were the same as for the dip formerly
interval.
invariable.
described, with the exception of that at Dorchester, which was near Mr. Bond’s
Observatory.
Place.
New Haven, Conn.} 18
oe
Dorchester, Ms.
“se
“ce
Providence, R. I.
[77
Princeton, N. J.
Philadelphia, Penn.
“cc
Hudson, Ohio.
“ec
sf 1840, Jan. 1,
oe
Date. Needle. |"Vitrations | Pee
39, Sept. 11, 94 53™ A. M. | Sabine 7605.64 | 81°.8 | 7553.21
Es 10 24 s6 cs 763 .34 | 83 .0 | '757 .59
“ 10 55 & Hansteen | 887 .04 | 76 .4 | 884 .27
“6 11 24 “ Henry 609 .95 | 74 .8 | 608 .90
Sept. 18, 4 48 P.M. | Sabine 178 .24| 78 .8| 773 .45
6 5 34 “ Hansteen | 907 .06 | 75 .7 | 904.35
ce 6 0 “ Henry 625 .08 | 72 .6 | 624 .17
Sept. 19, 4 59 “ Sabine 769 .32 | 70 .4| 766.70
6 5 22 “ Hansteen | 898 .92 | 68 .5 | 897 .46
Sept. 21, 4 51 “ Sabine 739 .24 | 80 .7 | 734 .22
“ 5 40 “ Hansteen | 865 .46 | 79 .2 | 862 .29
“ 6 3 “ Henry 595 .10| 76 .9 | 593 .93
Sept.23, 446 ‘« |Sabine | 729.26] 70 .3 | 726 .80
“ 5 23 & Hansteen | 851 .68 | 67 .6 | 850 .45
“ 5 47 “ Henry 585 .28 | 65 .7 | 584 .89
Nov. 2, 1 23 6 Sabine 733 .85 | 58 .1 | 734.21
66 1 41 Oo ce 734 .75 | 55 .1 | 735 .93
6s 2 7 6 Hansteen | 858 .13 | 54 .1 | 859 .09
“ 2-27, “ se 857 .66 | 51 .6 | 859 .03
se 252 oT Henry 592 .61 | 52 .1 | 593.15
‘“ 35 “ “ce 591.41 | 53 .0| 591 .89
Nov. 30, 1 46 6 Sabine 732 .70 | 47 .6 | 735 .68
se 2 3 sé &e 752 .76 | 42 .6 | 736 .94
ss 2 24 6s Hansteen | 858 .59 | 41 .0 | 861 .70
66 2 45 ss 66 858 .33 | 39 .8 | 861 .63
ss Sr10) 8 Henry 591 .78 | 39 .1 | 593 .21
cs 3 23 66 « 591 .54 | 38 .2 | 593 .04
1 40 “c Sabine 731 .48 | 23 .5 | 740 .23
46 1 55 ce ee 730 .36 | 21 .5 | 739 .57
“ 2 29 6 Hansteen | 856.63 | 25 .5 | 862 .26
ee 3 41 se Henry 590 .75 | 27 .0 | 593 .01
ce 3 55 ae & 592 .47| 16.9 | 595 .44
The mean of the preceding observations furnish us with the following table,
in which column third is computed from the formula te (7) , and column
sixth by multiplying the horizontal intensity by the secant of the dip. The
last column represents the total intensity, that of New York being called 1.803,
according to the determination of Major Sabine.
AT SEVERAL PARTS IN THE UNITED STATES. 65
Horizontal
intensity.
Total ‘Votal
Time. : z = =
ane inten-ity. intensity.
Mean. Dip.
New York, MHansteen | 8675.51 | .96105| .96707 | 72° 52'.2 | 1.00815 | 1.803
ss Sabine 737 .96| .96998
“ Henry 593 .81 | .97018
New Haven, Hansteen | 884.27} .92497} .92364|73 26.7] .99533 | 1.7800
“ Sabine 756.40} .92326
s Henry 608 .90 | .92269
Dorchester, Hansteen | 904.35} .88435] .88182|74 16.0} .99854 | 1.7858
‘“ Sabine 773 .45| .88301
ce Henry 624 .17| .87810
Providence, Hansteen | 897.46} .89798] .89830|73 59.6 | 1.00027 | 1.7889
“ Sabine 766 .70 | .89862
Princeton, Hansteen | 862 .29| .97273| .97414]72 47.1] 1.01066 | 1.8075
& Sabine 734 .22| .97989
cc Henry 593 .93 | .96979
Philadelphia, Hansteen | 850 .45 | 1.00000 | 1.00000 | 72 7.1 | 1.00000 | 1.7884
“ Sabine 726.80 | 1.00000
“ Henry 584 .89 | 1.00000
Hudson, Hansteen | 860.74] .97623| .97344 | 72 47.6 1.01040 | 1.8070
“ Sabine WShala| .97222
Henry | 593.29] .97188
—
—————————————————
_
From the preceding observations it may be inferred that New York and
Hudson have sensibly the same magnetic intensity, as well as dip.
The only published observations, so far as I am aware, with which the pre-
ceding can be compared, are those made by President Bache and Professor
Courtenay, and published in the Society’s Transactions, Vol. VL, pp. 427—457.
The horizontal intensity at New York, (that at Philadelphia being considered
unity,) was found, by observations in common air, .97202; by observations in
rarefied air, .94702. Mean of tht two determinations, allowing each its proper
weight, .94705. My own result is .96707. ‘The horizontal intensity at Pro-
vidence, by President Bache’s observations, is .89869; by my own, .89830.
Macnetic Dip.
The following observations of the dip in different azimuths were made with
the same instrument formerly described, for the purpose of testing the axles of
the needles. ‘They were made at Hudson, from August 27 to September 4,
1840, on the same spot formerly employed. ‘The same mode of observing was
adhered to, and each number in the two columns headed “ Poles direct,” ‘‘ Poles
reversed,” is the mean of twenty readings, five being made of each pole in one
position of the needle, and the same number after the needle was reversed upon
its supports. Thus, 1360 readings were made with each needle. The dip is
deduced from the formula cot.” 5 = cot.? 7 + cot.’ v.
VIII.—R
66 OBSERVATIONS TO DETERMINE THE MAGNETIC DIP
NEEDLE No. 1.
aa | Poles direct Poles reversed. | Mean. Dip deduced. | pe Poles direct. | Poles reversed. Mean. ‘Dip deduced.
0 | 72°26'.4 | 72°37'.8 2 | oo, i | 50) 78°2 7a 78°30!
180| 72 a1 9\7a ee: (2°45'.6 | '72°45'.6 || 939 is be ‘Ol 79 iD $2) re°40.8 7 78°45'.8 betbive
ee | 140| 76 47 .0| 77 3.6 2| 290 » oa
10/72 40 2 peopl at hy | 320| 76 23 .5| 7622.8 | ‘
190 | 73 11 .6| 73 24 .0 a
ia a fd 72 46 .1| |
100/869 .5| 87 18 .9 hic dt 60/81 9.7/ 8057-2 2| 9, 16
280 | 86 52 .4 86 35 .8 240 81 18 .5| 81 42 .1 "249 .5
| }150/ 75 3.5|75 24.02) ,, 55 9 ‘ |
20| 73 24 .6| 73 30 mS eee S | 330 | 74 40 .8| 74 46 .6
200| 73 52 .3| 74 3.7 aed ||
a ee ES | rs 72 46.1)
110 84 13 6] 84 82 8 2! gy at 70 | 83 42 .7| 83 34.3) | 25 56
290 | 83 49 .8| 83 38 .8 |250| 84 5.7|84 21.9 § 72.47 8
Sai 160) 795800174 °F") | 8 ae :
30| 74 36 .1 ee eae 340 | 73 29 .0| 73 34.2
210/75 4.4|75 19.7 jeete
sole 0 1 8135.1 I 72 47.7) g9| 86 45 .7| 86 31.1
300/81 1.8|81 ie SL it ce 260|87 2 .6| 87 17 aé Beret 2
oe 170/19 WO eV TB ely plan, og Goes
40 | 76 18 .8 eo at vadbuse 350 72 42 3/72 49.8 § ;
220/76 47 .1|77 4.3 =a arene
130 | 78 57 .8| 7912 4 0) ag ge g (| fed General mean, 72° 47'.4
310| 78 31 .1| 78 25 .8 ie
NeeEpte No. 2.
ae Poles direct. | Poles reversed. Mean. Dip deduced. | are Poles direct. | Poles reversed. Mean. Mem, | Dip deauesas|
9° Ray! 9° AD! | ° ' ° ,
Pea RR wave fess SEE PR eww)
; i : i hee
ak, 140|77 0.0|76 57.02| a6 72° 59.3 |
10/73 14.5] 72 ao a 320176 58.8/76 16.85 | ‘ |
190|'73 17.9] 73 20.8 E ||_— |
72 55.0)
eeolen mocelan da ac ee 8 J Soler Ge ele ee ee |
ed |150|75 21.6/75 10.42|,. 16 72 47.2 |
20173 54.4| 73 ae ee. 1330/74 59.7|74 35.2 |
i Fr |
eee etn atl S| soles s0-2|20 00-02 |y 0.
290/83 58.5|83 50.6 250/83 57.1| 84 23.1 S Pers fal
patna 160|74 3.7|74 1.7 maa
30|74 55.2|74 31 a upenae 1340| 73 47.9 | 73 B00 8
sole ye He Ae 72 46.6 |! 55] 86 97.586 41.5
300/80 56.4 | 80 er ph teeal 260/87 1.4|87 oa y ge
— 170| 73 14.5|73 16.72| 49 751.
40/76 51.2|76 aa vis ane 350/73 13.3|72 44.1
220/76 57.9|76 56.1 din ees Ts
130/79 11.7|79 8.6 78 51.9 General mean, 72° 52’.9
310/78 40.9]78 26.3 ;
AT SEVERAL PLACES IN THE UNITED STATES. 67
The results with needle No. 1 are quite satisfactory, the extreme range of
the values of the dip from observations in different azimuths being 4’.2. With
needle No. 2 the extreme range is 12’.7._ This discordance is ascribed to slight
rust which has formed upon one of the axles, but which is barely discernible
to the naked eye. The mean of the preceding 2720 readings with both nee-
dles is 72° 50’.2; the mean of the observations in the meridian is 72° 49’.6.
Difference 0’.6. In these observations 0 of azimuth is intended to indicate
the magnetic meridian. The dip may then be deduced by the formula
cot. 6 = cot. 7. sec. 6. The following table gives the result of this comparison:
NEEDLE No. 1. NEEDLE No. 2.
a) a i NGO
Azimuth. ; Inclination. Dip. Inclination. Dip.
0 | 72° 45’.6 | 72° 45’.6 || 72° 53’.5 | 72° 53'.5
10 73 1.7) * 46.9173 8.4) 63.7
20 73, 44.9 | 6 45:.9.1] 73: 550,.9.) $6:.= 52:2
30 44 57-20)| *© 45.61/75. (0.4) -¢6e= 49)29
40 76 39.8] * 48.2]176 45.8] * 55.8
50 78 46.3) * 50.2)/'78 52.4) 59.2
60 SL. -17.2) ** 57.6] 81 736) 6 39.7
70 84 0.0] * 55.0]] 84 3.6] 64.8
80 |86 49.2) “« 15.4]/86 55.1] * 46.3
Mean Dip, 72° 45'.6 || Mean Dip, 72° 52'.7
*Tuar the dips obtained by this method should not perfectly accord with each
other will not appear strange when it is considered that an error of one minute
in the observed azimuth at eighty degrees causes an error of nearly two mi-
nutes in the computed dip; and an error of one minute in the observed incli-
nation causes an error of more than five minutes in the computed dip. The
mean result with the two needles by the last method is 72° 49’.1; by the former
method of combination, 72° 50’.2; mean of the two methods, 72° 49'.6, which
accords perfectly with the result of observations in the meridian.
* The part of this paper which follows, was read November 20, 1840,
68 OBSERVATIONS TO DETERMINE THE MAGNETIC DIP
The preceding trial appears to me to justify confidence in the needles em-
ployed, and to give additional value to my former observations.
The following observations were made in the usual manner:
Magnetic Dip at Hudson, Ohio. Latitude 41° 15' N.; Longitude 81° 26' W.
Date. Hour. Needle. No. Readings. Dip.
1840, April 15th, 8;—11, A. M. No. 1, 40 72° 50'.3
“ “ “ & “ No. 1, poles reversed, 40 44 ,1
“ “ “ “ “ Mean of No. 1, 80 47 .2
6 ‘ 6s “ 7 No. 2, 40 69 .5
“ “ “ “ “ No. 2, poles reversed, 40 49 .0
“ Tn “ “ Mean of No. 2, 80 59 .2
“ “ “ 6 “ Mean of both needles, 160 72 53.2
Magnetic Dip at Aurora, Ohio. Latitude 41° 20' N.; Longitude 81° 20' W.
Place of observation thirty rods north-west of the Presbyterian church.
Date. Hour. Needle. No. Readings. Dip.
1840, Sept. 8th, 9—11, A.M. No. 1, 40 72° 51'.0
“ ss “ “6 No. 1, poles reversed, 40 48 .4
&s “as ‘6 “ Mean of No. 1, 80 49.7
“ “6 “ “ No. 2, 40 57.3
“ ee “ 6 No. 2, poles reversed, 40 65.1
“ ts “ “ Mean of N®. 2, 80 61.2
“ es ‘“ ‘“ Mean of both needles, 160 72 55.5
Magnetic Dip at Windham, Ohio. Latitude 41° 15’ N.; Longitude 81° 3’ W.
Place of observation fifty rods north of the Presbyterian church.
Date. Hour. Needle. No. Readings. Dip.
1840, Sept. 8th, 3—5, P. M. No. 1, 40 12° OT se
“ 6 “ “ No. 1, poles reversed, 40 59.7
“ 6s “ ‘6 Mean of No. 1, 80 58.5
“ “66 “ “ No. 2, 40 73 14.9
es ue 6 No. 2, poles reversed, 40 1.7
“ soe “ “ Mean of No. 2, 80 8.3
Mean of both needles, 160 MBie Bid
AT SEVERAL PLACES IN THE UNITED STATES. 69
‘ Magnetic Dip at Bazetta, Ohio. Latitude 41° 20’ N.; Longitude 80° 45’ W.
Place of observation near the centre of the township.
Date. Hour. Needle. No, Readings. Dip.
1840, Sept. 9th, 11;—1, P. M. No. 1, 40 72° 58'.4
“e eeu te oe ze No. 1, poles reversed, 40 57 .3
“ “ “ 6 ‘“ Mean of No. 1, 80 57 .9
6 s és “ Se No. 2; 40 61.1
‘“ sss & as No. 2, poles reversed, 40 61.8
‘“ soe ae ae Mean of No. 2, 80 61.5
“ “ “ 66 “ Mean of both needles, 160 72 59.7
Magnetic Dip at Kinsman, Ohio. Latitude 41° 30’ N.; Longitude 80° 34' W.
Place of observation half a mile south-west of the centre of the township.
Date. Hour. Needle. No. Readings. Dip.
1840, Sept. 10th, 9—11, A. M. No. 1, 40 73° 2'.0
“ “ “ “6 se No. 1, poles reversed, 40 8.9
ss 6s “ ss $6 Mean of No. 1, 80 5.5
se se «6 Lt se No. 2, 40 10.5
sc “ “ “ 6 No. 2, poles reversed, 40 2b War
“ “ “ és “s Mean of No. 2, 80 10.8
“ “ “6 “6 6 " Mean of both needles, 160 232; 6b)
Magnetic Dip at Hartford, Ohio. Latitude 41° 19’ N.; Longitude 80° 34' W.
Place of observation one mile south of the centre of the township.
Date. Hour. Needle. No. Readings. Dip.
1840, Sept. 10th, 4—5i, P. M. No. 1, 40 72° 55'.9
“ “ “ “ 6 No. 1, poles reversed, 40 51 .4
“6 “ “ “6 6 Mean of No. 1, 80 53.7
6s 6 “ ee “6 No. 2, 40 64 .0
ss “ “ “ ss No. 2, poles reversed, 40 68 .0
6 “6 “ ss 6 Mean of No. 2, 80 66.0
ss “ e ‘“ “s Mean of both needles, 160 72 59,8
70 OBSERVATIONS TO DETERMINE THE MAGNETIC DIP
Magnetic Dip at Warren, Ohio. Latitude 41° 16’ N.3 Longitude 80° 49’ WV.
