UBRARYflc DdllVD-JO : -CALIFO^ _ 2 -r .avaaiTi^ ^ % OS-ANGElfj> ^ rtl.i > HAIMfl-]^ s i ^UIBRARYQ^ \MEUNIVER% ^l tftL B3AINa-3\\V ^ * ^ ^. dOS-ANC im O uL_ A^C o o its IIBRARYQ^ 'I OJIIVJ-JO^ I I : =1 ^A/lin< A^' F-CAIIFO^ uivnan^ LOS-ANCElfx ....... . ....... l liirrl inrrl . lor II I I i % o 1 3 s i I "75 ^ s . V J o u_ J c ^1 1 % > \\r ^ ^\\r ^ -hd I II si ^- H^ I I I / ^- S fOr-1 II AN ESSAY MAGNETIC ATTRACTIONS, AN APPENDIX. AN ESSAY MAGNETIC ATTRACTIONS, AND ON THE LAWS OF TERRESTRIAL AND ELECTRO MAGNETISM; COMPRISING A POPULAR COURSE OF CURIOUS AND INTERESTING EXPERIMENTS ON THE LATTER SUBJECT, AND AN EASY EXPERIMENTAL METHOD OF CORRECTING THE LOCAL ATTRACTION OF VESSELS ON THE COMPASS IN ALL PARTS OF THE WORLD. WITH CONTAINING THE RESULTS OF EXPERIMENTS MADE ON SHIP BOARD FROM LATITUDE 61 S. TO LATITUDE 80 N. BY PETER BARLOW, F.R.S. OF THE ROYAL MILITARY ACADEMY; HONORARY MEMBER OF THE PHILOSOPHICAL SOCIETIES OF CAMBRIDGE AND NEWCASTLE, AND ASSOCIATE IN THE SOCIETY OF CIVIL ENGINEERS. SECOND EDITION, MUCH ENLARGED AND IMPROVED. ILLUSTRATED WITH PLATES, BY LOWRY. LONDON: PRINTED FOR J. MAWMAN, LUDGATE-STREET, AND ALSO SOLD BY J. TAYLOR, HIGH HOLBORN. 1824. QC / 9 TO DAVIES GILBERT, ESQ. M.P. F.R.S. MEMBER OF THE BOARD OF LONGITUDE, Sfc. Sfc. Sfc. SIR, THE great interest you take in all useful scientific pursuits, and particularly in those connected with Nautical Science, has made me solicitous of the honour of presenting to you this new edition of my " Essay on Magnetic Attrac- tions." And I am willing to hope, that however defective the work may be in its execution, you will at least approve of its design, and deem it not unworthy of your acceptance. I have the honour to be, Sir, With great respect and esteem, Your very obedient and humble Servant, R^yal Military Academy, THE AUTHOR OH. 22, 1822. 1189471 PREFACE. THE subject of the local attraction of vessels having engaged the attention of several eminent practical navigators and philosophers, I was induced in the year 1819 to undertake a course of experiments, with a view of deriving some principle of compu- tation, or other method, for correcting this source of error, it having been generally admitted that, at this time, no rule had yet been given that could be considered applicable to the purpose in all parts of the world. In the course of these experiments I was so fortunate as to fall upon an easy practical mode of correction, wholly independent of calculation ; I also discovered certain magnetic laws which seemed to me likely to pave the way to a mathematical theory of magnetism. These results were drawn together and pub- lished in the year 1820, under the title of "An Essay on Magnetic Attractions," and which may still be considered as the foundation of the present VI PREFACE. work ; although, having considerably extended my views, and multiplied my experiments and investi- gations, I have found it necessary to change, in a slight degree, the former title, whereby to compre- hend the science of Electro Magnetism, which forms one of the divisions of the present volume. The leading object of this edition, however, as of the former, is the developement of the mathe- matical principles of magnetism, and their appli- cation to the correction of the local attraction of vessels, which is of more and more importance, as every year is leading to some new application of iron in the construction and equipment of ships of war, and which, if persevered in without some mode of correction, would soon render the compass worse than useless as a nautical instrument. It may be observed, for example, that besides there being at present considerable more iron ballast than formerly, the water casks are now replaced by iron tanks presenting an immense attracting surface; iron knees, sleepers, plates, and in some cases the riders, have been introduced in lieu of those of timber ; even the hempen cables have' been put hors de service by the patent PREFACE. Vll cables of iron, gun-carriages of this metal are at this moment supplanting those of the usual mate- rial : the ingenious patent capstan of Captain Phillips, which will doubtless soon become generally applied, is principally of iron, and although of no considerable mass, is so situated as to affect the compass very sensibly ; and lastly, it seems proba- ble that even the masts* are to be attempted in this material. The work is now divided into three parts ; the first containing the greater portion of the matter de- livered in the former edition, with some additional experiments, which by the favour of my Lords Commissioners of the Admiralty, I have been ena- bled to make on board several of His Majesty's vessels, and the results obtained by a series of observations in H. M. S. LEVEN during a voyage of sixteen months. I have also added to this part the results of a series of experiments made with a view of ascertaining the effect which the iron of a vessel has upon the rates of chronometers ; and another series on the comparative magnetic power of different kinds of iron and steel ; and on the * See Addenda. Vlll PREFACE. effects of heat in changing the magnetic power of iron bodies. The second part is theoretical, in which I have endeavoured to show that all the laws deduced in the first part from experiment only, are the neces- sary consequence of a certain hypothesis, exceed- ingly simple in its principles, and general in its application. The formulae deduced in this part are shown to be easily convertible into others which embrace all the known laws of terrestrial magnet- ism ; and an attempt is made to compute the annual change in the inclination and declination of the needle. The third part is appropriated to the science of Electro Magnetism, which has had its birth since the former edition of this work was published. In the first section is given an historical sketch of the present state of this new science ; in the second are described the experiments I have been led to make with a view of reducing its laws to mathe- matical principles ; and in the third is given a course of interesting experiments, due to the several ingenious philosophers who have interested themselves in this pursuit ; and in which I have CONTENTS. PART I. Containing a Detail of Magnetic Experiments. SECTION PAGE I. Preliminary observations and experiments 1 II. Second course of experiments, description of ap- paratus, &c 14 III. Experiments made with a view of determining the inclination of the plane of no attraction. . 18 IV. Determination of the law of attraction, in re- ference to the latitude 22 V. Determination of the law of attraction in re- ference to the longitude 28 VI. Determination of the law of attraction as regards the distance 40 VII. Determination of the law of attraction in refer- ence to the mass 46 VIII. Supplementary experiments relative to the quan- tity of attraction as regards the thickness of metal 52 IX. Summary of the preceding deductions 56 X. Experiments on a twenty-four pounder on a tra- versing platform 61 XI. On the local attraction of vessels 71 XII. Method of determining the local attraction of vessels by experiment* 79 XIII. Account of experiments made on board H. M. S. Leven, Conway and Barraconta 89 XIV. On the effects produced on the rates of chrono- meters by the proximity of masses of iron. ... 110 XV. On the relative magnetic power of different de- scriptions of iron and steel at different degrees of temperature 129 * See also the Addenda. Xll CONTENTS. PART II. Containing a Theoretical Investigation of the Laws of Induced and Terrestrial Magnetism. SECTION PAGE I. Investigation of the laws of magnetism peculiar to iron bodies 150 Of the horizontal needle 160 Of the dipping needle 166 General results 171 II. On the change of magnetic intensity of a needle as affected by iron spheres 177 III. On the magnetic action of bars of iron 183 Supplementary experiments on the action of iron plates 189 IV. Application of the preceding formulae to the mag- netism of the terrestrial sphere 193 V. On the situation of the terrestrial magnetic axis, and on its annual motion 204 PART III. On Klect.ro Magnetism. I. Sketch of the present state of electro magnetism 221 II. On the mathematical laws of electro magnetism 232 III. Containing a course of electro magnetic experi- ments . . . 256 ERRATA. Page 12 line 19, for Lecourt read Lecount 19 last line of the note, for the inclination read tan. of the in- clination 22 line 4 from bottom, for distance read distances 24 line 14,/bj- there read therefore 84 line 5 from bottom, for c read C 171 line 1 5, for number of vibrations rend times of vibration 172 line 2 from bottom, far cos reail cos / 273 line H>,fr plate 5 rtrci plate 4 PREFACE. IX endeavoured to show their mutual dependence on each other, and their general agreement and par- ticular connection with the mathematical theory advanced in the second section. I am not aware that it is necessary to enter in this place into a more minute analysis of the con- tents of the present volume ; but I cannot conclude this Preface without expressing my grateful ac- knowledgment for the generous and flattering manner in which the former edition of this work was received, both by the nautical profession and by the most distinguished philosophers and mathe- maticians. I am also highly indebted to my Lords Commissioners of the Admiralty, and to the Honourable the Principal Officers and Commis- sioners of His Majesty's Navy, for the various facilities I have experienced in carrying my expe- riments into execution ; and I am willing to flatter myself that these public Boards will feel satis- fied that I have made the best use in my power of the opportunities I have thus enjoyed. Royal Military Academy, Oct. <2<2, 182*2. AN : ESSAY ; ON MAGNETIC ATTRACTIONS, &c. PART I. Containing a Detail of Magnetical Experiments. SECTION I. PRELIMINARY OBSERVATIONS AND EXPERIMENTS. 1 . I FIRST undertook the experiments, which form the basis of the following Essay, with a view of finding some method of correcting the local attrac- tion of a ship's guns, and other iron on the com- pass, and it accordingly formed the prominent object in the former edition of this work. In the present instance, I have attempted something more, but I have still preserved the original form and arrangement, as far as the matter has been retained, and have only added such chapters, and made such alterations as have been rendered ne- cessary, from subsequent experiments and investi- gations. B 2 PRELIMINARY OBSERVATIONS, &C. When I begun my experiments, the laws of magnetic attractions were unknown ; the doctrine of magnetism consisted merely of a mass of de- tached experimental facts, which were, indeed, in some instances connected with each other by means of certain hypotheses, as we still endeavour to generalize the phenomena exhibited by an elec- trical machine ; but in the former case as in the latter, no successful attempt had yet been made to reduce the results to the dominion of analysis. This then was the task which I proposed to my- self, when I undertook the following experiments, and which my situation, at Woolwich, enabled me to pursue upon a very extended scale, as I could procure with facility, not only very considerable masses of iron, but those of the most uniform shape ; viz. balls and shells of every denomination, from those of a pound weight to others of half a ton, and from whose regularity of figure I had every reason to expect such a series of results as would, in all probability, enable me to detect the general principle of action. Having, however, no similar operations to refer to, my first steps were necessarily slow, and in some instances useless, many of which I shall therefore omit the recital of in this section. At the same time, in order that the reader may see the views by which I was in a great measure guided, I propose to take a glance of the whole course, from my first PRELIMINARY OBSERVATIONS, &C. 3 attempt on balls of a few pounds weight, to the gun of 58 cwt., and my deduction with reference to the most irregular masses, and to ships of every denomination. 