Place of observation a few rods east of the village.
Date. Hour. Needle. No. Readings. Dip.
1840, Sept. 1lth, 12—13, P.M. No. 1, 40 72° 55'.2
“ “ “ 6 “ No. 1, poles reversed, 40 59 .9
‘“ 66 “ “ “ Mean of No. 1, 80 57 .6
“ “ “ ‘“ “ No. 2, 40 73 «44.2
‘“ “ “ “ “ No. 2, poles reversed, 40 3.4
“ “ “ “ “é Mean of No. 2, 80 3.8
rT: 6s “ “ “ Mean of both needles, 160 Ws "Ole
Magnetic Dip at Cleveland, Ohio. Latitude 41° 30’ N.; Longitude 81° 42' WV.
Place of observation half a mile south of the American House.
Date. Hour. Needle. No. Readings. Dip.
1840, Sept. 22d, 2—4, P.M. No. 1, 40 o> LA
“ 6 & 6 s No. 1, poles reversed, 40 16.0
6 6 a 6 ue Mean of No. 1, 80 16.7
“ce e Ge es OY No. 2, 40 7.0
“ 6 ce % No. 2, poles reversed, 40 7.6
6s “ 6 6 sé Mean of No. 2, 80 hrs:
66 ce e OF ss Mean of both needles, 160 73 12.0
This result accords better with other observations than my former observa-
tion at this place, and is believed to represent more accurately the true dip.
Magnetic Dip at Bedford, Ohio. Latitude 41° 24’ N.; Longitude 81° 32’ WV.
Place of observation a quarter of a mile south of the village.
Date. Hour. Needle. No. Readings. Dip.
1840, Sept. 23d, 1—3, P. M. No. 1, 40 72° 50'.6
“ “6s se ‘s No. 1, poles reversed, 40 58 .3
“ gs ce M cc Mean of No. 1, 80 54.5
is SR 0 sf ce No. 2, 40 64.8
ae ce xs - Gc No. 2, poles reversed, 40 58 .5
ee sot 6 6 Mean of No. 2, 80 61 .6
Mean of both needles, 160 72 58.1
AT SEVERAL PLACES IN THE UNITED STATES.
71
Magnetic Dip at Twinsburgh, Ohio. Latitude 41° 20’ N.; Longitude 81° 26' W.
*
Place of observation a quarter of a mile north of the village.
Date.
1840, Sept. 23d, 4—5, P.M.
se “ee “oe ee
Hour.
ee
Needle.
No. 1,
No. 1, poles reversed,
Mean of No. 1,
No. 2,
No. 2, poles reversed,
Mean of No. 2,
Mean of both needles,
No. Readings.
40
40
80
40
40
80
160
Dip.
72° 54’.8
48 ..7
51.8
48 .2
53 .3
50.8
72 51.3
Magnetic Dip at Tallmadge, Ohio. Latitude 41° 6' N.; Longitude 81° 26’ WV.
Place of observation half a mile south-west of the village.
Date.
“ee as a7 “e
Hour.
1840, Sept. 28th, 8—9i, A. M.
“oe
Needle.
No. 1,
No. 1, poles reversed,
Mean of No. 1,
INOS;
No. 2, poles reversed,
Mean of No. 2,
Mean of both needles,
No. Readings.
40
40
80
40
40
80
160
Dip.
72° 43'.6
54.1
48 .9
53.8
49 .0
51 .4
72 50.1
[ have always aimed to remove all iron from my person before commencing
a series of observations; but after concluding the preceding, I found, to my sur-
prise, an iron key in my coat pocket.
sequently repeated in the same place.
Magnetic Dip at Shalersville, Ohio.
The observations were, therefore, sub-
Latitude 41° 15' N.3 Longitude 81° 13' W.
Place of observation forty rods west of the Presbyterian church.
Date.
1840, Oct. 15th, 2i—4, P.M.
Hour.
Needle.
No. 1,
No. 1, poles reversed,
Mean of No. 1,
No. 2,
No. 2, poles reversed,
Mean of No. 2,
Mean of both needles,
No. Readings.
40
40
80
40
40
80
160
Dip.
72° 59'.1
51.9
55 .5
54 .3
61.0
57 .6
72 56.6
72
OBSERVATIONS TO DETERMINE THE MAGNETIC DIP, ETC,
Place of observation a quarter of a mile west of the village.
Date.
1840, Oct. 16th,
Hour.
9—11, A.M.
Magnetic Dip at Tallmadge, Ohio.
Needle. No. Readings.
No. 1, 40
No. 1, poles reversed, 40
Mean of No. 1, 80
No. 2, 40
No. 2, poles reversed, 40
Mean of No. 2, 80
Mean of both needles, 160
Magnetic Dip at Streetsboro, Ohio. Latitude 41° 15' N.; Longitude 81° 20’ W.
Dip.
72° 46'.2
55.8
51.0
52 .6
57 .4
55 .0
72 53.0
Latitude 41° 6’ N,; Longitude 81° 26' WV.
Place of observation the same as formerly.
“ee
6e
Date.
1840, Oct. 31st,
a7
se
ee
ee
Hour.
2—33, P.M.
ae
“ce
Needle. No. Readings,
No. 1, 40
No. 1, poles reversed, 40
Mean of No. 1, 80
No. 2, 40
No. 2, poles reversed, 40
Mean of No. 2, 80
Mean of both needles, 160
Dip.
72° 53/.5
44.1
48 .8
47 .6
47 5
47 .5
72 48.2
This result is almost identical with the former observation, indicating that
the effect of the iron key was scarcely appreciable.
The preceding observations, as well as those which I have formerly made in
Ohio and Michigan, are tolerably well represented by parallel, straight, and
equidistant isoclinal lines, running from N. 80° W. to 8, 80° E.; and the line
of 73° passes five or six miles south of Cleveland.
ARTICLE VI.
On the Perchlorate of the Oxide of Ethule or Perchloric Ether. By Clark Hare
and Martin H. Boye. Read December 4, 1840.
THE energetic properties of perchloric acid, and its stability, compared with
the other compounds of chlorine with oxygen, led us to the belief that this acid
might be combined with the substance which performs the part of a base in
that class of organic salts which are generally designated by the name of ethers,
and for which Berzelius, in consequence of his theoretical views, has adopted
the name of oxide of ethule. For this purpose a concentrated solution of per-
chlorate and sulphovinate of barytes, in equivalent proportions, was subjected
to distillation. The sulphovinate of barytes may be considered as a double
sulphate of barytes and the oxide of ethule; and we anticipated that, when heat
was applied, a double decomposition would take place between the latter and
the perchlorate of barytes. So long as the salts remained in solution no reac-
tion occurred, but as soon as they became solid in consequence of the distilla-
tion of the water, a reciprocal decomposition ensued, and a sweet ethereal
liquid distilled into the receiver. This quid is the perchlorate of the oxide of
ethule.
As this substance is extremely explosive, in order to prepare it with safety it
is necessary to operate on small quantities. We have employed from seventy to
ninety grains of crystallized sulphovinate of barytes, with an equivalent propor-
tion of perchlorate of barytes*; but we would recommend, especially on the first
* The amount of barytes in the perchlorate should be ascertained by an experiment, as it retains
water with great tenacity. It may be worth while to mention, that the perchlorate of potassa can-
Vill?
74 ON THE PERCHLORATE OF THE OXIDE OF ETHULE,
performance of the experiment, the employment of considerably smaller quanti-
ties. The salts should be intimately mixed in a mortar, and placed in a small
retort attached to a refrigerator containing ice, and a receiver similarly cooled.
The retort is to be heated in an oilbath, in which a thermometer is suspended,
so as to indicate the temperature. A wooden screen, furnished with openings
covered with thick plate-glass at such intervals as to afford a full view of the
different parts of the apparatus, should be erected in front of it, and strings
passed around the screen and attached to a bar traversing on a pivot, and sup-
porting an argand spirit lamp, by which heat is communicated to the oilbath,
so as to enable the flame of the lamp to be removed from or applied to the ap-
paratus, according to the indications of the thermometer, without exposing the
person of the operator. After the heat has reached 212° F., below which the
salts employed do not react on each other, it should be raised very gradually,
and the distillation finished below 340° F. Under these circumstances but
little danger is to be apprehended from the retort, but the ether in the receiver
must be treated with the greatest caution, since it has exploded in our hands
in attempting to remove it with a pipette from the stratum of water which
covers it. This water, therefore, should be removed by the cautious use of
strips of blotting paper, moistened at the end, and introduced into the tube
employed as a receiver.
To avoid the danger attendant on the management of the ether in its pure
state, it may be received in strong alcohol, since it is not explosive when dis-
solved in alcohol. If the experiment be performed with seventy grains of sul-
phate of barytes, from one to two drachms of absolute alcohol will be found
sufficient for this purpose. By the addition of an equal volume of water, the
ether may subsequently be separated from this solution, in small quantities, for
the purpose of examination. But, in this case a loss of ether is sustained, by
the decomposing influence of the water employed.
The perchlorate of ethule obtained in this way is a transparent, colourless
liquid, possessing a peculiar, though agreeable smell, and a very sweet taste,
which, on subsiding, leaves a biting impression on the tongue, resembling that
of the oil of cinnamon. It is heavier than water, through which it rapidly
not be substituted for the perchlorate of barytes, since the sulphovinate is decomposed without
acting on it. We were equally unsuccessful in an attempt to procure the ether by the distillation
of perchlorate of barytes and concentrated sulphovinic acid.
OR PERCHLORIC ETHER. 75
sinks. It explodes by ignition, friction, or percussion, and sometimes without
any assignable cause. Its explosive properties may be shown, with but little
danger, by pouring a small portion of the alcoholic solution into a small porce-
lain capsule, and adding an equal volume of water. The ether will collect in
a drop at the bottom, and may be subsequently separated by pouring off the
greater part of the water, and throwing the rest on a moistened filter, sup-
ported by a wire. After the water has drained off, the drop of ether remaining
at the bottom of the filter may be exploded either by approaching it to an ig-
nited body, or by the blow of a hammer. We are induced to believe that, in
explosive violence, it is not surpassed by any substance known in chemistry.
By the explosion of the smallest drop, an open porcelain plate will be broken
into fragments, and by that of a larger quantity, be reduced to powder. In
consequence of the force with which it projects the minute fragments of any
containing vessel in which it explodes, it is necessary that the operator should
wear gloves, and a close mask, furnished with thick glass-plates at the aper-
tures for the eyes, and perform his manipulations with the intervention of a
moveable wooden screen.*
In common with other ethers, the perchlorate of ethule is insoluble in water,
but soluble in alcohol; and its solution in the latter, when sufficiently dilute,
burns entirely away without explosion. It may be kept for a length of time
unchanged, even when in contact with water; but the addition of this fluid,
when employed to precipitate it from its alcoholic solution, causes it partially
to be decomposed. Potassa, dissolved in alcohol, and added to the alcoholic
solution, produces, immediately, an abundant precipitate of the perchlorate of
that base, and, when added in sufficient quantity, decomposes the ether en-
tirely. It would appear, therefore, impracticable to form either perchlorovi-
nates or perchlorovinic acid.
We have subjected the perchlorate of ethule to the heat of boiling water
without explosion or ebullition.
It may be observed that this is the first ether formed by the combination of
an inorganic acid containing more than three atoms of oxygen with the oxide
of ethule, and that the chlorine and oxygen in the whole compound are just
sufficient to form chlorohydric acid, water and carbonic oxide with the hydro-
gen and carbon.
* Having suffered severely on several occasions from the unexpected explosion of this substance,
we would earnestly recommend the operator not to neglect the precautions mentioned above.
76 ON THE PERCHLORATE OF THE OXIDE OF ETHULE, &c.
The existence of a compound of the oxide of ethule with an acid containing
seven atoms of oxygen led us to attempt to combine, by the same method, this
base with nitric acid. For this purpose we subjected a mixture of sulphovi-
nate and nitrate of barytes to the same treatment as described above, but the
reaction, even when conducted with the greatest possible care, is destructive,
hyponitrous ether and gaseous matters being the principal products obtained.
Nor were we more successful in our attempts to procure a sulphurous or hy-
posulphuric ether by the same process.
ARTICLE. VIL.
Observations on the Storm of December 15,1839. By William C. Redfield, A. M.
Read January 15, 1841.
In the table and map which are annexed to these remarks will be found the
observations which have been obtained of the direction of wind in this storm,
in the states of Connecticut, Rhode Island, Massachusetts, New Jersey, and
parts of the states of Maine, New Hampshire, Vermont, and: New York.
The arrows on the map denote, approximately, the direction of wind, at or
near the hour of noon, at the several places of observation. The concentric
lines, drawn at intervals of thirty miles, were added, not as precisely indicating
the true course of the wind, but to afford better means of comparison for the
several observations.
It will be seen, that of forty-eight distinct sets of observations, which are
comprised in the annexed schedule, about thirty are derived from the meteoro-
logical journals of scientific and intelligent observers, or from the log-books of
vessels exposed to the storm. And I take this occasion to offer my thanks to
the gentlemen who have so kindly furnished me with their observations,
The position assumed for the axis of the gale, at noon, should, perhaps, be
nearly in line with the position of the ship Morrison and Cape Cod Bay; at
which places the wind was then blowing from opposite points of the compass,
but not in actually opposing directions. 'The Morrison was from China, bound
to New York; and I have reason to believe that her position at noon may be
safely relied on. The violence of the gale was here so great that the ship, as
I am informed, was lying to without canvass. This ship had encountered the
VIII.—vU
78 OBSERVATIONS ON THE STORM OF DECEMBER 15, 1839.
western side of the gale, suddenly, at 7, A. M., and the sun shone chiefly un-
obscured during the greater part of the day.
The gale was severe over the entire surface comprised in the map, except,
perhaps, on its extreme northern and north-western portions, and excepting,
also, the lighter winds which were observed near the apparent axis of the gale,
in the region of Buzzards’ and Cape Cod Bays, &c., in the afternoon and even-
ing. A very heavy fall of snow accompanied the gale in the states of Connec-
ticut, Rhode Island, Massachusetts, New Hampshire, and Maine; also, in some
parts of New York and southern Vermont. Some snow also fell in the west-
ern and northern parts of New York and Vermont, but attended with more
moderate and variable winds, chiefly from the north and west.
The south-westerly and southerly winds, which connect the south-easterly
with the westerly winds in the circuit of rotation, are found at Nantucket in
the afternoon, by the farther advance of the storm, and also in the log-books of
a number of vessels whose positions were eastward and southward of the ship
Morrison, but beyond the limits of the map.
The barometric minimum, as in other storms, appears to have nearly coin-
cided, in its progress, with the apparent axis of the gale.
My main object in collecting the observations contained in the subjoined
schedule has been to establish the course of the wind in the body or heart of
the storm at a given time, and apart from all other considerations. I am in
possession, however, of more extended observations of this gale. Many of
these appear to agree with some of the following characters or modes of
action which pertain, more or less, to many of the storms or gales that visit the
United States and other regions. These characters have claimed attention
from almost the earliest period of my inquiries.
1. The body of the gale usually comprises an area of rain or foul weather,
together with another, and perhaps equal, or greater area of fair or bright
weather.
2. The fall of rain or snow often extends, in some direction, greatly beyond
the observed limits of the gale.
3. The gale itself not unfrequently exhibits an apparently unequal extent of
action, or degree of violence, on different sides of its apparent axis of rotation.
This peculiarity, as well as the second, is most common in winter storms,
and in those which sweep over an extensive continental surface; and, like other
OBSERVATIONS ON THE STORM OF DECEMBER 15, 1839. 79
irregularities, is less noticeable in the storms which are traced solely on the
ocean.
4. The barometric indications of a gale commonly extend much beyond the
observed limits of its action.
5. The body of the gale constitutes a determinate sheet or stratum of moving
air; and of this sheet or stratum a large portion sometimes overlies another and
more quiescent stratum of air, the latter having, perhaps, a different motion; as
in common winds of the temperate and higher latitudes: in which case the gale
is either not felt at the surface of the earth, or the observed changes of wind
are found, in part, unconformable to the whirlwind theory.
6. Owing to the convergent and somewhat variable courses of storms in the
extra tropical latitudes, as well as to their unequal rates of progress, two storms
will sometimes cover, in part, the same field, one of which will overlie the
other, and, perhaps, thin out at its margin, in the same manner as common
winds. This, also, may occasion a different order of change in the observed
winds and weather from that which is more commonly noticed in a regular
whirlwind storm.
Owing to such causes, the oscillations of the barometer are often irregular;
and this is particularly noticeable in the higher latitudes.
7. In most gales of wind there is, probably, a subordinate motion, inclining
gradually downward and inward in the circumjacent air, and in the lower por-
tions of the gale; and a like degree of motion, spirally upward and outward, in
the central and higher portions of the storm. This slight vorticular movement
is believed to contribute largely to the clouds and rain which usually accompany
a storm or gale; and is probably due, in part, to the excess of external atmosphe-
ric pressure on the outward portions of the revolving storm.
8. In storms which are greatly expanded there is sometimes found an exten-
sive area of winds of little force and variable direction, lying within the circuit
of the true gale, and attended throughout, with a depressed state of the baro-
meter. ‘This more quiescent portion of air in the centre of a gale has been
found to extend, in some cases, to a diameter of several hundred miles.
In the case now before us, the direction of the arrows representing the course
of the wind at noon, as carefully drawn on a larger map, shows an average con-
vergence, or inward inclination, of about six degrees. But it is not deemed
safe to rely upon this result in a single case, which is liable to be affected by
80 OBSERVATIONS ON THE STORM OF DECEMBER 15, 1839.
the errors of observation and the deflecting influences of the great valleys and
lines of elevation, as well as by the errors of approximation which often arise
from referring all winds to eight, or, at most, to sixteen points of the compass.
It is not intended, on this occasion, to support the foregoing characteristics
by such extended details of evidence as their discussion would necessarily de-
mand; and they are mentioned here only because the true character of the ro-
tation in these gales, as well as the necessary or incidental connexion of this
rotation with other phenomena which attend them, has seemed to be often
misapprehended.
As relates to the whirling or rotary action in the case before us, it may be
remarked, that had we obtained no observations from the north-western side of
the axis of this gale, it would have been easy, in the absence of more strictly
consecutive observations than are usually attainable, to have viewed the initial
south-easterly wind of the gale,* and the strong north-westerly wind which
soon followed, as two distinct sheets, or currents of wind, blowing in strictly
opposing directions: and if we could so far lose sight of the conservation of
spaces and areas, the laws of momentum and gravitation, together with a con-
tinually depressed barometer within the storm, we might then have supposed.
one of these great winds, if not both, to have been turned upward by an unseen
deflection, and doubled back upon itself in the higher atmosphere. But the
case neither calls for nor admits these speculations. If, however, the axis of
this gale had chanced to pass westward and northward of our limits of correct
observation, in pursuing its north-easterly course, as did, perhaps, that of the
storm of December 21st, 1836, which has been ably examined and discussed
by Professor Loomis, it is, in such case, more than probable that its whirl-
wind character would not have been established.
* Observed between the coast of Massachusetts and latitude 25° N,
t Trans. Am, Phil. Soc., Vol. VIL, p. 125—163,
VIII.—vV
[AP
Showing the Direction of the Wind
a loonas ebserved at various
placesinthe Storm oF
Dee.15 1839
By
W.CREDFIELD
1840
fe, ral
{0 Lgtsh miles 450
Schedule of Observations on the Direction of Wind an the Storm of December 15th, 1839: With a Map indicating the Direction
of the Wind at or near the hour of Noon.
By Witt1am C. Reprievp.
No. Places of Observation. A. M. Noon. P.M. Observers and Authorities. °
“1 Nantucket, Ms. . E. S.E.atlp.m. . S. W. Report of James Mitchell, as published by Mr. Espy._ [ Nantucket.
2 Woodville, Ms. . : - | A little S. of E.” |Clouds broke at W.| Observations on board Steamboat Telegraph, by William Mitchell of
before 2 P. M.
3 Barnstable, Ms. . N.E. at 7 a.m. B E. at 2 p. m.: 8. E.|Report to Editor of Boston pare I take the mean of E.and S. E.
Do. Gale from 8. E. . } [ESE : SW. pom Clear Letter of Wm. H. Brown toW. C.R. $ fortruedirection at Noon. w.c.R.
t Sunse’
4 New Bedford, Ms Sunrise, N.E. mod.) 2 E.byN i 2p. m. E. N. E.: 34, Joseph Congdon’s Meteorological et Ttake E.by N.as the mean
¢ . . 5 s.
Do. do. E. fresh, ) [E.by N.] do|E: SunsetS S £/Sam’l Rodman’s. do. as publ’d by Mr. Espy.) for Noon.
5 Newport, R. I. Ni dispce E Nov Es N. E. . |Meteorological Journal published at Newport.
6 Cape Cod Bay, . E.S. E. E.'S: E. E.S.E.at2 p.m. |Report of Capt. Slemmer, Brig Columbus.
7 Provincetown, Ms. E. S. E. . E. 8. E; E. S. E. . |Marine Reports in Boston Newspapers.
8 Providence, R.I.. Niger ° N. E. . IN. Ex. Professor Caswell’s Meteorological Journal.
9 Norwich, Ct. INS Es 6 N. E N.E.*: Norwich Courier.
10 Culloden Point, N.Y.
11 Boston, Ms.
Do.
12 Gloucester, Ms. .
13 Salem, Ms. 5
14 Waltham, Ms. .
15 Worcester, Ms. .
16 Middletown, Ct. .
Do. :
17 New Haven, Ct. .
Do. J
18 Ship Morrison, at sea:
Lat 39° 35 N. Lon.71° 50 W.
19 Portsmouth, N. H.
20 Nashua, N. H.
Northampton, Ms.
oe Ms.
22 Litchfield, Ct.
Stratford, Ct.
Concord, N. H. .
Keene, N. H.
West Point, N.Y.
New-York City, .
Fort Wood, N.Y. Harbor
Flatbush, N.Y.
30
31 Portland, Me.
32 Hanover, N.H.
33 Salem, N.Y.
epee, iN...
Lansingburgh, N.Y.
35 Kinderhook. N.Y.
36 Kingston, N.Y. .
37 Goshen, N.Y. .
33 Bark Ann Louisa, off Ab-
secom, N. J:
39 Trenton, N. J.
40 Cape May,N.J..
Fire Island Beach, N.Y.
Sandy Hook Bay, N.Y.
“changed to
Sunrise, N.E. .
E. by N. $
E. S.E.
Eastward. .
IN. Eas.
. by W.
Night of 14, 15, N.E
N. by W.
Midnight, N.E. :
veered by N.
Northeasterly.
NOE: . A
N. é 5
N. by W.: N. N.W.
222524252212
W...N.'W.
N. W. .
N. W.
N. W. at Noon.” .
RINSE 2
E. by xen nif
EsscE. ¢ ©.
Eastward. .
[E.N.E.]
N. Ea *k,
[N. by E.] i
} IN. 3° E.] i
W.N.W. .
Nie S: 7,
} (N.N.E.] ;
[N.N.E.]
N. by W.
N.N.W. .
N.E..
N. E.%
Nev aie
N.N.W. .
[N.N.W.]
[N.N.W.] .
N.W..
LE. 6° S. mean.].
EN: Ese
NES
} [N. 28° E.J i
N.E..
Natiog =
[N.N.E.] .
N.W..
NW...
N.W.
Sunset, E. S. E.
E. by N.
E.8-E. «
Eastward. . .
E. A 5
NES 2 .
N. :
N. N. E.
IN; NAW! 4c
N.N. E. till 13 p.2.
W.N. W..
E.
N. E. 5
ING UR ee
N.by W. .
N. at Night of 15th.
N. by W.
N. N. W.
N.E. and more N’ly
N. E. .
N.
N.W. by N
N. W. a
N. W. a
N. W.
byS .
Capt. Green's Account, as published by Mr. Espy.
Wm. Cranch Bond’s Meteorl. Journal. ; I take the mean of the observa-
Robert Treat Paine’s Observations. tions at Noon.
Letter from Gloucester, in the Boston Newspapers.
Salem Gazette.
Monthly Met. Jour., by C. F., in the Boston Daily Centinel.
Met. Journal at State Lunatic Hospital—in National gis.
Reported by Professor oe ,
Dr. Barrates Met: Jourial I take N. by E. for the mean at Noon.
; Ttake the mean of
Report of Capt. Woolsey, Steamboat Providence.
Judge Darling’s Meteorological Journal. N. 3° E.
Ship’s Log Book—also, Statements of Capt. Benson and his Officers.
Weekly Meteorological Journal, published at Portsmouth.
Nashua Telegraph.
Observations of W. Atwill and others. ; T assume the approximate mean
Professor Snell’s Met. Journal. of N. N. E. for Noon.
Litchfield Enquirer, Assumed mean for noon of 15th, N. N. E.
Rev. J. R. Linsley’s Meteorological Journal.
Captains Cartwright and Skiddy, employed at the Beach.
Letter from Concord to S. G. Arnold; from Mr. Arnold.
Rev. Z. 8. Barstow’s Meteorological Journal.
Meteorological Journal of the Medical Department.
Meteorological Journal of W. C. Redfield.
Met. Journal of Medical Officer. Mean of N. N. W. taken for Noon.
Rev. T. M. Strong’s Met. Jour. Mean of N. N.W. assumed for Noon.
Log Book of Bark Osceola.
Met. Report of Keeper of Marine Observatory : Published at Portland.
Professor Young’s Meteorological Journal.
William Brand and W. Larkin; Meteorological Journal.
T. Romeyn Beck, M. D. Met. Journal, i Mean assumed for Noon,
E. T. Foote, Meteorological Journal. ) N.28° E.
Silas Metcalf, Meteorological Journal.
Isaac Blauvelt; Meteorological Journal. ~~ — [noon, N.N. E.
Nathaniel Webb and John 8. Crane; Met Jour. Mean assumed for
Ship’s Log Book, and Statement of Capt. Wilson.
Dr. F. A. Ewing’s Meteorological Journal.
Marine Reports, and Letter from Cape May, in Philad. Newspapers.
* — Abbreviations.—N. H. State of New Hampshire; Me. Maine; Ms. Massachusetts; R.I. Rhode Island; Ct. Connecticut; N.¥. New-York; N. J. New Jersey— Note. My wn observa
tions on the 15th P, M. have on a former occasion been erroneously printed N. W. by W.; for which read N. W. by 1.
ARTICLE VIII.
On the Purturbations of Meteors approaching near the Earth. By Benjamin
Pierce, A. A., Hollis Professor of Mathematics and Natural Philosophy in
Harvard University; in a Letter to S. C. Walker, Esq. Read January 15,
1841.
My Dear Sir,
Many sources of almost unceasing occupation have prevented my giving Mr.
Erman’s* paper on Meteors that early attention which I intended. I shall now
turn my attention to the point which you suggested of the earth’s attraction. Al-
most the whole labour has fortunately been saved for me by Laplace, in the Mec.
Cél., Vol. IV., Book IX., Chap. II., “On the Perturbations of a Comet, when
it approaches very near to a Planet.” He has there proved (8038, Bowd. Ed.,)
that “we may, in the calculation of such a comet, suppose the planet to have
a sphere of activity, in which the relative motion of the comet is affected only
by the planet’s attraction; and that beyond this point the absolute motion of the
comet about the sun is performed in exactly the same manner as if the sun
alone acted upon it.” The radius of this sphere is by (8035)
r.\/ (4m);
in which
y = the radius vector of the planet,
m = its mass divided by the sun’s mass;
so that, in the present case, this radius, which we denote by 7, 18
r, = 0:0053,
in which the unit is the same as Erman’s.
Now the relative orbit of the meteoric ring is directed nearly to the centre
* Schumacher’s Astr. Nachr., No. 385.
84 OBSERVATIONS ON THE ORBITS
of the earth, and I shall regard it as exactly directed towards this centre; in
which case, the only effect of the earth’s attraction is to increase the relative
velocity without changing the relative direction. The only change which is,
therefore, required in Erman’s paper is to increase the relative velocity v’ by
this increase of velocity. The increased velocity is determined by the formula
nto 4 fo =8
in which
R = the earth’s radius,
g = the attractive force of the earth at the unit of distance,
v,' = the increased velocity,
Hence
29 _ 29 _ 9-13932, v,/? = v'? + 0713932
To
and the five values of v,', corresponding to the five values of v’, calculated by
Erman, are
0-91118, 141818, 169177, 193830, 2:17363.
Nothing farther seems needed upon this point, and I therefore leave it to notice
an omission by Professor Erman.
He has neglected the negative sign of the radical in the equation
vi =—ecos.uty (v?— é sin. *u),
and this sign may be used as long as the resulting value of v’ is not negative.
Thus, for the value of v
= 0°77382
we should find
vo’ = 0°29426
velocity in perihelion = 2°235
perihelion distance = 0°4186
T = 060973
@ = 12° 3’
which shows that Erman’s conclusions, regarding the relative velocity and the
inclination of the orbit, are unsound.
In reviewing some of his numerical results, I differ a little from him, but
the difference is of no practical importance.
Another most important point for consideration is the difference of direction
AND VELOCITY OF METEORS. 85
of the different meteors. Now this difference of direction amounts to more
than 10° on the average (according to Erman) from the mean direction, and
cannot, for the maximum, be less than 25°. This difference of direction may
arise
1. From the difference in their elliptic orbits about the sun.
2. From their mutual action.
3. From the earth’s attraction.
1. Supposing, with Erman, the breadth of the ring to be 2°, the difference
arising from the first cause cannot be more than 1° from the mean direction.
2. The deviations arising from their mutual attractions must be trifling;
they cannot, for stance, be supposed greater than they would be if all the
meteors but the disturbed one, which we may be considering, were combined
into one planet, about which this disturbed one moved as a satellite. Now if
we consider that the variation in the moon’s absolute direction from the earth’s
is only about 2°, we shall have no hesitation in neglecting this second cause of
disturbance.
The difference in direction arising from the first two causes is absolute, and
may be somewhat magnified when converted into relative direction, but not
much, unless the relative velocity v’ is very small. There is also a difference
of absolute velocity, which will produce a difference of relative direction of
about the same order of magnitude with that arising from the difference of ab-
solute direction.
3. The observed difference of direction must then be chiefly referred to the
principal disturbing cause, the earth; and the following method of calculation
is sufficiently accurate for the present case. Let
,
v
the relative velocity of the meteors at the moment of entering the
sphere of the earth’s influence, which sphere we may, for this cal-
culation, suppose to be infinite,
@ = the angular deflection of the meteor’s relative motion,
then no other meteor will be so much deflected as the one which just grazes
the surface of the earth; and for this meteor we have
age 54
coset. p= 1+ 7
v'? = — (cosec. p — 1)
an
R
Vill. W
86 OBSERVATIONS ON THE ORBITS AND VELOCITY OF METEORS.
whence, for a deviation of 15°, v’ must be less than one-third of the earth’s ve-
locity; that is, far less than either of Krman’s supposed values of v’; and for
the least value of v', which Erman has given, namely,
vy’ = 0'83122,
we have
cca) = ae 38’,
which appears to be entirely contrary to a large majority of the observations.
Now, for
vo’ = 033333 = 4
we find
m=14°10, v= 75 =}
so that the plane of the meteors cannot differ much from that of the ecliptic,
and their relative velocity cannot exceed one-third of the earth’s velocity. The
other elements of the orbit are of less interest, and I shall not stop to calculate
them. A ring so nearly in the plane of the earth’s orbit must be subject to
very great perturbations, and if there is one, I think that no observations which
we can make will enable us to calculate its motions with any degree of ac-
curacy.
Believe me, my dear sir,
most sincerely yours,
B. PIERCE.
CaMBRIDGE, December 24, 1840.
ARTICLE IX.
Researches concerning the Periodical Meteors of August and November. By
Sears C. Walker, A. P. S. Read January 15, 1841.
§ I. OF THE RELATIVE VELOCITIES OF SHOOTING STARS.