2. First course of Experiments. In these I began by describing on a level platform several concentric circles, from 8 inches to 16 inches radius, drawing through the centre a line, in the direction of the magnetic meridian ; I then set off my east and west points ; and, lastly, divided the whole circle into equal parts of 10 degrees each. Having now adjusted my compass over the centre of the circle, I applied successively at every point of division, and at different distances from the centre, the shells belonging to the 5 inch, 8 inch, and 10 inch howitzers, weighing respec- tively 141bs.,481bs., and961bs., and noted the de- viation caused by each in. every position in which it was placed ; expecting thus to be able to draw some law, or to establish some relation between the masses, distances, and positions of the shells, and the deviation of the needle. In this, however, I was disappointed, and it would therefore be use- less to give these results at length. It will be sufficient to observe, that the general effect was to produce a deviation of the north end of the needle towards the west, while the shell was passed from the north through the east to the south ; and then an opposite deviation, while it was carried 4 PRELIMINARY OBSERVATIONS, &C." through the other semicircle ; the greatest deviation being in all cases when the shells were situated between the south and east, or the south and west points of the circle. 3. Although the deviation, being all in one direc- tion during the motion of the shell in each semi- circle, was contrary to what I had anticipated ; yet I did not consider the circumstance as very extra- ordinary, till I applied a small solid ball of two inches diameter. I was then much surprised to find that this caused a directly contrary effect ; that is to say, it produced first an eastern deviation, which arrived at its maximum between the north and the east ; it then decreased to zero, between the east and south: after which, the deviation became west, attained its maximum, and again vanished when the ball was due south. The same happened again in the contrary order, while the ball was passing from the south through the west to the north. I could perceive no cause for this apparent anomaly, and was, at length, obliged to leave it as an experimental fact, at that time wholly inexplicable. 4. I now proceeded with my experiments on the shells, exactly in the same manner as above stated ; except that I raised the compass in the centre to the level of the equator of each ball respectively, when I again observed a similar result to that above mentioned ; that is, in this instance I found PRELIMINARY OBSERVATIONS, &C. 5 first an eastern deviation, which vanished when the ball was due east ; then a western deviation, while the ball was passed from east to south ; and the same in the contrary order while passing from south to west, and from west to north. After this, raising the compass ten inches from the platform, I found, instead of the deviation being first western, as in my leading experiments, or first eastern and then zero and western, as in the last, that it was wholly eastern in the first semicircle, and western in the second : the results in this case were therefore exactly the reverse of those in the first instance. 5. It was thus rendered obvious, that the devia- tion, both as regards its quantity and direction, depended upon the position of the centre of the ball with respect to the compass. In fact, I found hat at every point, except the north and south, if I moved the ball from above downwards in the same vertical, I produced first an eastern and then a western, or first a western and then an eastern deviation : consequently, in each of those verticals there must be some one point in which the devia- tion was zero ; that is, in which the matter of the ball had no effect. These points of no action, I conceived, would in all probability be found posited in one plane, and my next object was therefore to ascertain whether this was the case ; and if so, to determine its inclination to the horizon, for it was obvious that it was not parallel to it. 6 PRELIMINARY OBSERVATIONS, &C. 6. With this view, I had a strong table made with copper fastenings, fixed with its feet in the ground, and rendered tolerably secure, and in its centre a circular hole, a little more than ten inches in diameter, was formed, through which, by means of a block and pulley, the ten inch shell could be raised and lowered at pleasure. The upper surface of the table, which was covered with paper, was, as in the former instance, divided according to the points of the compass ; the magnetic meridian being first accurately determined. The compass being now carried round the ball, instead of the latter being passed round the former, as in the first experiments. This being prepared, I elevated the ball till its action was imperceptible ; and then gradually lower- ing it, I noted the deviation at various altitudes of the ball, with the compass at each point of division of the circles, but more particularly in that of eight inches ; observing also very accurately the height or depth of the centre of the shell above or below the pivot of the needle, when the deviation was zero. These last results, indeed were the only ones applicable to my present inquiry ; and from these I ascertained that