Tue discovery of the existence of a radiant, or its antipode, the convergent
point for the relative paths of the shooting stars composing the splendid specta-
cle of November 12th, 1833, and its confirmation on several subsequent, but
less brilliant displays of these bodies, has opened the field for fresh researches
concerning their geometrical relations. The earliest attempt to deduce the
necessary inferences from such a discovery was made by Prof. Olmsted,’ shortly
after the great shower of 1833. In this inquiry he was followed, in 1834, by
Prof. Twining? and Mr. Espy*; in 1835, by Arago*, Biot*® and others; and, in
1836 and 1837, more concisely, by Quetelet’ and Olbers’, and, subsequently, by
Mr. Herrick* and Prof. Lovering.’ Finally, in 1839, a full and systematic inquiry
on the subject was instituted by Prof. Erman," Jr., of Berlin. An abstract of the
* Silliman’s Journal, vol. xxvi., p. 144. See also subsequent volumes.
2 Idem. vol. xxvi., art. viii. 8 Journal Franklin Institute, vol. xv., p. 9.
* Annuaire du Bureau des Longitudes, 1836. 5 Sill. vol. xxxi., p. 181.
® Quetelet’s Catalogue des Principales apparitions d’étoiles filantes. Nouveaux Mémoires de
VAcadémie, &c., de Bruxelles, 1839. Also Annuaire de l’Observatoire de Bruxelles, 1837.
7 Die Sternschnuppen, Schumacher’s Jahrbuch for 1838, p. 319, note. Also Schumacher’s As-
tronomische Nachrichten, Nos. 372, 384.
8 Sill. vol. xxxiii., art. xx., and vol. xxxv., art. xix.
8 Idem. vol. xxxv., art, x. 1° Astr, Nachr., Nos. 385, 390, 402, and 404.
88 RESEARCHES CONCERNING THE PERIODICAL
limits assigned by this author for the elliptic elements of some of these bodies,
considered as asteriods, has been published in the proceedings of this Society
for August 21st, 1840. An examination of Professor Erman’s analysis having
led to the conclusion that his limits for these elements are too restricted, and
that more simple formule might be obtained by adopting instead of the earth’s
actual velocity, the well known Gaussian constant as the unit of linear velo-
cities, induced me to undertake the discussion afresh. In doing so, however,
it is proper to remark, as must be obvious to every one, that the nature of the
subject is such as to deprive the discussion of that demonstrative character
which distinguishes the results of astronomy proper. Such a circumstance,
however, should not deter us from aiming at the greatest precision in our
knowledge of the geometrical relations of these small bodies, which the nature
of the case permits.
The principal data which the theory of shooting stars derives from observa-
tion are their relative velocities and directions as seen by an eye in motion, and
the dates of remarkable showers, or brilliant meteoric displays. These data,
if furnished with precision, are sufficient for the completion of their theory,
considered as cosmical bodies. In the case of a newly discovered planet or
comet, a single observation furnishes only a geocentric position, the distance,
relative velocity, and direction of motion, being as yet unknown. Hence
three successive positions, at known intervals, are required in order to deter-
mine, by Kepler’s and Newton’s laws, the (geocentric or heliocentric) distance,
velocity and direction of motion, at one of the three dates,—from which all the
elements of the elliptic orbit of the planet or comet may be derived. When
we consider the precision of observation, and the length of elapsed time, which
are requisite for determining the path of a planet or comet, it will appear sur-
prising at first, that enough should ever be known concerning the geometrical
relations of a body, which appears for a moment and then vanishes for ever, to
enable us even to form a conjecture concerning its true motion in the heavens
for an indefinite period past and to come. There are, however, several impor-
tant advantages in the case of shooting stars which do not present themselves
in a single observation of a newly discovered planet or comet. The shooting
star or asteroid is necessarily within a few seconds of its node, and its helio-
centric radius vector differs from that of the spectator by a quantity so small
as to be safely neglected in computations for the approximate elements of its
orbit. A similar remark applies to the heliocentric longitude of the observer
METEORS OF AUGUST AND NOVEMBER. R9
and asteroid, which may be regarded as common. By the ordinary computa-
tions for the transfer of co-ordinates from the centre of the earth to the position
of the spectator, or quite as well by neglecting quantities so small, it is always
possible to determine three data for the orbit of every meteor that is seen,
namely, the node, radius vector, and time of passing the node. To complete the
six elements it is only necessary to know, at the same time, three other quan-
tities, the asteroid’s true or relative velocity in space, and its direction with
reference to two given planes, the equator or ecliptic, for instance, and a se-
condary to the same. The determination of the first of these three requisites,
the relative velocity of shooting stars, was first undertaken in 1798, by two
students of Gottingen, Brandes and Benzenberg,"* and was pursued with a zeal
which terminated only in the death of the former. A notice of their labours
has been given by Olbers, and by Quetelet. An abstract by Professor Loomis
of the results obtained by Brandes, in 1823, may be found in Silliman’s Jour-
nal,”’ giving the results of corresponding observations in Breslaw and its vicinity.
In 1824, Quetelet’* and others in Brussels and its neighbourhood engaged in
similar researches. On the memorable occasion of the display of November
12th, 1833, among the myriads of meteors seen, one only was known to have
been beheld at several places. It was distinguished by its extraordinary size
and brilliancy, and by the duration (ten minutes at least) of its train, which,
after assuming various serpentine shapes, “terminated in a luminous nebula
of several times the diameter of the moon, floating onwards with a velocity
greater than that of the clouds.” Mr. Twining,” after a full discussion of all
the facts connected with this meteor, concludes that its apparent path was about
forty-eight geographical miles, and its duration about three seconds, making
a mean relative velocity of about sixteen miles per second. Corresponding
observations were made at Breslaw and its vicinity by Boguslawski and others,
Noy. 13th, 1836, and August 9th, 1837. I have not been able to obtain the
single results, and therefore quote the remark of Olbers,’’ that results obtained
for the November meteors of 1836 “ show that the periodical meteors also have
the same height and relative velocity as the ordinary shooting stars hitherto
1 Versuche, die entfernung, &c., der Sternschnuppen zu bestimmen. Hamburg, 1800.
Bestimmung der geographischen Liinge durch Sternschnuppen, Von I. F. Benzenberg. Ham-
burg, 1802.
12 Vol. xxviii., p. 95. 18 Catalogue, &c., p. 5. 44 Silliman, vol. xxvi., p. 46.
*§ Schumacher’s Jahrbuch, for 1838, p. 322. Note.
VINX
90 RESEARCHES CONCERNING THE PERIODICAL
observed.” Also, Quetelet remarks that Mr. Boguslawski obtained “ results
analogous” to those of his table for the relative velocities of the meteors of
August 9th, 1837. On the 29th of August, 1838, the younger Littrow * ob-
tained corresponding observations of several meteors in Vienna and its vicinity.
An effort by Mr. E. C. Herrick and others, in April, 1839, in New Haven,
Middlebury, Williamstown, Cambridge, and other places, was unsuccessful for
want of coincidences, like a similar attempt of Brandes and others in 1817. The
method adopted in all instances is to prove the identity’ of the meteors seen
at two different places. Then the space traversed, and the duration give the
relative velocity. The Vienna observations of 1838, for relative velocities,
have not been fully reduced, the memorandums for duration not being
complete. Such results, as far as obtained, are given in Table I., chiefly
from Quetelet’s Memoir on Shooting Stars. ‘The results obtained by Twi-
ning, and the remarks quoted from Olbers and Quetelet are important in the
present inquiry, as they show that the mean relative velocity, 18.3 geogra-
phical miles per second from all the results yet obtained, may be taken for a
first approximation in estimating the elements of the elliptic orbits of those
meteors or asteroids whose relative direction is known. It is much to be
desired that Table I. should be farther extended, and, as an encouragement to
enterprise in this department of meteorology, we have the high authority of
Bessel,'? who “ doubts not that every desirable degree of perfection is attainable
by observation, in so far as regards our knowledge of the geometrical relations
of shooting stars.”
On examining Table I. it will appear that the single results arrange them-
selves on both sides of the mean result 18.3 miles per second, with an average
discrepancy of about 5.2 miles per second. As far as we can judge from so
small a number of results, necessarily somewhat imperfect, it would seem that
the mean relative velocity of shooting stars tends towards that of the earth in its
orbit, namely, 16.4589 geographical miles (of 60 to a degree) per second, with
16 Catalogue, &c., p. 6. Note.
17 Annalen der K. K. Sternwarte in Wien, 1838. p. xviii.
48 See Loomis’ Notice of Brandes’ Memoir, above quoted, p. 98.
29 Uber Sternschnuppen Astr. Nachr. 381, p. 50. ‘*Ich zweifle nicht, dass die Kentniss der
Sternschnuppen, in so fern von den geometrischen Verhiltnissen, die man daran wahrnehmen
kann, die Rede ist, so vollstiindig gemacht werden kann, als man zu wiinschen berechtigt ist.”
METEORS OF AUGUST AND NOVEMBER. 9]
average discrepancies of less than one-third of that value. The first result is
such as we should naturally expect, since, in the case of bodies moving with
all varieties of directions and velocities, there must be a compensation of these
velocities resolved each at the time of visibility in the direction of the ob-
server’s tangential motion. The second result—the smallness of the average
discrepancy—if it leads to any conclusion at all, shows that the average true
velocity of the meteors is small, or the mean discrepancy of the relative veloci-
ties would be greater. Lastly, this mean relative velocity of shooting stars is
so great as to preclude the possibility of a terrestrial or lunar origin. Since
it follows from the laws of gravity, according to the remark of Olbers,”°
Laplace,*' Hassler,” and others, that the mean relative velocity of a satellite
of the earth, at its nearest possible approach to the observer, is only about 4.29
geographical miles, and its maximum in a re-entering orbit only 6.06 geogra-
phical miles. Hence all bodies of our system which, when visible to us, have
a relative velocity beyond this limit, must be moving relatively to the earth in
a hyperbolic orbit, and must, in a few hours, leave the earth’s sphere of acti-
vity, and again become, as they must have been before, cosmical bodies. 'The
grounds for the latter remark, that bodies having a relative velocity of 18.3
miles cannot have acquired the same by any force belonging to the atmo-
sphere, nor by any volcanic or other explosive force in the earth or moon, are
manifest. Indeed, the explosive force of gunpowder communicates a velocity
of only a fourth of a geographical mile per second,” and a velocity of seventy
times that amount cannot be ascribed to any force known to exist in the earth or
moon; and certainly no such force must, on account of this observed relative
velocity alone, be presumed to exist, when other phenomena point to the sun’s
central force as amply sufficient to furnish such a relative velocity as the re-
sultant of a cosmical body’s true and the observer’s known tangential motion.
*° Jahrbuch, for 1887, p. 56. Note. * Systeme du Monde, L. iv. chap. v.
** Mem. Am. Phil. Soc. Vol. vi., P. II., Art. xv.
* Monat. Corr. June 1812, p. 564. ‘The velocity of a twenty-four pound cannon-ball is stated
by Lagrange at 1398 Paris feet per second.
92 RESEARCHES CONCERNING THE PERIODICAL
Taste I.
Relative Second’s Velocities of Meteors in Geographical Miles.
A = Second’s Observer
Date. Desig tion: voce Geet
1798. a 24, Brandes.
se b 18, ce
1823. a 20. es
“ec b 24. “ce
| ‘“ c 32. “
1824. a 15: Quetelet.
ce b 22.8 ae
| 6s c 13.5 se
6c d 9, 73
ee e 15. “ec
se f 10.2 ei
1833, November 12. a 16. Twining.
1836, November 13. abed average | Boguslawski.
1837, August 9. unknown average 6c
Mean second’s velocity, 187.341" .4=1.112=y
Earth’s mean do., 16™ ,4589 — x
The mean value of Table I. is further confirmed, by considerations derived
from the mean duration and mean length of the visible paths of meteors. Mr.
Custodes* found, from ninety-eight shooting stars, seen 9th August, 1837, at
Dusseldorf, that the mean duration of visibility was 1” 12." 7; that of twenty-
eight of the largest size 1’ 45.’ 9—none over 3." Benzenberg, from observa-
tions at various seasons of the year, concludes that the mean duration was
more than 1.” These observations were made by means of a clock marking
thirds, (tertian-clock.) The length of the paths of the four meteors seen at
Breslaw and at a station in its vicinity, are given by Olbers.** Also those
of ten coincidences at Vienna and Calvarienburg, August 29th, 1838, are
given by the younger Littrow,” both, as follows, in geographical miles of sixty
to a degree.
1836, November 12, meteor a, visible path 5.96 miles.
UC SDS 24.88
3 oe ec, 32.88
ce ee d, 43.52
1838, August 29, ea; 12.28
66 7)
a<+@
“ a= G.
«“ = — Gost +V (7 — G sin? v)
“ a4=+0
“ 7 1
a= =
13) Re
Minimum of g = G sin
at g=Gsny
_ y=— Goosy
“ce Y=
ce = I
=
R — G’ sin’
The limiting value of g’, or R is adopted by Olbers *° and Professor Erman,
Jun.,*’ for the orbits of these asteroids. 'Their reasons for the restriction are
not, however, stated. Professor Erman, Jun., has overlooked the limits which
have the negative sign over them, and has, therefore, too much restricted
the limits of the elliptic elements of these anniversary asteroids, possible ac-
cording to the principles of the geometry of position. This oversight pervades
the results and conclusions throughout that interesting paper. Its effect is
particularly manifest in the formule there given for computing the maximum
motion of the convergent point in a finite period, which he makes about 0°.1
per hour in a retrograde direction. Now, by applying the proper limit to the
reciprocal of y, which Professor Erman makes a coefficient of this motion,
(since the limit of y is 0, and that of is + ©,) we may have, without any
* See passage already quoted. 87 Astr. Nachr. 385.
132 RESEARCHES CONCERNING THE PERIODICAL
contradiction from the geometry of position, a motion of the convergent point
in a finite period of time indefinitely great, instead of 0°.1. There are other
variable elements omitted in Mr. Erman’s formule for computing this motion,
which will be referred to in the next section. It remains to point out the use
of the formule of @ in computing the elliptic elements from observed values
of y, 4, and @, and the known values of X, Y,and Z. These equations may
assume the following well known forms:
ten J Lh in A cos 8 _Y+"
X + y cos % cos 3 X+6
_Z+ysin@ _Z24+¢
hid eee TR
_Z+ysin8 ee SR ee
=7 ym itae Vay
(14)
_X+y¥ cosa cosB _ X+6E
I= cos / cos } ~ cos Z cos &
_Y+ysin/cos @ _ Y+n
oz sin J cos b ~ sin / cos 6
_~Z+ysin 8 _2+¢
~ sin & ~ ‘sin &
In making the computations, either of the formule may be used as a
check to test the accuracy of the computation. The subsidiary quantities, G.,
L., and B. = 0, are readily obtained thus:
® = the earth’s longitude
e= c eccentricity
e= sun’s longitude = @ + 180°
R= earth’s radius vector
(15)
Gov R. = v(2 — R.)
vy (1 — 2) = G, R, sin (L, — 8)
(~) = 39°.95
G, = 0.011644 = 365.2564 x sin a cos (?)
Now the quantities Z and B differ from D, and (B. = 0) by less than a degree,
and the deflection of the convergent point from the plane of the Z, and B., or,
in other words, from the ecliptic, being in a southerly direction, and also south-
erly with respect to the plane of L and B, the true motion of the meteor must
be southerly, and it must be tending towards its descending node. Also, the
METEORS OF AUGUST AND NOVEMBER. 133
meteor’s radius vector and heliocentric longitude being sensibly the same as
the observer’s, and within quantities of the order of the earth’s mean distance
divided by its semi-diameter, the same as those of the earth’s centre, those of
the latter may be employed in the computation with sufficient precision, and
we shall have, denoting by a the heliocentric longitude of the point [7] and
making w = the angle of inclination of the meteor’s tangential direction to its
radius vector, reckoned in the plane of its orbit in the order of the actual
motion,
16)
2=O+4u
Q = ©, for northern =
2—-2Q2=-a—-60 * =
cot ¢ = cot b sin (J — Q)
cos u = cos b cos (1 — @)
gTSNMU=VP= v4 cos o
p = Semiparameter
1
>
mee |
e for southern convergent point
2 e ce “cr ““
sin @ = e = sine of angle of eccentricity.
= true anomaly
E = eccentric do.
=mean do.
ercosv=p—r=aco’>
rsinv=acos¢@sin E-
M=E—esnE
—r
t=Oe—v=2—Uu—v
A = Gaussian constant = 0.0172021
@ = 206264.67 = radius in seconds
a
n=ky(l+u)a-,=a-;, fork=1,andu=0.
T = @ = periodic time in siderial years.
t, = interval since preceding new year
H=x+M— nt, = epoch for preceding new year.
The values of Table VI. were computed by formule «4, as), and as. The
numerical values of the fundamental equations are here subjoined, as they may
save the labour of fresh computation by others who may engage in similar
VIII.—2 I
134 RESEARCHES CONCERNING THE PERIODICAL
inquiries. The numbers, 1, 2, 3, below the letters, refer respectively to the
group of meteors of 1833, November 12.734, 1840, August 9.456, and 1838,
December 7.333.
Z, = — 0.80025 + 0.80423 x y,
y, = + 0.62056 — 0.57905 x y,
Zz, = + 0.00336 — 0.13385 x y,
ll
2, = + 0.66830 — 0.45439 x y,
y, = + 0.74084 — 0.63354 x y,
z, = — 0.00252 — 0.62622 x y,
(17)
2, = — 0.98371 — 0.45439 x y,
Ys = + 0.27412 — 0.63354 x y,
2; = — 0.00445 — 0.62622 x y,
y, = + 1.00337 + yv[g? — 0.01874]
¥. = + 0.77144 + v[g} — 0.40035]
Y: = — 0.27612 + v [gg — 0.96660]
§ IX.—OF THE VARIATIONS OF THE RELATIVE VELOCITY AND CONVERGENT
Point.
The convergent point on ordinary nights, according to the observations of
Mr. Herrick and Mr. Forshey, varies with the point which is opposite the ob-
server's true direction. And if there is a similar tendency to compensation of
the relative velocities, then the mean relative velocity of shooting stars varies
with that of the observer. I have already referred to Professor Erman’s
formule for this variation, and have shown that the restrictions are too great,
from an unnecessary limit of the value of the reciprocal of y. Let us suppose
that the observer, in his annual and rotary motion, falls in with a group of
these bodies having nearly the same elements, and that he encounters the in-
dividuals at successive dates, ¢, ’, t’, &c. It is manifest that if all the other
elements were common, the position of the plane of the orbit of the successive
meteors must vary with the observer’s change of position, so that the elements
METEORS OF AUGUST AND NOVEMBER. 135
cannot be identical. The differences may be embraced in two classes, those
which increase with the time, and those which arise from discrepancies of the
elements. Denoting the former by A, and the latter by d, and their joint
effect by 6, we have in the interval (¢’ — 2),
bf =i —E=E+dx4+A(x—X)
as) dn =n' —n=n+dy+A(y— Y)
o¢=0 —FC =F +dz4+A(z— Z)
for the variations of £, 7, and ¢. Hence, in estimating the variations dy, Oa,
and 62, some allowance must be made for the quantities dy, da, and d@,
arising from discrepancies of the true elements of the meteors seen at the dates
t,t’, &c. Professor Erman’s formule, on the contrary, proceed upon the pre-
sumption of df = — AN, &c. Now, as dz, + Az, &c., cannot, even in the
thickest flocks of meteors, vanish entirely their aggregate effect in a finite in-
terval of a few hours, may be such as to preponderate over that of A (—_X), and
in this manner the variation 62, in a few hours, may come out positive, as re-
ported by Professor Forshey, August 9th, 1840. Also, on ordinary nights, if
a convergent point is found to prevail, we should have
(19 b§=& —E=E4(dx+Azx)—AX=S5x—AX
and so on for dy and 6¢: now if during an interval ¢’ — ¢ of several nights we
find by observation, with Mr. Fitch and Mr. Herrick, 64 = A (L + 180,)
63 =—AB=0, we are led to the inference that dy = A(— G), and dé = —
AX, &c. And that a compensation has taken place among the true velocities
and directions of the meteors seen near each date, so that the convergent point
has corresponded, in position and variations, with those of the antipode of the
observer’s actual direction.
On the occasion of great displays like that of November, 1833, when tele-
scopes were directed to the radiant point, and its altitude was measured with
a sextant, it is probable that d z, d y, and d z were very small; in such a case
a precise measure of the position of this point in the heavens might possibly,
by giving the value of §4 and 4 in a finite interval, enable us to determine y
from the terms dz, dy, and dz, of which it would be a function. I do not,
however, think such a precision can ever be obtained.
There is another point of view in which the knowledge of the values. of d z,
136 RESEARCHES CONCERNING THE PERIODICAL
dy, and d z, for variations of y, 2, and @, may be useful, and that is in enabling
us to estimate the probable errors of any system of elements for a group or
cluster of these meteors derived from assumed values of y, 2, and 2. The
formule for computing variations of elements for a change of radial positions
and distances in an orbit, or of geocentric positions and distances in the heavens,
are stated at length by writers on the laws of elliptic motion, Gauss, Littrow,
Santini, and others. As I do not recollect to have met with similar expres-
sions for the variations of tangential directions and velocities, or relative direc-
rections and velocities, I shall here point out the method employed in preparing
the requisite formule.
In the formule «), making 7’ = y cos (, g’ = g' cos d, and differentiating,
we obtain, after making the requisite reductions,
dg! = +c0s(4—1) cos B. dy—*sin aD. aa—Y cos (A—J) tan B.d8
di= © sin (A—D) cos 8. dy + % cos(a—1). da—” sin (A—I) tan 8.8
9 g g
o db= 5 cos* b | tan @—tan bcos (A— 1) cos 0. dy
+7 cos sin b sin (A—l).da
+% cost ji + tan } tan 3 cos (a—d)|. dé
Expressions equivalent to those given by the authors above quoted for the
variations of positions and distances, as might be expected from the symmetri-
cal form of the fundamental equations, from which they are derived. Also, as
before, 2° = 2 + v + u, denoting the longitude on the orbit of the point [7 6]
towards which the true motion of the asteroid is directed, anda — Q=na+u
+u— Q, being the argument of latitude, the equations
tan (J — Q) = cosz tan (t+ 0+u— Q)
sin 6 = sin7z sin (4+ 04+ u— Q)
tan 6 = sin 7 tan (a7 + v +u— Q) cos (I— Q)
= tanz sin (J — Q)
cos (1 +V+U— Q) = cosbcos (1 — Q)
tf
g =g9 cos.
21)
give by differentiation, substitution, and reduction,
METEORS OF AUGUST AND NOVEMBER. 137
dg’ =cosb.dg—S sind sin (l— Q) .di—S sind sini cos (I— Q) (de + dv+du—d Q}
cost
soa plde tdvtdu—dQ]
db=sin (J— Q). di + sini cos (J— Q)[dxetdv+ du—dQ]
Expressions which I do not recollect to have met with before. They differ
from the formule given by Gauss, Theoria Motus, p. 49, and by Santini, Ele-
menti di Astronomia, Vol. I., Cap. XVII., Prob. IX. and X., and by other
writers on the theory of elliptic motion, in containing tangential directions and
velocities instead of orbital positions and distances, and having in the bracket an
additional variable, w, which does not enter into the expressions for the varia-
tions of the latter class, and which here introduces new relations between the
2 d/=—d Q —tan bcos (Im Q).di+
remaining elements $ and n, of which it is a function.
In order to obtain dg’, d/, and d 3, in terms of the variations only of the ele-
ments proper, we must substitute the values of dg, dv, and dw, in terms of
those of the elements. From the Theorta Motus, p. 15, with small modifica-
tions, we have
(2 +e cos v) sin vg
cos
dv = “cos [dH +t,dn—dz7] + >
dr=".da+“tangsinv [dH +t,dn—da] —4 cosg cosv.dg
a) a)
and from the equations
n=a-‘
(24)
p=a@cos*o>.= 9’ r* sin? y = ( — a) r sin? u
by means of differentiation, making, for conciseness, N’ = — and put-
ting for tan w, its value = tan (0 — (a+ v))
3H
d =—-—.-. d a
‘ 2 a
(2) ag'= 1 na os ogy
2aag Tro
du = tan (2 —(x+»)) Eig Ce Nic a 7 —tang de |
3 n Tr
expressions which, substituted in @), would, after reduction, furnish the gene-
ral solution of the problem for all relations of an orbit to the ecliptic,
VIU.—2 kK
138 RESEARCHES CONCERNING THE PERIODICAL
In the present case, the asteroid being near the observer, or (neglecting the
small quantities already mentioned) near the earth’s centre, and consequently
near its node, recollecting that
tan uv = tan (n — (a +0)) = tan (2 — @) = tan (no — Q)
sin (1 — Q) = + sin (I— ©)
cos (J — Q) = + cos(/ — ©)
tan = tan 7 sin (J — Q)
dgz=0
dzxa+dv=d@=0
(26)
and using the upper sign for a convergent point north of the ecliptic, and ob-
serving that d H may be neglected, since it could only be introduced into these
formule by making part of the value of dv, which, in this instance, disappears,
z — , and substituting and reducing, there result for
the case of a meteoric asteroid, the following expressions of the meteor’s true cur-
tate velocity and direction, in terms of those of the three independent elements,
and calling N=
4 , o’
dg! = Stand sin(—@) di + © N[ stan]. dn + F tant tan 9. dg
_ * ; tan (/— ©) tan(J—@) tang ,_
2) dl=xtanbcos(I—©®).di+ WN. eaatb “da— cos? b ae
db=+sin(1— @).di+ NMtand.dn—tand tan 9.d¢@
More simple expressions for the variations of some of the elements may be de-
rived from the equations « and from the expression
(28) JVacos¢sint=grsindb=rZ+rysin8s
thus respectively
dna = —3n? a (y+ Geos y).dy—3n'Gy'sin(L—2).da+3n? Gy’ [ cos (Z—+) tang—sin BI. dé
29)
Ay ee rn sinB rnvy’
do =cot p cot?.di— soe dn— = z
sinz sino * sini sin"
These expressions establish the principle stated in Section IV., No. 6, that
the independent elements may be reduced to three. They would, if the data
of Tables I., II., and III. possessed the requisite precision to warrant the pre-
sumption that the elements of Table VI. are approximations towards the real
values, enable us to estimate the effect of the uncertainty of the assumed values
of y, 2, and @. At present this cannot be considered the case. It is worthy
METEORS OF AUGUST AND NOVEMBER. 139
of remark, however, that by proceeding from the values of Table VI. for the
November meteors, and making y, 2, and @ vary within limits assigned to
their probable errors by Professor Twining, while the general character of 7
and @ remains the same, that is to say, retrograde or highly inclined, and infe-
rior, the value of @ may approach nearly to 90°, and the perihelion distance,
; P , may approach the value of the sun’s semi-diameter, or sin (16’ 1.)
+e
This will readily be inferred from the largeness of the negative coefficient
of dy in the last equation of e. This circumstance gives to the remark-
able serpentine meteor of the great November display, as has been already
stated, the character of an emanation from the sun’s atmosphere. How far
such a conclusion, founded on this single result, may be considered as
plausible, must be left to others to decide. I will merely remark, that if the
position of the convergent point had been such as to give this value of @, with
2 small, and a consequent motion direct, this circumstance would be somewhat
confirmatory of the nebular hypothesis of Laplace; since, if one class of small
asteroids may with reason be supposed to have had their origin in the sun’s
atmosphere, analogy may authorize us to suppose a similar origin for the pro-
jectile motion of the larger asteroids and planets, in the gradual condensation
of the nebulous portions of matter composing the system, the motion of rota-
tion being converted into an orbital motion. The analogy fails, however, on
account of the high inclination of the orbit of the meteor derived from the
same data.
NOTE.
In Section I. of this paper I made mention of the observations of Professor Locke, published in 1884, in
the “Cincinnati Daily Gazette.” Those of the 8th and 10th of August, 1834, published on the 1th
and 12th of August in the same year, are worthy of being reprinted from the files of that paper, as they
show that, although the periodicity of the August meteors was first discovered by Quetelet in 1836, the
position of their radiant and convergent points was first discovered, and pointed out with precision by an
American, in 1834, as had been done the previous autumn by Professor Olmsted and others for the No-
vember meteors.
Cincinnati Dairy Gazerre, August 11th, 1834.
“METEORS.
‘““Mr. Eprror,
“On the evening of August 8th I observed, in the course of two hours, thirty meteors or ‘ shooting stars.’
As I could not have in view more than one-fourth of the visible heavens at once, there were probably one
hundred and twenty meteors to be seen in that time. I do not mention this as any thing uncommon, but
140 RESEARCHES CONCERNING THE PERIODICAL
merely to draw the attention of astronomers to the subject. If they will mark the course of remarkable
meteors upon the fixed stars, and note the time, we can obtain the parallax of some identical one, and thus
ascertain its place in the regions of space. If observers at Dayton, Oxford, Lexington, Louisville, &c., will
join me, I will devote the hours from 6 to 10, and, in some cases, from 8 to 11, to observations of this kind.
«The following observations were made on the evening of the 8th:—
“1. 9h. 25m. 30s. A meteor passed from half way between Alpha and Beta of Capricornus to Delta of
Sagittarius.
“©2. 9h. 30m. From Beta of Sagittarius to Alpha of Delphinus. The course of this was nearly upward.
“3. 10h. 18m. 34s. From one degree below Beta Aquarius to Epsilon of Sagittarius, nearly parallel to
the first.
“4. 10h. 40m. From Eta of Draco to Epsilon of Corona. This was a brilliant meteor, leaving a phos-
phorescent train after it for a few seconds. These observations were noted by Carey’s nine-inch globe of
1816. Iwas surprised to discover that most of these meteors had such apparent motions as would be pro-
duced by bodies moving parallel to each other in straight lines. That is, they describe parts of great cir-
cles, which, if produced, would all meet and cut each other in two opposite points, like the meridians of a
globe cutting each other at the poles. They appeared to move from a point in the north-east above the
horizon to an opposite one in the south-west, below the horizon. By tracing the track of the above ob-
servations on the globe, the radiating point or pole was found near the star Algol, in the constellation Per-
seus, and the opposite, or convergent point, in the constellation Lupus. This was the course of most of
the meteors. Others again, as the 2d, had a course nearly at right angles to these. But I saw none which
was not referrible to one of these two courses. The poles did not appear to move with the earth, but they
retained their places amongst the fixed stars. Are these phenomena, as suggested by Professor Olmsted,
indeed celestial in their origin, and independent of the earth’s rotation ?
“Yours, &c.
“JOHN LOCKE.”’
“METEORS, No. II. (Ibid., Aug. 12th.)
‘Mr. Eprror,
‘Since the 8th I have continued my observations on the 9th and 10th. The results are as follow :—
* * * * * * * * * *
«On the 9th many other meteors were seen, but not noted. No common point of radiation or con.
vergence was ascertained.
“ Aug.10. 1st Obs. 9h. 12m. A meteor passed above, and very near to Beta of Libra, and thence ob-
liquely downward, below and near to Gamma of the same.
«2d Obs. 9h. 14m. 20s. From m of Antinous to Mu of Sagittarius, downward in the eastern edge of
the milky way.
«3d Obs. 9h. 18m. 29s. From Beta of Aquarius to Psi of Capricornus.
“4th Obs. 9h. 26m. From Zeta of Serpentarius to Sigma of the same. Course downwards along the
western edge of the milky way. The course of all these, as well as that of all others observed this even.
ing, was towards one common point in the constellation of Ara. This point was south about eighteen de-
grees west, and fifteen degrees below the horizon. “JOHN LOCKE.”
* * * * * * * * * *
ERRATA.
Page :f02, Table [V., heading of the second and third columns, for “ @”’ read “@.”
Page 93, line 12th, for « August”’ read ‘ September,”
ARTICLE X.
Astronomical Observations made at Hudson Observatory, Latitude 41° 14’ 40’
North, and Longitude 5h. 25m. 45s. West. By Elias Loomis, Professor of
Mathematics and Natural Philosophy in Western Reserve College. Read
April 2d and 16th, 1841.
THE instruments of the observatory and the mode of using them have re-
mained unchanged since my former paper was communicated to the Society,
and the objects observed have been generally the same. The clock has been
once stopped. In my former communication I remarked that the pendulum
appeared to be over-compensated. ‘This opinion was confirmed by subsequent
observations, and on the 31st of January, 1840, 6.2 ounces of mercury were
taken from the cistern, leaving the column 6.12 inches in height. Since that
time the clock has been constantly running, and its rate has been tolerably
satisfactory.