the several points of no action- were (as I had suspected) all situated in one plane ; the inclination of the plane itself to the horizon being found nearly equal to 20 degrees, declining directly from the magnetic north point to the south. PRELIMINARY OBSERVATIONS, &C. 7 This plane is therefore either exactly, or very nearly perpendicular to the direction of the dipping needle. The cause of the apparent anomaly which I had observed, relative to my small solid ball, now became obvious ; for the centre of this ball being but a little above the pivot of the needle, the plane of no attraction passed above or below that pivot, according to the position of the former ; whereas in the larger shells it passed above it in all their positions, except when the compass was elevated, and then the same happened in these cases as in that. (See Art. 3, &c.) I omit the detail of the experiments and compu- tations here referred to, as they will be found repeated in a subsequent section, with a larger ball and with a more perfect apparatus. 7. Having established this point, I could not but consider it as an important step towards attaining the object I had in view ; and I wished therefore to improve the construction of my apparatus, and to employ a ball or shell of larger dimensions. I accordingly procured from the Royal Arsenal a solid thirteen inch ball, such as is employed in proving the mortars of that dimension, weighing 2881bs. ; and having ordered a new table, and pro- cured a better system of pulleys, I repeated my former experiments, and confirmed the results I 8 PRELIMINARY OBSERVATIONS, &C. had drawn from them, as far as related to the incli- nation and direction of the plane of no attraction. Being thus assured that there are in every ball of iron two planes, in which the compass may be any where posited, without being influenced in its direc- tion ; the one that of no attraction, as stated above, and the other the vertical plane, corresponding to the magnetic meridian ; my next object was to ascer- tain how far the angle of deviation of the needle was influenced, and what law that deviation observed when the compass was removed out of those planes. But before I proceed to describe the experiments performed with a view to this determination, it may not be amiss to examine the deductions already made, which may be stated as follows : 8. In the first place, it has been shown that every iron ball has what (from analogy to the case of terrestrial magnetism) may for the present be deno- minated a magnetic equator, lying in the plane of no attraction, above mentioned. 9. That like the earth, also, it may be supposed to have two magnetic poles ; the one directed towards the north, and the other towards the south ; the line joining those poles being parallel to the natural magnetic direction of the dipping needle. 10. These experiments likewise seem to indicate that the effect produced upon the needle by the iron, (the distance being the same,) depends entirely PRELIMINARY OBSERVATIONS, &C. 9 upon the position of the centre of the ball, with reference to the pivot of the needle, and not to its position with regard to either extremity. 1 1 . Having made these deductions, I conceived an ideal sphere to be circumscribed about the ball of iron ; and assuming the circle of no attraction as an equator, and the poles of that circle as the poles of the sphere, I imagined circles of latitude and longitude to be described upon it, and wished, if possible, to pass the compass round the ball in these several circles, keeping it always at the same distance from the centre ; so that, in taking the deviations, I might separate the effect due to posi- tion, from that which might otherwise have arisen from a change in the distance. I determined also, in order to disengage the effect due to the longitude from that which had a reference to the latitude, to pass the compass in the first place over circles of latitude only, viz. in circles perpendicular to the magnetic equator : and finding after a few trials what I had indeed anticipated, that the deviations were the greatest in that circle which passed from the poles through the east and west points of the equator, I made this my first or principal meridian, and considered its longitude as zero. 12. My plan being thus laid, and my table now divided in equal parts of five degrees, and these again in certain places subdivided into less portions, I began by computing how much the centre of the 10 PRELIMINARY OBSERVATIONS, &C. ball ought to be raised or depressed when my compass stood on any given division, and how much the compass ought to be approximated towards the centre of the circle, in order that the former might fall upon the surface of the imaginary sphere ; and then again what was the latitude of its position. These, as is obvious, required the solution of so many spherical problems, in which there were given the angle on the plane of the table from the mag- netic east or west points of the horizon, which may be considered as the base of a spherical right angled triangle, and the angle at the base, equal to the natural dip of the needle 70 30', to find the hypo- thenuse and perpendicular. The former gave me the point in the circle in which the compass would be placed, or its latitude ; the sine of the latter to any given radius, equal to the proposed distance, the height or depth of the centre of the ball above or below the plane, passing parallel to the horizon through the pivot of the needle ; and the cosine of the latter to the same radius, the distance of the compass from the centre of the table. 