I. LatirupEe or Hupson OBSERVATORY.
During the past season I have observed nine culminations of Polaris. The
observations were made alternately direct, and, by reflexion from mercury,
generally a dozen at each culmination. The three microscopes were invariably
read at each observation; the observations were reduced to the meridian by the
usual method, and corrected for refraction by Bessel’s tables. The errors of
the microscopes were found to be as follow:
North Polar Distance. A. B. Cc. Mean.
358° 25'—30’ — 2.6 + 0.1 + 0.2 — 0".77
279 O0O— 5 —2 2 —0.9 — 6.6 — 3 .23
VIlI.—2 L
142 ASTRONOMICAL OBSERVATIONS.
The following are the results of the observations:
Lower culmination of Polaris, June 4, 1840, 41° 14’ 40.4
8, 40 .2
9, 42 .2
13, 42 .3
15, 42 .6
16, 41 .3
18, 45 .0
19; 43 .1
23, 43 .4
Mean of nine culminations, 41 14 42 .3
The result of last year’s observations of Polaris was 41° 14’ 38.1. The
places of Polaris were taken from the Nautical Almanac, and the above results
are both affected by the error of the tables, but with opposite signs, as the lat-
ter result was derived from upper, and the former from lower culminations.
The mean of the two is 41° 14’ 40’.1, the value which I at present employ.
II. OBSERVED TRANSITS OF THE Moon AND MOON CULMINATING STARS AT
Hupson OBSERVATORY.
The following list is supplemental to that given on pages 49, 50. The
observations are all reduced to the central wire. When the object is observed
at all the wires, the reduction is equal to 0°.112 x secant of the declination,
which correction is readily taken from a table, and is sensibly constant for all
the following stars. When an object is not observed at all the wires, each ob-
servation is separately reduced to the central wire. For a star, this reduction
is equal to the equatorial interval multiplied by the secant of the declination.
For the moon this factor is computed by the formula
1 — sin 2 cos ¢ sec 3
Saree 4 . 3600 sec 3
Where a = the moon’s horizontal parallax.
= latitude of the place.
§ = moon’s true declination.
A = moon’s hourly motion in right ascension, expressed in seconds of
time.
*.
°
AT HUDSON ODBSERVATORY. 143
Two imperfect transits of the moon contained in my former paper, namely,
Nos. 29 and 35, were incorrectly reduced. The seconds should read, instead of
41*.39 41*.23
49 .70 49 .96
| No. Date. Star. Wires Meridian Transit. Clock’s Rate.|| No. Date. Star. Wires Meridian Transit. |Ciock’s Rate.
| | 1839. | ia | 1839.
| |Oct. 14 8 Sagittarii | 5 | 18" 10™13*.66 | — 0*.23 | Nov. 16 ¢ Aquarii 5 | 23h 5m 9*.04 | — 05.87
151) Moon1L.| 5 |18 50 17.20) | k Piscium 5 |23 17 50.58
| + Sagittarii | 5 | 18 56 25.74 (62) Moon1L.| 5 |23 48 4.20
15) Sagitarii | 5 | 18 56 25.50 —0.24/ » Piscium 4 |23 50 12.61
| | h* Sagittarii | 5 (19 26 27.00 | d Piscium | 5 | 0 11 29.06 |
52 | Moon1L.| 5 |19 47 2.12} 17/« Piscium 5 |23 50 12.60)/—0.20
¢ Sagittarii | 5 |19 52 17 80 d Piscium 5 | 0 11 28.76
'o Sagittarti | 5 |20 9 38.64 (63 Moon1L.| 5 0 41 7.70)
16 ¢ Sagittiarli | 3 | 19 52 17.41 |—0.45) « Piscium 5 | 0 53 45.68 |
| ¢ Capricorni | 5 (20 9 38.12. 18 « Piscium 5 | 0 53 44.40/—1.28_
53 Moon1L. | 5 | 20 42 33.62 64 Moon1L.| 3 | 1 37 31.88
, Capricorni 5 20 54 46.46) B Arietis 5 | 1 44 54.18
s Capricorni 5 (21 6 22.18) 6’ Arietis ar] ‘2928, 19)-67,
17 ~ Capricorni | 5 |20 54 45.80|—0.74| 65 19| Moon1L.| 5 | 2 38 34.24]—0.75
s Capricorni 5 |21 6 21.36 (8 Arietis 5 3 1 34.24
| 54 | Moon1L.| 5 |21 36 35.64) 22 8 Tauri 5 | 5 15 13.34|—0.94)
|8 Capricorni | 3 | 21 37 40.63 | x Aurigae 5 | 6 4 12.36
| 55 18| Moon1L.| 5 |22 29 30.08 |—1.37| 66 Moon2L.| 5 | 6 8 9.24
| | 2 Aquarii | 5 |22 43 43.20 1840.
20\% Piscium 5 23 33 19.18 —0.71 Feb. 156 Caneri 5 7 53 43.82)/—0.26
'q Piscium 5 |23 53 3.62 9 Cancri 5 | B 22 30.86
56 | MoonlL. | 5 0 15 40.82 67 Moon1L. | 5 8 47 43.80
's Piscium | 5 | O 39 49.44 € Cancri 5 | 9 O 12.12
: 21\/8 Piscium | 5 | 0 39 47.68|—1.76 q Caneri 5 | 910 5.7
57 | Moon1L.| 5 | 1 11 29.20 Mar. 11/3 Tauri 5 | 516 2.92/—0.41)
bond | |, Piscium 5 | 1 22 20.72 C. Tauri 5 | 5 43 8.86
\3 Arietis | 5 | 1 45 13.42 68 Moon1L.| 5 | 6 22 44.74
| 22, Piscium 5 1 22 19.26|—1.42 je Geminorum) 5 6 33 58.10
|8 Arietis | 5 | 1 45 12.08} |x Geminorum! 5 | 7 O 50.28
58 Moon1J..* 5 | 2 10 50.46) 13/8 Geminorum| 5 | 7 35 23.04] —0.40
Moon2L.| 5 | 2 13 16.54 '» Geminorum| 5 | 7 43 34.32
59 23 Moon2L.!| 5 3 16 57.10 — 0.61 69 Moon1L.} 5 8 26 48.18
, Tauri 5 | 3 37 21.58 8 Caneri 5 | 8 35 27.58
7") | A’ Tauri 5 | 3 54 37.38 | a? Cancri 5 | 8 49 35.98
| 24, Tauri 5 3 37 21.48 —0.25 17 = Leonis 5 | 11 28 36.30) —0.32
At Tauri 5 | 3 54 36.90 70 Moon1L.| 5 |11 49 8.06
60. Moon2L.| 5 | 4 24 22.32 Moon2L.| 5 |11 51 14.58
« Tauri 5 | 4 32 1.32 Virginis 5 |12 11 34.52
« Tauri 5 | 4 52 54.60 April 8 « Geminorum) 5 | 6 33 41.96 |—0.66
Nov. 15) 3 Aquarii 5 | 22 21 18.10|—0.56/ 71 | Moon1L.| 5 | 7 7 28.52
61) Moon1L.| 5 | 22 56 51.92 '¢ Geminorum| 5 7 15 24.10
¢ Aquarii 5 |23 5 9.90 |B Geminorum; 5 | 7 35 8.04
, k Pisciom 5 |23 17 51.46 9'. Geminorum) 5 | 7 15 23.44|/—0.66
’ * Limb somewhat deficient.
.
.
ASTRONOMICAL OBSERVATIONS
Date.
1840.
| April 9
72 |
May 10,
June 8)
aq 4-09 --
|
8)
| 9}
| Star.
|
8
| Moon 1 L.
g Cancri
6 Cancri
Leonis
lo Leonis
Moon 1 L.
Leonis
Leonis
Leonis
Moon 1 L.
Virginis
/b- Virginis
|y’ Virginis
Moon 1 L.
Virginis
Scorpil
5 Scorpii
a Scorpii
Moon 2 L.
x Leonis
Moon 1 L.
Leonis
Moon 1 I.
Virginis
Virginis
Virginis
Virginis
Moon 1 L.
Virginis
» Virginis
20 Libre
Moon 1 I.
Moon 1 L.
A Ophiuchi
6 Ophiuchi
a Leonis
Moon 1 L.
y’ Virginis
Moon 1 L.
a Virginis
Moon 1 i.
a? Libre
20 Libre
a? Libre
20 Libre
Moon 1 L.
b Scorpii
6 Scorpii
b Scorpii
8 Scorpii
a Scorpi
i
Moon 1 L. |
Geminorum
No.
Wires
Obs.
Ooo an OV ot oT B® OW OF OF OF Ot OF OT OF Or OT OF OD Ot OT OH OT OF Or OF OT OF Oh Ot OF OT OF OT ON TE Ot OF Ot OT Or St Or St Gr St Or St St
Meridian Transit.
7h 35m
_——
eK oocowuseowmwm em
8
22
35
22
32
57
7.3
56
38
-50
Clock’s Rate.|| No. Date.
1840.
July 10} 2
lljoa
a
87
— 05.69 16
13 | >
88
— 0.53 x!
h?
15|\v
89
Ss
— 0.60 £
90) 16)
t
— 0.60 6
91; Aug. 4
a2
5 | a2
— 0 .95 || 92) °
93 6
oO
—l1 10 | | Qa
T\o
a
—1.19 | 94
A
7]
| 95) 8 |
— 0.64 i
| nr
| aa
— 0.64, a
96
| t
—1.15 | x’
Eg?
—1.15 || 97
yi
13 | 6
— 0.80 t
98
nq
— 0.66 h
14 |»
Xr
99
Xn
—1.04 | 17\«
100
B
21),
Star.
Scorpii
Scorpil
Scorpii
Moon 1 L.
Ophiuchi
Sagittarii
Sagittarii
Moon 1 L.
Sagittarii
Sagittarii
Capricorni
Moon 2 L.
Capricorni
Capricorni
Moon 2 L.
Aquaril
Aquarii
Moon 1 L.
Libre
Libre
Moon 1 L.
Moon 1 L.
Scorpii
Scorpii
Scorpii
Scorpil
Moon 1 L.
Ophiuchi
Ophiuchi
Moon 1 L. |
Sagittarii
Sagittarii
Sagittarii
Sagittarii
Moon 1 I. |
Sagittarii
Sagittarli
Capricorni
Moon 1 L.
Aquarii
Capricorni |
Aquaril
Moon 2 L.
Aquaril
Aquaril
Aquarii
Aquarili
Moon 2 L.
Piscium
Piscium
Moon 2 L.
Arietis
Tauri
N
Obs
ELS OU TT UT HT TU OU BT TT OT TT OT BT TU TT UOT TT OH TT TST THT HTH HH
Vo.
Wires} Meridian Transit.
Clock’s Rate.
16% 25™ 228.38
19
88
87
—1.20
103
104
105
106)
107)
108
109)
113,
Oct.
12}
13
14
17
Star.
Moon 2 L.
Virginis
Moon 1 L.
Sagittarii
o Sagittarii
Moon 1 L.
| h® Sagittarii
57 Sagittarii
57 Sagittarii
Moon 1 L.
Capricorni
Capricorni
Piscium
Piscium
Moon 2 L.
Piscium
Piscium
Piscium
Piscium
Moon 2 L.
Piscium
Arietis
Arietis
Moon 2 L.
Arietis
Arietis
Tauri
Tauri
Moon 2 L.
6 Sagittaril
Sagittarii
Moon 1 L.
x Sagittarii
h? Sagittarii
ce Sagittarii
| 8? Capricorni
Moon 1 L.
Capricorni
Capricorni
Capricorni
Capricorni
Moon 1 L.
3s
no UD
6 Capricorni
« Aquarii
Moon 1 L.
Aquarii
Aquarii
Arieus
Moon 2 L.
Arietis
Arietis
Arietis
VIll.—2 M
AT HUDSON OBSERVATORY.
Wires Meridian Transit. |Clock’s Rate. | No. Date. Star.
iS. Ws aE Tae
I 1840.
5 5h 45m 115,34 (114 Oct. 13 Moon 2 L.
4 /13 16 13.46 — 15.26 v Tauri
5 {13 59 11.44 e¢ ‘Tauri
5 118 35 2.88|/—0.89 Nov. 2} Capricorni
5 |18 44 44.10 1115] Moon 1 L.
5 |19 21 29.18] y Capricorni
5 |19 26 21.54 5 Capricorni
5 1.942) 9 171.26 ‘116 3 Moon 1 L.
5 119 42 16.26;/—1 .00 || 9 Aquaril
5 120 14 50.88 | os Aquaril
5 120 17 31.82 5 | x? Piscium
5 |20 30 18.60 y Piscium
5 |23 39 0.44/—0 .95 /1117] Moon | L.
5 1/23 50 22.94 n Piscium
5 0 26 35.12 » Piscium
5 0 39 40.48 6/n Piscium
5 0 53 55.86 o Piscium
5 | 0 39 39.34/—0.91 118) Moon 1 L.
5 0 53 55.18 6 Piscium
5 1 18 49.86 « Piscium
5 | 1 22 12.44 9|y Arietis
5 | 145 5.18 \ ies « Arietis
5 1 45 4.30}/—0.88 | 119 Moon 1 L.*
5 J. 14, 25.34 Moon 2 L.
5 | 2 28 59.92 | mq ‘Tauri
5 | 2 49 19.92 I} A’ Tauri
5 | 4 31 51.16|—0 .98 | 10, Tauri
5 4 52 44.34 | A’ Tauri
5 5 24 6.30 /120 Moon 2 L.
5 /18 9 38 .84|/—1 .32 «© Tauri
5 |18 17 59.38 8 Tauri
5 /18 59 0.20 15/ q Caneri
2, {19 0. .8.15 € Leonis
5 {19 26 51.96 121 Moon 2 L.
5 119 52 39.90|/—1 .23 |} a Leonis
5,120 11 52.22 | 16 » Leonis
5 120 44 6.64 | a Leonis
5 120 55 8.92 \/122 Moon 2 L.
5 |21 6 44.04 30} « Capricorni
5 |20 55 7.02}/—1.71 123 Moon 1 L.
5 |21 6 42.52 | « Capricorni
5 |21 34 12.84 30 Aquarii
5 |21 38 1.78 Dee. 1) Capricorni
5 |21 57 36.98 30 Aquarii
5 |22 23 17.48 |—1 .22 ||124 Moon 1 L.
5 |22 26 55.94 x Aquarii
5 |22 44 4.12 » Aquarii
5 | 2 21 45.34|—1.07|| 2) x Aquarii
5 | 2 51 33.20 | a Aquarii
5 3 2) 12.30 )125 Moon 1 L.
5 Sila isoee k’ Piscium
5 3.14 34.50}/—0 .92 2 Piscium
* Limb somewhat deficient.
Aaa» awonnan»nqananna1annanna°anananananaanawarnananannaananna&»wniaanw41aanwaa4cn
145
Meridian Transit.
3h 55m 415.28
_
SOUHNUVUOSCOURPRWWWHWwWNNS
is]
pa
21
26.96 |
Ictock’s Rate
— Is.1l
-10
18
36
-80
-83
26
146 ASTRONOMICAL OBSERVATIONS
II]. OBsERVED OCCULTATIONS OF FIXED STARS aT Hupson OBSERVATORY.
a ae Oe Remarks.
| 1839.
1 | Oct. 17|8 Capricorni 21 56™ 48°.79 22" 10™ 7.79 | Imm. pretty good; Em. tolerable.
1840.
2 | April 11} « Leonis 10 48 13 .54/| Tolerable observation.
3 | “ 19] ¢ Scorpii 16 36 44.15/17 33 50.65 / Imm. uncertain to 2° or 3°; Em. good.
4 |May 6)’ Cancri 11 82 43.00 Good.
Sl Ss fei 7 Mag. 11 37 42.20 Good.
6 | Oct. 13] Phiadum 20 29 12.94) Perhaps 3° or 4° late.
7 |Nov. 2|¢ Capricorni 20 44 50.52)22 1 19.57| Imm. tolerable; Em. perhaps 2° late.
IV. Seconp Comet or 1840.
On the 14th of March, 1840, I received a letter from Mr. S. C. Walker, con-
taining the elements of two comets recently discovered at the Berlin Observa-
tory by Mr. Galle, accompanied by an intimation that one of them might be
still visible. I immediately computed an ephemeris, and on the first succeed-
ing pleasant evening, the 18th, readily found it nearly in the place expected.
I observed it afterwards, on the 19th, 21st, and 25th of March, as, also, on the
1st and 2d of April. After this there was no clear evening until the 7th, when
I searched for it in vain. The atmosphere was quite transparent, and there
was nothing to interfere with observations but the moon, now five days old. I
did not search for it afterwards. When first discovered, the comet was faint,
but brightest in the central parts, resembling a small nebula, nearly circular,
and about one minute in diameter; but its margin was exceedingly ill-defined.
On the 19th the nucleus was remarked to be somewhat eccentric, and on the
lower side of the comet, as seen in an inverting telescope. No remarkable
change in the comet’s appearance was subsequently observed, except that its
brightness diminished somewhat more rapidly than had been anticipated. As
it would not bear an illumined field, I could make no use of the spider-line
micrometer, and was compelled to confine myself to a more inconvenient and
less satisfactory mode of observing. For right ascension, I brought the comet
into the middle of the field of the equatorial, and counted the seconds elapsed
between its egress from the field and that of some neighbouring star. This
process was repeated six or eight times. or declination, I again brought the
AT HUDSON OBSERVATORY. 147
comet into the middle of the field, and, by rapidly turning the screw of the de-
clination circle, brought it to the margin of the field. The graduation, which
is to 10”, was then read off. I performed the same operation with the star of
comparison, and repeated the process several times. These observations occu-
pied nearly the whole of the evening that the comet could be conveniently ob-
served. I thus obtained differences of right ascension and declination between
the comet and known stars. The following table exhibits a summary of the
observations. The place of a Arietis is from the Nautical Almanac; of 6’ Arietis
from Pond’s Catalogue of 1112 Stars; and of y and ¥ Arietis from the Astro-
nomical Society’s Catalogue.
| Se eat Apparent Places of the Stars. Comet minus Star.
> eSlderia Ime
1840. at Hudson. ate Meg: A. R. Dec. AR. Obs. Dec. Obs.
March 18,74 45™ 28°,67/a Arietis| 3 [12 58™ 95.76 + 32°80) 5
(7 56 12.98 + 22° 49’ 16".3 + 7'30’.9| 2
197 39 15.25 158 9.76 + 140.94) 8
7 40 38.96 +22 42 16.2 — 25 14.213
218 11 13.89% Arietis| 6 (2 3 50.54 + 12.80/10
7 39 26.77 +20 27 20.6 +47 11.8] 3
258 7 43.766’ Arietis| 6/2 9 14.21 + 85.80) 5
'8 29 19.58 +19 9 34.9 + 5 48 .2| 4
April 18 45 10.65\y Arietis| 6 +16 59 44.1 — 51 42.9] 1
28 49 41.00 222 2.12 + 38.00 3|
‘8 24 21.01 +16 59 44.2 — 77 29 .3| 2
From these data we obtain the apparent places of the comet affected by
parallax, and the difference of refraction of the comet and stars of comparison.
In the following table these corrections are applied, and the times reduced to
Berlin Observatory, by adding 6" 19" 22°.3 for difference of longitude.
1840. Berlin Mean Time. Comet’s A. R. Comet’s Dec.
March 18 | 14" 18™ 125,34 | 29° 40’ 43’.8
14 28 54.89 + 22° 49’ 51’.8
19/14 8 4.04/30 7 45.1
14 9 27.52 22 17 5.9
21/14 32 5.63)31 1 2.5
| 14 0 23.72 21 14 49.0
| 25)14 12 52.44/32 40 7.8
| 14 34 24.72 19 15 35.1
| April 1|14 22 41.82 16 7 29.7
2|14 23 15.53/35 39 25.0
13 57 59.69 15 42 2.0
148 ASTRONOMICAL OBSERVATIONS
Continuation of Mr. Loomis’ Paper. Read April 16, 1841.
Berne desirous of determining the comet’s orbit with the greatest possible
accuracy, I sought for a collection of European observations. For such as I
have obtained I am indebted to the kindness of Mr. 8. C. Walker. They em-
brace thirty-four observations at Hamburg, from January 29th to March 24th,
which are published in an abridged form in the Society’s proceedings, Vol. I.,
p. 275; twenty-six observations at Bonn, from February 3d to March 19th,
given in connexion with Kyseus’ Ephemeris, in the Astronomiche Nachrich-
ten, No. 399; and twelve observations at Berlin, from January 25th to Feb-
ruary 2ist. These, together with my own, make seventy-eight observations,
and are all which I have been able to obtain. In comparing the observations
I availed myself of Kyseus’ Ephemeris, which was found to represent the
comet’s course tolerably well. The Hamburg observations are given more
fully in the Astronomische Nachrichten, Nos. 402 and 405. The comet’s place
for February 4th, 17" 47", does not accord with the other observations, and I
have therefore rejected it, presuming it must contain some error, and have em-
ployed the mean of the remaining observations for the same evening. The
declination for March Ist is also obviously erroneous, and I have rejected it
entirely. The Hamburg places are called apparent, by which I understand
that they are corrected for refraction merely. I have computed the correction
for parallax, and applied it to each observation. The Berlin observations were
supposed to have been already corrected for parallax. The following table
exhibits the corrections of Kyseus’ Ephemeris by each of the observations:
AT HUDSON OBSERVATORY. 149
| | CorgEcTIoNs, | Corrections.
| AR, Dec. | A.R. Dec.
Jan. 25|Berlin |— 2”.7) 4 ESE Feb. 28) Hamburg |— 357.61 1 18”.4}
26 ce = 24 .6;+ 10.4 28 | Bonn |— 27 .6|+ 18.4
2 id j}+ 8.2/+ 3.7 | 29| Hamburg — 39 .4| + 24.3
29| «6 eso l= Geen) 29) Bonn —24.4/4+ 16.9
29|Hamburg + 9.4|— 33.9 | March 1) Hamburg | — 27 .2
30 | Berlin +21.0|/— 3.7 1 | Bonn — 20 .0|/+ 14.0
30 | Hamburg) + 18 .2)— 13 .3 1 2 Bonn — 25 .6|+ 22.7
Feb. 2|Berlin | + 25.1/— 10.9 el. 3| Hamburg) — 31 .8|+ 12.0 $4,
Hamburg | 0.0 — 23 .3 | 3 Bonn — 21.3/+ 19.0
| 3|Berlin |+16.1/— 8.4 4 Hamburg — 25 .9|+ 17.8
} 3 | Hamburg, + 20.3) — 27.5 | 4)| Bonn — 24 .5/+ 17.0
| 3 | Bonn | + 29.5) + 4.9 | 5 Hamburg — 39.5|+ 6.3
1 4/Hamburg|}+ 7.3) — 7.5 >| Bonn — 23.5) + 17.6
4| Bonn |-+39.0/+ 1.0) 6| Hamburg ; — 32 .4/ + 19.9
8| Hamburg) — 8 .6| + 16.3) 6) Bonn — 20.9] + 21.5
8 | Bonn [+ 1.5/— 1.3 7 | Hamburg | — 41 .7| + 23 a
9 | Berlin (+ 4.6—I11.1 7) Bonn — 27 .5/+ 15.4
9 | Hamburg | — 17 8/+ 8.9 8} Bonn — 30.4] + 22 .2
| 11) Berlin | —21.3);— 4.6 | | 9| Hamburg | — 32 .4| + 24.1
11| Hamburg; — 8.2;+4+ 1.9 11 | Hamburg | — 39 .5| + 25 .2 Ls
11| Bonn |; — 8.4/— 3.262, 11 | Bonn — 32.1} 422.1"
12| Hamburg! — 8.0) + 10.2 | | 16 | Hamburg | — 30 .0} + 25 .0
12|Bonn =| — 27 .5| — 26 .5 17 | Hamburg | — 22 .3| + 22 .4
13} Hamburg) —16.7|++ 4.3 18 | Hamburg | — 28 .5| + 17 .9 |
13| Bonn f= 5.9)) —— 20 18} Hudson |— 41.6] + 26.3)
17 | Hamburg Se SS ye 19} Bonn — 33 .2| + 22.7)
17! Bonn —12.3/+ 3.5) 19| Hudson |— 45 .4|— 23.3!
19 Berlin |—21.8)+ 2.8) | 20 | Hamburg | — 53.1} + 23.9
20|Berlin |—18.0/+ 3.3] | 21 | Hamburg | — 26 .9| + 35.0
20} Hamburg! — 14.6)+ 4.0 21|Hudson |— 42.3) + 0.6 6
21| Berlin - |— 8.1)/+ 5.5 22 | Hamburg | — 40 .4/ + 20.7 f
21 | Hamburg | — 30.5|+ 1.3! 24| Hamburg | — 34.6) + 23.5
21! Bonn =) 2A ae: 25|Hudson |— 42 .5| + 18.3
22 Hamburg ee 28.0);+ 9.7 April 1 Hudson + 61.7
22 Bonn | — 22 .9|— 0.6 S3 2|Hudson |— 56.0) + 27.2
| 23 Hamburg, — 10 .2| + 10.4
| 23 Bonn — 7.7/+ 15.2
| 24 Hamburg|— 18.5} + 2.5 |
24 Bonn |— 7.1}/+ 15.3
25 Hamburg |— 24.0}/+4+ 7.1
25 Bonn — 8.6/+ 18 .2
26 Bonn — 28 .6/ + 23.4
27|Bonn |—25.2|+4 11.9)
The preceding observations I have divided into six groups, and taken the
average of all the corrections. This may be regarded as the mean error of the
ephemeris for the middle date of each group, and applying this correction to
the ephemeris with an opposite sign, we obtain the comet’s true places. The
VIII.—2 N
150 ASTRONOMICAL OBSERVATIONS
Hudson observations in right ascension accord with each other quite as well
as the European observations; the declinations seem entitled to very little
weight. The results are shown in the following table.
| a Corrections of Ephemeris.| Comet’s Places by Ephemeris. Corrected Places freed from Aberration.
| Berlin Mean - —— —
| ame A.R, | Dec. | A.R. Dec. A.R. Dec. |
| Jan. 31, 8"| 4+ 14”.7|— 8”.1| 326° 24’ 50”.6| + 61° 25’ 23”.5| 326° 25’ 5”.3| + 61° 25’ 15".4 |
|Feb. 12, |—12.7/— 1.1/358 837.6] 51 251.8/358 824.9) 51 250.7)
| 23, —17.3)+ 7.8| 13 19 53 .3 40 11 24.7| 138 19 36.0} 40 11 32.5
| Mar. 3, —28 .0/+17.6) 21 145.4 32 39 1.4] 21 117.4) 32 3919 0
12, — 32 6 + 22 .4) 26 35 13 .5 26 27 52 .4| 26 34 40.9) 26 28 14 8
24, —40 .2)+ 25 0) 32 10 37 .8 19 51 50 .7| 32 9 57 .6 19 52 15 .7
It is important to know the probable error of the preceding results. If we
regard the corrections in each group as observed values of the same quantity, we
obtain the probable error of the mean by the formula E = eee
n(n —
These errors are exhibited below, those in right ascension being each
multiplied by the cosine of the corresponding declination. The last co-
lumn represents the probable error of the entire observation, being equal to
V A. R. error? + Dec. error’.
ALR. Dec. Total Error.
January 31, 155 22:3 Dhue f
February 12, i ae 2.3 2.25
23, 1 erst | 1.3 1 az 6
March 3, 9 8 1.2
12, 1.3 oll 1.5
24, 1.7 8 Lo
The supposition that the correction of the Ephemeris remains constant
throughout the entire period embraced by one group is incorrect, and we
should obtain a more satisfactory result if we knew the proper correction of the
Ephemeris for the date of each observation. As, however, the above correc-
tions follow no obvious law, it is impossible to obtain, very satisfactorily, the
correction for each date by interpolation. I have therefore contented myself
with the above numbers, and conclude that if an orbit can be found, whose
errors are confined within these limits, nothing more can reasonably be de-
manded. The preceding right ascensions and declinations were converted into
longitudes and latitudes by employing the apparent obliquity of the ecliptic,
AT HUDSON OBSERVATORY. 151
and the longitudes were referred to the mean equinox of J anuary 1, 1840, by
applying the precession and nutation.
The perturbations remained to be computed. In this operation I followed
the method of Bessel for the comet of 1807. I employed intervals of eighteen
days, the middle days of the several intervals being February 9th, February
27th, and March 16th. The values of A, B, and C for their dates, being the
united effects of the planets Mercury, Venus, Earth, Mars, Jupiter, Saturn,
and Uranus, expressed in ten thqusand millionth parts of a unit, are as follow:
A. B. c.
February 9, — 115342 — 39226 + 64303
27, — 81595 — 61489 + 36573
March 16, — 104112 — 76746 + 25572
From these are deduced
Al. BI. Cl
February 9, + 22805 + 132129 — 31608
27; — 44625 + 98296 — 11076
March 16, — 98327 + 83979 — 25737
Hence were computed the variations of the elements of the comet’s orbit for
each interval of eighteen days, and from them the total amount of variation
from January 31st to March 25th. The perturbations in longitude and lati-
tude were thence deduced for January 31st, February 18th, March 7th, and
March 25th, from which were obtained, by interpolation, the perturbations for
intermediate dates. The following is the result:
Longitude. Latitude.
January 31, 0’.0 0’.0
February 12, 0.0 —1.1
23, —0.2 —1.9
March 3, —0.4 —2.3
12, —0.7 —2.5
24, —1.1 —2.7
Applying these corrections with opposite sign to the comet’s observed places,
we obtain the places such as they would have been observed had it not been
for the disturbing action of the planets. The following table exhibits the
comet's corrected places, together with those of the earth for the same times,
from the Nautical Almanac.
152 ASTRONOMICAL OBSERVATIONS
EEE
Comet. Eartu.
Berlin Mean Time. | Longitude. Latitude. | Longitude. Latitude. Log Radius Vector.
Jan. 31, 8>| 15° 0°50".0 | + 65° 37’ 49”.6 | 131° 3'29”.6| 4+ 0".3| 9.9936814
Feb. 12, 24 50 22 3 46 10 41 .5|143 12 42 .4 i 9.994579]
23, | 29 22 27 8 31 27 35 5 | 154 17 46 .9|/-+4+ «5 9.9956259
March 3, | 32 2 14 .6 22 O 28 .2/163 19 40 .4;— .1 9.9966147
12; | 34 14°52 14 26 39 .0)172 19 2.2|;— .4 9.9976458
24, | 386.45) 47 6 27 27.7| 184 13 40 .3|+ .7 9.9991232
The longitudes are referred to the mean equinox of January 1, 1840. As-
suming Kyseus’ approximate elements, the preceding places furnished me
twelve equations of condition, from which were deduced the following parabo-
lic elements, by the method of minimum squares:
Perihelion passage, Berlin mean time, March 12. 981921.
Longitude of perihelion, . . . . 80° 20’ 24.4
ce ascending node, . . 236 48 39.3
Inclination of orbit, . . . . . 59 14 2.4
Log. of perihelion distance, . . . 0.0870185.
The errors of this orbit are as follow, the errors in longitude being multi-
plied by the cosine of the corresponding latitude :
Longitude. Latitude.
January 31, + 4.4 + 2.6
February 12, —14.4 —1.9
23, —6.1 + 1.5
March 3, —2.7 —1.7
12, = Yl — 7
24, + 5.9 + 1.1
These errors certainly are not very great, yet they exceed what has already
been assigned as the limit of the probable error of the observations. It is, then,
probable that the orbit was not a parabola, especially as the errors follow an
obvious law, the extremes being positive, and the middle ones generally nega-
tive. It remains to vary the other element, namely, the eccentricity. This
was done by means of the following equations of condition, computed by the
formule of Gauss and Bessel, in which the variations of the elements were
d = 0.0002
t = 0.01
pHn=si=tl
e = 0.001
AT HUDSON OBSERVATORY. 153
The first six of the following equations are dependent upon the longitudes,
and are severally multiplied by the cosine of the corresponding latitude.