13. Having prepared myself with these numbers, I began my series of observations with three dif- ferent compasses, noting very carefully the deviation due to each position, limiting myself principally to the circle of twelve inches radius : and having thus obtained a very extensive series of results, I made PRELIMINARY OBSERVATIONS, &C. ' 1 1 various comparisons between the trigonometrical lines of the angles of deviation, and those of latitude ; and after a few fruitless attempts I succeeded in de- ducing the following law ; namely, that the tangents of the deviations are proportional to the rectangle of the sine and cosine of the latitude, or to the sine of the double latitude. I omit giving the particular results of these expe- riments, for the reasons already assigned ; namely, that they were afterwards repeated in a more accu- rate manner, the detail of which will be found in a subsequent article. Having thus established the law of deviation as it depended on the latitude, I made a very few experiments with a view to a similar determination in reference to longitude ; from which I concluded (though not without some hesitation), that, all other things being the same, the deviation was propor- tional to the cosine of the longitude ; and with this deduction I concluded my first series of experi- ments, finding, that notwithstanding the improve- ment I had made in my apparatus, it was still not sufficiently accurate for pursuing my inquiries according to the more extended view I had now formed on the subject. 14. I had arrived at the above conclusions about the beginning of May, 1819, while the vessels designed to explore a north-west passage were still in the river ; and knowing that the attention of 12 PRELIMINARY OBSERVATIONS, &C. Captains Ross and Sabine had been in their late voyage a great deal engaged on the subject of local attraction, and considering these deductions as bearing strongly upon that inquiry, I wrote to Captain Sabine, stating the result of my inves- tigations, and expressing my wish that he would endeavour to ascertain whether the plane of no attraction (which doubtless exists in all latitudes) was every where inclined to the horizon at an angle equal to the complement of the dip, or at least whether it was so in those parts which he might visit ; to this letter I received an answer, which led me to hope that he would have been able to decide the question : but on the return of the discovery ships here alluded to, I found that Captain Sabine had not had an opportunity of try- ing these experiments ; [my deduction, however, has been very satisfactorily confirmed by Mr. Le- court, by a long series of experiments from the Cape of Good Hope to England, of which a more particular notice will be found in a subsequent page of this Essay. 15. Soon after the above communication to Captain Sabine, having drawn up a statement of my experiments and deductions, I transmitted it, through the favour of General Mudge, to the Royal Society ; and it was accordingly read at the meeting of the 20th of May, 1819, and I was afterwards informed that it had been deposited in PRELIMINARY OBSERVATIONS, &C. 13 the archives of the society, and that I could not have it returned, nor a copy of it, without paying for its being transcribed. Not being desirous of complying with the latter condition, particularly as it might occasion some delay, I drew up the preceding statement, principally from memory and the few rough notes I had by me : I had, indeed, the detail of my experiments ; but, for the reason before assigned, I have purposely refrained from giving them. My principal reason for stating the above parti- culars, is to make the circumstance an apology for any want of order and arrangement that may be apparent in the preceding and following sections ; for the latter having been all written upon a sup- position that it would appear with the former, I had not been so explicit in some points, as be- came necessary after I found it was to be published without its precursor ; and I have therefore been obliged to introduce explanations in certain parts that were before mere matters of reference : this may occasion some want of order and perspicuity ; but these cases, I hope, will be but few. 14 DESCRIPTION OF APPARATUS, &C. SECTION II. SECOND COURSE OF EXPERIMENTS J DESCRIPTION OF APPARATUS, INSTRUMENTS, &C. 16. HAVING explained, in the preceding articles, the general purpose of my experiments, and the nature of the deductions I had already drawn from them, I shall without farther introduction proceed to the description of the present series, which are nearly of the same kind as the foregoing : in fact, the only difference is, that my apparatus are here of a more accurate construction, the instruments more perfect, and the experiments performed with them, more varied and extensive. Description of the Apparatus. The table de- scribed in my former paper being found too small for carrying on my operations to the extent which seemed desirable, and as the place in which it was erected on my own premises, was not so convenient as I could have desired, General Mudge, who had taken considerable interest in the subject, very readily complied with rny request, to be allowed the model room belonging to the Royal Military Academy, for the further pursuit of my inquiries ; at the same time giving me permission to have such an apparatus constructed as seemed best to answer my intended purpose. I accordingly ordered a very DESCRIPTION OF APPARATUS, &C. 15 firm and solid round table to be made, 4 feet 8 inches in diameter, and 3 feet 2 inches high. In the centre of this table, a hole 13? inches in diameter, was cut, for the purpose of allowing the ball to pass freely through it. A piece of wood of the same thickness as the top of the table was made to fit this hole very accurately, and which might therefore be removed, or employed, as occasion required, three buttons being placed under the table near the edge of the hole for the purpose of resting it upon when employed, and which were turned back when it became ne- cessary to pass the ball through. In order now to prevent any shaking or trem- bling in the needle, four holes were cut in the floor, and piles driven into the earth below, to set the feet of the table upon, which effectually pre- vented any inconvenience of that kind, and the whole was rendered perfectly steady and horizontal. The centre piece being now fixed in its place, and a small brass centre sunk in it, to prevent the galling of the hole; the plane of the table was very accurately divided into equal parts of 2 5 each, by lines passing from the centre to the circumference, and all parting from one prin- cipal diameter, drawn in the direction of the mag- netic meridian. The table being thus prepared, a gm consisting of three poles twelve feet high, copper mounted 16 DESCRIPTION OF APPARATUS, &C. and tied, was erected over the centre of the table; and from the vertex of the former the ball was suspended by a system of pullies on Smeaton's principle, the power of which was as 12 to 1, whereby the purchase was reduced from 2881bs., (the weight of the ball) to -^=241bs. ; consequently the raising or depressing of the latter became easily manageable without a second person to assist. 17. Description of the Instruments. The com- passes which I had employed in my former ex- periments could only be read off to quarters of degrees, which therefore, although very perfect in their construction, I wished to replace by some one which might be read to minutes. My friend, Francis Baily, Esq., knowing that Mr. Arrowsmith, the celebrated geographer, had an excellent instru- ment of this kind, which had been made under the directions of the late Dr. Lorimer, he introduced me to the former gentleman, who very politely entrusted his instrument to my charge. The needle of this compass was six inches in length, of the bar form, and very powerful ; it was suspended in a brass box seven inches in diameter, the circle graduated to half degrees, which together with the vernier carried on the north end of the needle, enabled us to read off very accurately to minutes. 18. I have been particular in describing this DESCRIPTION OF APPARATUS, &C. 17 instrument, not because I made much use of it in my experiments, but because I found a defect in it, wbich may probably more commonly appertain to compasses of this description than is usually imagined, and which I conceive is important to mention. Having, immediately after my apparatus was erected, repeated, with the above instrument, a few of my former experiments, I found myself considerably perplexed with certain anomalies and irregularities, which I could not account for on any principle ; till at length it occurred to me, that they were precisely what would take place, if any part of the brass box itself had become magnetic ; and on trial "I found this actually to be the case ; for, on removing one of the pieces of brass attached to the box for the purpose of setting the instrument and fixing the sights, I found it to be strongly magnetic, sufficiently so to produce a vibration of the needle (when applied outside the glass) of 14 or 15 degrees, and to retain the same H degree out of its natural direction, and the lighter needles belonging to my other compasses were drawn and retained by the same piece of brass 4, 5, or 6 degrees from their true magnetic bearing, although applied outside the glass, and therefore at nearly a quarter of an inch from the extremity of the needle. This piece of brass was by far the most powerful in 18 DESCRIPTION OF APPARATUS, &C. its effects ; but still every screw and attached piece in the instruments had acquired the same quality to a certain degree, so that no dependence could be placed upon the needle except when these were all removed, which rendered its application incon- venient; I was therefore reluctantly obliged to discontinue the use of this fine instrument, and to have recourse to those employed in my former experiments. Besides the above instrument of Mr. Arrow- smith, the late Mr. Berge, veiy obligingly, on the application of Major Colby, favoured me with the loan of an excellent dipping-needle constructed by Nairne, exactly corresponding with the descrip- tion of that made by the same artist for the Hon. H. Cavendish, as given by the latter gentleman in the Philosophical Transactions for 1776, to which I beg therefore to refer. It was on this instrument I made the experiments on the dipping-needle described in the folio wing section. SECTION III. EXPERIMENTS MADE WITH A VIEW OF DETER- MINING THE INCLINATION OF THE PLANE OF NO ATTRACTION. 19. IT being rendered obvious by my former ex- periments, that the laws of attraction depended PLANE OF NO ATTRACTION, &C. .19 principally upon the position of the iron or compass, with reference to the circle denominated, in Section I. the magnetic equator : my first ob- ject was with the new apparatus, to repeat my former experiments, employing now a radius, or distance, of 20 inches, in lieu of that of 12 inches, which I had adopted in my former experi- ments. The compass, with this view, was placed suc- cessively on every second division of the table; viz. at every 5 in the entire circumference, keeping its centre in every case, exactly upon the circum- ference of the circle of 20 inches radius. The ball was then gently raised or depressed till the needle had attained exactly its proper magnetic bearing, when the height of the centre above, or its depth below the pivot of the needle, was accurately measured, and the inclination of the plane corresponding to each position of the compass computed, by means of the formula tan / = = sec. a* r cos a r where /denotes the inclination, r the radius of the circle, which in the present instance was 20 * Or by the proportion, As the radius of the circle (20 inches) , To the height or depth of the centre. So is the secant of the angle from the east or west points, To the inclination of the plane. 