= — 32.6255 + 6.603¢ + 30.1092 — 32.467» + 40.720. — 4.672:
= — 23.3885 — 0.510 + 10.100 — 28.875 + 36.707 — 5.400
E=—17.756 — 4.192 — 1.295 — 25.476 + 27.782 — 3.631
E=— 14.750 — 6.078 — 7.428 — 22.914 + 20.407 — 1.879
£E=—12.88l1 — 7.296 —11.611 — 20.726 + 13.814 — 0.186
£=— 11.604 — 8.241 — 15.225 — 18.389 + 6.335 + 2.002
E = + 24.462 — 34.932 — 64.694 + 22.945 + 19.768 — 34.780
E=+ 16.770 — 35.444 — 61.086 + 30.666 — 1.309 — 26.121
E=+ 7.297 -~. -.135 —51.018 + 32.773 — 8.379 — 14.846
E=+ 1.240 —-7.124 — 43.649 + 32.861 — 8.888 — 6.763
£=— 3.118 — 23.649 — 38.145 + 32.375 — 7.202 — 0.600
E=— 7.146 —20.085 — 33.374 + 31.510 — 3.734 + 5.529
From these equations I obtained the following elliptic elements:
Perihelion passage, Berlin mean time, March 13. 158768.
Longitude of perihelion, . . . . 80°12’ 3.52
a ascending node, . . 236 50 34 .67
Inclination of orbit,. . . . . . 59 12 36.14
Log. of perihelion distance, . . . 0.0865202
Eccentricity, . . . . . . . 0.99323412
Semi-axis major, . . 180.383
Periodic time, . . . 2422.6 years.
The errors of this orbit are as follow:
Longitude. Latitude. Total Error.
January 31, + 0".6 “Pres 1”.9
February 12, + 0.4 —3.9 3.9
23, —2.6 + 2.0 3.3
March 3, + 0.1 + 0.6 0 .6
12, + 0.5 saat Lae | 1 .3
24, n07.9 —1.45 1 es
The total error of four of the observations is less than the limit of probable
error before determined, and that of the other two is greater. The excess and
defect are nearly equal. On the whole, then, the accordance is highly satis-
factory. ‘The sum of the squares of the errors in the elliptic orbit is 34.62; in
VIII.—2 0
154
the parabolic, 117,85.
between the two orbits.
ASTRONOMICAL OBSERVATIONS, ETC.
There seems, then, no room for hesitation in the choice
It is much to be regretted that observations could not
have been made for a longer time after the perihelion passage.
tainty.
In Proressor Loomis’ AstRonomIcaL OBsERVATIONS, Ist Series, Vor. VII.
ERRATA
Page 44, line 22, for “ pin”’ read “ pier.”
45,
45,
45,
50,
51,
10, for “ division” read “ divisions.”’
21, for “* 120°” read “110°.”
31, for “ pin” read “ pier.”
44, first column, for “‘o Capricorni’’ read “ § Capricorni.”’
8, for “ Piradum”’ read ‘‘ Pleiadum,”
Errata in Prorrssor Loomis’ Seconp Macnertic Articxe, Vor. VII.
Page 102, line 24, for “ Aug. 18” read “ Aug. 19.”
103, 105, 107, 109, 111, running title, for “dips” read “dip.”
106, line 11, for ‘*8h”’ read “4b.”
106, line 12, for ‘‘ Hampton” read “‘ Hamden.”
Errata 1n Prorressor Loomis’ Storm Articre, Vor. VII.
Page 125, line 10, for ‘‘seems’”’ read ‘“ seemed.”
125,
127,
127,
130,
141,
145,
146,
19, for “‘ Register” read “ Regents,”
46, for “ Casinovia” read ‘* Cazenovia.”
47, for “ Genornem”’ read “‘ Gouverneur.”
11, for “nich” read “inch.”
4, for “ships” read “‘ ship.”
’ Pp: Pp
31, for “‘ Rendues’’ read “ Reudus.”’
25, for ‘“ appearances”’ read appearance.”
2 P'
They would
have served to determine, with greater accuracy, the eccentricity of the orbit,
an element which must now be admitted to be liable to considerable uncer-
ARTICLE XI.
Expansion of F (x +h). By Pike Powers, of the University of Virginia.
Read April 2, 1841.
A FUNCTION may be regarded as the general expression of a series of num-
bers which vary according to some given law; the place or number of the
term being denoted by z, and its value by Fz. The series may always be
represented wholly or in part by a curve whose ordinates correspond to the
different values of F'z, and its abscissas to those of z.
In any function certain values may always be assigned to 2, between which
the difference of any two consecutive values of Fz will not be infinitely greater
than the difference of the corresponding values of z.
The only functions which the writer can conceive of as not subject to the
preceding remark are, 1. Such as undergo, incessantly, abrupt changes from
increase to decrease, or the reverse: 2. Those which, while they vary in the
same sense through a finite interval, yet undergo always an infinite change for
a finite change in z. It seems obvious, however, that if such functions can be
analytically expressed, they cannot admit of Taylor’s theorem. (See note.)
Supposing z to be confined within the limits referred to above, we have
Ae tPF @ 9 (e.); (1)
(z.h) reducing to a finite quantity @ (x. 0) when h = 0.
In like manner we may write
oo ee) (x. h),
or o(z.h)=o(x.0) +h. o' (xz. h),
where h 9’ (x. h) = 0 whenh=0.
Now if @' (z. h) should be finite when h = 0, we should have
(2. h) =o" (z 10) +h. O(a. h);
156 EXPANSION OF F (x + h).
and, by continuing this process, and substituting for 9” (7. h), 9’ (~-h), » (x. h)
&c., their values, we should get easily the common development of F (x + h).
But let us suppose that 9’ (x . 0) is infinite, that is, that as 2 approaches 0,
9’ (x . h) increases without limit according to a law depending upon the form
of the function.
Whatever this law may be, as functions vanishing with / admit of an infi-
nite diversity of form, it seems obvious that there must be some one fh, such
U Agee)
that © shall increase with the same rate as 9’ (z. h), 9" (x . 0) being
finite. We may write, then,
h. 9) eed) = 5: o’ (x. h).
As fh is inferior to h in degree, since h. 9’ (x . h) vanishes with h, and as
the powers of h admit of every shade of magnitude, and diminish towards 0
with every possible degree of rapidity, it appears evident that for very small
values of h, fh may be replaced by h? where v <1. Hence
Fi (2 hah? Q =k Q,
where a = 1 — v, and Q’ is so chosen as to agree with Q’” (x. h) for very
small values of h. By similar reasoning we have
Q' = 9" (¢. 0) ¢h*. Q”.
Putting Q for (z.h) we may write (1) under the form
F(a#+h)=F2rr+h.Q.
And if we replace ? (2 . 0), * (z. 0), &c., by P, P’, &c., we shall have
Fi(¢ith) =j=F2hoQ;
Q’* =P +h’. Q;
‘Q being finite when k= 0. Multiplying the 2d equation by h, the 3d by
h*+*", &c., adding, and putting a for 1 + a, 6 for 1 +a +4, &c., we have
F(¢+h)=F2+ Php PR Pl. Sh. os. h’. Q; (2)
which differs only in the 2d term from the development assumed by Poisson.
The equation
F(z+h)=Fa+Ph+h. R,
EXPANSION OF F (x + A). 157
which is derived from (1) by a simple transformation, R taking the place of
h. ¢ (x. h), and consequently vanishing with h, is sufficient to establish all
the rules of differentiation.
Observing that in the preceding investigation z was confined within certain
limits, while h remained arbitrary, we may replace 2 by a number r within
the limits supposed, and h by z — r which denotes the variable difference be-
tween the general and special values of z. Equation (2) will then become
“u=Fe=Fr+p(e¢—r)+p' (2—r) +p" (gim—r)y eee... M;
where p p’ p’”, &c., denote the values of P P’ P”, &c., when z=7, and M the
value of h*. ‘Q when z = 7, andh = 2—r.
Differentiating successively, and denoting the differential coefficients of M
by M M", &c., we have
= SP ep Ae 1) POE 1)? Fathers M,
Tae a(a—1)(2—1)*~* + 6(6—1) p" (24) iF to. os M", (3)
du
= a(a—1)(a—2) (~—r) *—? 4+.5(b—1) (b—2) (x—r)'— 3M".
az
We may suppose that each term in these equations is the only one which con-
tains the power of z — r peculiar to it, for if there were several terms contain-
ing the same power of z — r, they might be united into one.
Observing, now, that the exponents a, 8, c, &c., are each greater than unity,
: ; du d?u
and are arranged in ascending order, if we make z = 7, and suppose Aaa
dx dx
&c., to remain finite, the first of equations (3) becomes
i=»
a result already established, and implied in the process of differentiating.
With regard to the 2d equation we must have
a> 2,ora <2, ora = 2.
If a> 2, every term in the 2d member antecedent to M” will vanish, and if
M"' does not vanish, it must either be finite or infinite. But, since @ es) 18
ax
finite, M’’ cannot be infinite. If it reduces to a finite quantity A, then M’*
* See Mr. Bonnycastle’s paper, pages 245, 246, Vol. VII. of these ‘Transactions.
VIlI.—2 Pp
158 EXPANSION OF F (z + h).
must contain a term A (xz — r), and Ma term A (z — 7)’, and it is only ne-
cessary to give this term its proper place in the series in order to get the same
result which @ = 2 will furnish. If a <2, the lst term will be infinite, and
cannot be cancelled by any of the terms antecedent to M”, since they all con-
tain powers of z — different from the first; nor by any term in M”, since
that term would then contain the same power of z — 7 with the first, which
is contrary to the arrangement of the series. We must have, then, @ = 2.
Therefore a (a — 1) =1. 2,—all the terms after the first vanish, simce M”
cannot remain finite for the same reason as in the preceding case,—and we
have
2
=) RS ee ees |
In the same way we can show that
- 1 d*u
P= 7-3-3 (Gas) &
As is any value of z between the supposed limits, the results obtained are
du
rok
evidently general, and will give all the terms of the series until we reach a co-
efficient which becomes infinite for z = 7, and then the remainder of the ex-
pansion must be supplied in some other way. Using the notation of Lagrange,
we have generally, therefore,
Fos Fr4F'r(2—r) 4 F'r Ea) 5 ee (z+ r)*.q;
which, when 7 = 0, becomes |
Fa =F (0) +2. F (0) +2, F’ (0) + i: Reade tie kale Sot 1 a
Equation (2) also becomes
F(z+h)=F2 +h. Faeep yen ae ee ee ae a O.
The limits within which the value of the last terrn is found may be deter-
mined by the method of Lagrange, and the development will be complete.
The reader will find a summary view of this method in the subjoined note,
furnishing itself an exact though indirect solution of the problem.
EXPANSION OF F' (x + h). 159
NOTE.
The validity of the reasoning used in the foregoing demonstration, to show the existence of F’
in a finite form in all cases where z is confined within certain limits, will perhaps appear more
evident from the following remarks.
Postulate 1, There are no functions which, throughout their whole range of values, change in-
cessantly from increase to decrease as x varies, and that by quantities infinitely greater than the
change in x. It is scarcely possible to give the graphic representation of such functions, much
less their analytical expression. A line continually returning upon itself thus, sgl > or a spiral
whose coils are compressed into almost absolute contact, would be an approximative expression of
them. We conclude, then, that in any function #2, values a and a + n h may be assigned to x,
differing by a finite quantity h, and such that from Fa to F (a + 7h), Fx shall constantly in-
crease or constantly decrease.
Postulate 2. There are no functions which, while they undergo a constant increase or decrease
through finite intervals of value, yet always receive an infinite change for a finite change in 2.
And here we again appeal to observation, and the apparent impossibility of exhibiting such func-
tions in either a geometric or algebraic form.
Theorem 1. Now suppose that i At ie ks approaches infinity as h approaches 0, for all
h
values of z. Then the following ratios,
F(x+h)—Fr F(x+2h)—F(t+h) F(e+3h)—F(z+2h) -.. Fa@+nh)—F fie+ (n—1) hJ
“hrs 4 Ee h Y h ;
will all be infinitely great when A is infinitely small.
Let n be taken so great that nf shall be finite, and let x be such that Fx constantly increases or
constantly decreases from Fx to F(x + nh). The numerators of the preceding ratios will be
all of the same sign; their sum is obviously F' (« +h) — Fx; and if P denote the least of these
numerators,rn P< F(x +nh)— Fx. But
Poo nP
poh 7 ee
But this result is impossible by postulate 2, Hence in any function F'z there must be some values
of z, such that
F(z +h)— Fx :
h
From which we readily derive
F(e+th=Faeth.F'ext+h.R,
= a finite quantity 7’, when h = 0.
R vanishing with h.
As to the method used by Lagrange to determine the limits of the expansion of F’ (x + h), it
may not be amiss to observe that when the existence of the differential coefficients in a finite form
is admitted, this method furnishes in all cases an exact and simple mode of exhibiting the true
value of F(x +h). This fact has been most singularly overlooked.
160 EXPANSION OF F (x + h).
Cauchy apparently, and De Morgan confessedly, have made Lagrange’s method the basis of
their demonstrations of Taylor’s theorem. We will now exhibit the method of Lagrange, after
premising that the equation
F(i«th=Fet+h.F’x+h.R
will readily establish the following well known theorem.
Theorem 2. When #” z is positive, x and w vary in the same sense, and when negative, in
an opposite sense; consequently, if #’(0) = 0, and F” (0) be not infinite, #’x will be positive or
negative at the same time with z, when #” z is positive.
Let us suppose that for 2 = a, and a = 8, and for all intermediate values, F’ 2, F”r.... Fax
are all finite and continuous, and let us replace 2 by a + h, h admitting all values from 0 to 6 — a.
Now let .2 and B be the greatest and least values of #” (a + hf): then
A— F' (a+ h)> 0, and F” (a+ h)— B> 0.
Hence the primitives of these expressions taken with regard to h, and so as to vanish with h, will
likewise be positive. Theorem (2).
Ah—F(a+h) + Fa> 0, and F(a + h)— Bh— Fa> 0.
Next let .2’ and B’ be the greatest and least values of F” (a + /): then
A' — F" (a+ h)> 0, and F” (a + h)— BD 0.
By taking the primitives as before, we have
Ah— F’ (a+h) + F’a> 0, and FY (a + hh) — Bh— F'ad 0;
and by taking them again, we have
3
A Path) th. Pat Fa>0, and F(a+h)— Bh. Pa—Fa> 0,
or
Pp 2
Fath) < Fath. Pat, ami F(a+h)> Fath. Pat 3B.
By continuing this process, we shall finally get
h he hn
/ a “” UG Fi ae see SA)
F(ath)< Fath. Fat 5 oldk near a er Te gs pe
Flath)>Fath.F' LSS ee es et Be
Gh) 2G le Padi are 2 8 hare west ut ita eeonmaaieinane wh
™ and B representing the greatest and least values of #™ (a + h).
Hence if £” (a + A) be continuous, and h = 6 — a, there will be some value #” (a + 4 h)
intermediate between 4 and B(” such that
he
1 ec tee Oe
where 6 <1. This is precisely the expression obtained by Cauchy. It is general, since a is
Fath) = Fath. Pat”. Frat e gehen iaiue -F" (a+ oh),
any value of x subject to the conditions stated, and it gives always the exact value of F(x + h)
= will always finally
nr
when x and h are such that #” (« + ¢h) shall be finite, since a
converge.
EXPANSION OF I" (x + A). 161
With regard to the negative values of h, we shall have, by theorem (2),
A— F' (a—h)> 0, F’ (a—h) —B> 0,
Ah— F(a—h) + Fa<0, F(a—h) + Bh— Fa <0,
or F(a—h)> Fa— Ah, F(a—h) < Fa— Bh;
and the reasoning continued as before will lead to a similar result.
It may be observed, in conclusion, that the integrations effected above are perfectly allowable,
since the equation
F(eth)=Frth.F'e+h.R
is sufficient for all purposes of differentiation and integration. And it is immaterial whether any
other primitives than those obtained exist, since we are not seeking the only expansion of F(x + h),
but one true expansion of it. (See Calc. des Fonctions, Lecon 9me.)
vill.—2 Q
: iy eh
i oe bbw i 7
5 pies
* va'MRdE bie
¥
Ae) ivi ae Wt ta
Og aime} cis Ae
> ARO yhesa ies ut + i seh
ad {AG