20 PLANE OF NO ATTRACTION, &C. inches, h the observed height or depth of the centre of the ball, and a the angle from the north or south point of the circle. To facilitate the computation, I have, in the following table, taken the mean of the four heights or depths due to the corresponding similar positions, from the east or west points. Experiments. 8 Observed Heights and Depths. B . s, . <* 1 S K 2*5 . 2 ** +3 "o I *!- 00 ^ if Ij I 1 si J| S H IJ I- jH i I! J Depth. Depth. Height. Height. li 5 7'10 7-00 7'05 7'05 7'05 19 29 r 10 7'05 7'00 6-95 7'OO 7'00 19 34 15 6-80 6-80 6-80 6-80 6-80 19 23 20 6-65 6'70 655 6'50 6'60 19 21 25 6-40 6-40 6-4O 6'40 6-40 19 27 30 6-05 6-10 6-10 6-15 6-10 19 24 35 5-80 5-80 5-80 5' SO 5'SO 19 30 40 5-50 5-40 5-40 5-50 5-45 19 11 45 5-00 5-00 500 5-00 5OO 19 28 5O 4-55 4-50 4-50 4-45 4'50 19 18 55 4-07 4-05 4-06 4-06 4-06 19 27 60 3-57 3-52 3-52 3-55 3-54 19 26 65 3-00 3-00 3-00 3-00 3'OO 19 35 70 2-35 2'37 2-37 2-35 2-36 19 01 75 1-85 1'80 1-85 1-82 1-83 20 26 80 1-25 1-25 1-22 1-20 123 19 30 85 Mea * Inclination, j 19 24 20. We have thus 19 24' for the inclination of PLANE OF NO ATTRACTION, &C. 21 the circle of no attraction, which approaches very nearly to the complement of the dip of the needle, as determined by Captains Kater and Sabine in the Regent's Park, who found it to be 70 34', April 13, 1818. Having, however, the opportunity of ascertaining the dip correctly for Woolwich, on the needle so obligingly entrusted to my care by Mr. Berge, I made the following experiments, with a view to this determination. f Mean time of per- 3 forming 100 vibra- Mean result of ten trials,) (tions.* face to the East.. ..F ' 35 '' 1 8 ' 25mi ' Mean result of ten trials,! . face to the West . . . . J Poles Inverted. Mean result of ten trials g . lg face to the East Mean result of ten trialO face to the West . . . . J Mean of the above results 70 30'"45 for the dip at Woolwich, July 13, 1819- The extremely near approximation of these several results towards the complement of the angle obtained for the inclination of the circle of no attraction, shows that an obvious relation subsists between the two angles, viz. that the -one is the complement of the other, and at the same time * First arc of vibration 70. LAW OF ATTRACTION renders it highly probable that this law obtains m every part of the globe.* SECTION IV. DETERMINATION OF THE LAW OF ATTRACTION IN REFERENCE TO THE LATITUDE. 21. HAVING thus determined, by a new series. of experiments, the position of the circle of no attraction, which I shall henceforward, as in the preceding series, call the magnetic equator ; my next object was to determine the law of attraction: ut of this circle, and first in the circle SEN, drawn perpendicular to the equator QQ', and passing through the east and west points of the horizontal circle H R. I have already explained * These results have been since verified by Mr. Christie, en the same apparatus which I employed. He proceeded as follows : Having assumed the inclination of the plane of no attraction to the horizon, at 19 SO 7 , he computed the heights at which the ball ought to be found, when the dis- turbing force on the needle should cease, and having then actually observed the same, he found the computed and the experimental situation to agree very nearly with each other j not differing more than T Vth of an inch for distance, which were not less than 14 inches. See Mr. Christie's Memoir on this subject, in Part I. of the Transactions of the Cambridge Philosophical Society. IN REFERENCE TO THE LATITUDE. 23 my motive for selecting this circle, the computa- tions I employed, and the method I pursued in order to cany the compass round the ball in it : but it may not be amiss to be a little more explicit, and to illustrate what I have before stated, by means of a diagram. 22. Let H Z R fig. 1 . represent a sphere concen- tric with the iron ball C ; N,S, the north and south poles, with reference to Q Q' the equator, or circle of no attraction ; Z the zenith of the sphere, H R a circle parallel to the horizon, and S E another circle passing through the magnetic east and west points of the horizon, where it also meets QQ': imagine also the quadrant Z L V to be drawn to any point V in the horizon, cutting S E in some point L ; from L let fall the perpendicular L M, which will meet the plane of H R in the line joining V with the centre C. Now, the arc E V being supposed given, we may readily compute the point L, where the arc S E is intersected by the quadrant Z V, and then the arc L E will be the latitude of that point, with reference to Q Q' as an equator ; and the line L M and C M, (the sine and cosine of the arc V L, to any assigned radius,) will show how much the compass ought to be elevated above the centre of the ball, and at what distance it ought to be placed from the centre of the table, to correspond with that point L. 24 LAW OF ATTRACTION The formulae for these computations are as follow ; viz. In the right angled spherical triangle V E L, we have given, the right angle at V, the angle LEV, and the arc E V ; to find the hy- pothenuse LE, or the latitude, and the side or perpendicular L V. For the former we have tan L E = tan VE see V E S * and for the latter tan V L = sin V E tan V E S from the sine and cosine of which latter arc, the values of L M and C M are readily determined for any proposed radius. We have there only to assume for VE, the several arcs or divisions of the table, viz. 2| , 5 , 7|, 10, &c. ; and for the angle VE S the dip of the needle (which for simplicity I have taken 70 30') and all the several particulars stated above are already found, as in the following table, except the numbers in the last column, which are deduced * Or which is the same, As radius Is to tangent of arc V E So is,, secant of angle V E S To the tangent of arc L E t and As radius Is to the sine of arc V E So. is tangent of V E S To tangent of arc V L. IN REFERENCE TO THE LATITUDE. 25 from the empyrical law, derived from the first series of experiments ; namely, that the tangent of the deviation of the needle is proportional to the sine of the double latitude ; or, which is the same, the sine of the double latitude divided by the tangent of deviation is a constant quantity, the longitude being zero. EXPERIMENTS. 23. In the Circle SE, of which the Longitude is QP. Ball 288/fo. RADIUS OF CIRCLE 12 INCHES. Position of Compass. Latitude. Longitude. Height centre. Distance from the centre of the table. Deviation of com- pass East. Deviation of com- passWest. Mean deviation. Ratio of sin. 2\* tun. A 2 30 7 ! E.orW.j 7" 27' 00' inches. 1-465 inches. 11-91 10 O 7 10 ] 5' 10 ?!' 1-439 5 14 41 ditto 2-87 11-65 19 3O 19 45 19 371 1-375 7 30 21 31 ditto 4-15 11-26 26 30 26 30 26 30 1-369 10 27 51 ditto 5-28 10-77 32 31 30 31 45 1-335 12 30 33 35 ditto 626 10-28 34 15 34 34 7 1-365 15 38 45 ditto 7-08 9-68 35 45 35 30 35 37| 1-363 17 30 43 22 ditto 7'76 9-15 36 15 36 15 36 15 1-362 2O 47 28 ditto 8'33 8-63 35 30 36 36 15 1-32S 25 O 54 24 ditto 9'20 7'76 34 35 34 30 1-378 30 O 59 58 ditto 979 6-93 32 15 32 30 32 221 1-367 35 64 3O ditto 10'21 6-30 30 29 45 29 52i 1-353- 40 O 68 18 ditto 10-51 5-79 26 45 26 45 26 45 1-363 50 74 21 ditto 10-88 5-03 21 21 O 21 1-354 60 O 79 6 ditto 11-10 4-54 15 15 15 15 15 15 1-362 70 S3 4 ditto 11-22 4-23 1O 1O 10 1-359 80 86 38 ditto 11-30 4O5 5 4 45 4 52| 1-375 Mean . , 1-365 X here denotes the latitude, and A the angle of deviation from the magnetic nortU. EXPERIMENTS. 24. In the Circle S E, of which the Longitude is 0. Ball 288//>.s\ RADIUS OF CIRCLE 15 INCHES. Position of Compass. Latitude. Longitude. Height of centre. Distance _ from the Deration centre of 38 45' oc/ inches. 12 35 18' 35 37' + 19 J 17- 43 22 ditto 12 35 54 36 15 + 21 } 20 47 28 ditto 12 35 50 35 5O (25 54 24 ditto 12 34 28 34 3O + 2 38 45 ditto 14 24 2 24 2 J !7| 43 22 ditto 14 24 31 24 30 1 ^20 47 28 ditto 14 24 28 24 30 + * Us 54 24 ditto 14 23 23 23 3O + 7 (15 38 45 ditto 16 16 37 16 30 7 17- 43 22 ditto 16 16 59 17 + 1 \2O 47 23 ditto 16 16 56 17 + 4 25 54 24 ditto 16 16 9 16 9 r 15 38 45 ditto 18 11 51 11 52 + 1 J !7* 43 22 ditto 13 12 7 12 15 + 8 S 20 47 28 ditto 18 12 5 12 r 5 Us 54 24 ditto 18 11 30 11 15 15 /IS 38 45 ditto 20 8 42 8 35 7 17- 43 22 ditto 20 8 53 8 52 1 ^| 20 2 47 28 ditto 20 8 52 8 42 1O Us 54 24 ditto 20 8 26 8 20 6 r 15 38 45 ditto 22 6 34 6 30 4 S 20* 43 22 47 28 ditto ditto 22 22 6 42 6 41 6 40 6 30 2 11 Us 54 24 ditto 22 6 22 6 25 + 3 {15 17* 20 25 38 4o 43 22 47 28 54 24 ditto ditto ditto ditto 24 24 24 24 5 4 5 11 5 10 4 55 5 5 15 5 10 5 A + 4 O + 5 * This number in the former edition was 'OOO798125, it has not been thought necessary to recompute this column of deviations ; the difference being necessarily very in- considerable. 46 LAW OF ATTRACTION 46. The remarkable coincidence, or at least the close approximation, between the observed and computed results in these experiments, can leave no doubt that the law of attraction as respects the distance is, that the tangents of the angles of deviation are reciprocally proportional to the cubes of the distances. Since the magnetic force varies inversely as the square of the distance, and the tangent of deviation inversely as the cube of the same ; it follows that the square of the tangent of deviation is directly as the cube of the force ; or that the tangent of deviation varies directly as the f power of the force. SECTION VII. DETERMINATION OF THE LAW OF ATTRACTION IN REFERENCE TO THE MASS, &C. 47. IT seemed highly probable that the effect, or power of attraction, would be found to follow the direct law of the mass ; but in order to proceed as I had hitherto done, rather on the ground of experiment than hypothesis, I procured a solid 10 inch ball, such as is employed in proving the 10 inch mortars, the weight being 1281bs. viz. just ths of the weight of the 13 inch ball ; and with this I repeated the series of experiments given at pages 23 and 24. The following are the results of these operations : IN REFERENCE TO THE MASS, &C. 4/ EXPERIMENTS. 48. In the Circle S E, with Balls of 2SSlbs. and 128/Zw. RADII 15 INCHES AND 12 INCHES. Position Distance 12 inches. Ratio of Distance 5 inches. Ratio of of Com- pass. Deviation Ball 288lbs. Deviation Ball l-28lbs. Tan- gents. Deviation Ball288lbs. Deviation Ball l-28ll)s. Tan- gents. 2 30' 5 10 7$' 19 37| 4 O / 8 30 2-552 2-385 5 IV 10 7* 2 15' 4 30 2-279 2-267 7 30 26 3O 11 45 2-397 14 7| 6 30 2-2O7 1O 31 45 15 15 2-269 16 521 7 45 2-227 12 30 34 7| 17 2-216 18 37i 8 30 2-254 15 35 3*2 17 3O 2-272 19 45 9 2-267 17 30 36 15 18 15 2-353 20 15 9 15 2-265 20 36 15 18 15 2-353 20 7i 9 15 225O 25 34 3O 17 2-248 19 15 8 45 2-269 30 32 22 15 45 2-246 17 375 8 2-259 35 29 52i 14 15 2-261 16 7 15 2-254 4O 26 45 12 2-386 14 5 6 15 2.319 50 21 9 45 2-238 10 45 4 45 2-285 60 15 15 7 2-222 7 30 3 20 2261 70 1O O 4 O 2-521 5 2 15 2-227 80 O 4 52 2 15 2-172 2 30 49. The mean of the first ratios is 2 -.31 8, and of the second ratios 2*259; and the mean of the two 2'288. Now the ratio of the masses, or of the cubes of the diameter, is 2 '25, whence then we may conclude that the tangents of the deviations are proportional to the cubes of the diameters* all other things being the same. 50. The cube of the diameters being proportional to the masses, the obvious conclusion seemed to be, that the tangents of the deviation were also pro- portional to the masses ; and such, in fact, was 48 LAW OF ATTRACTION the conclusion I had drawn, when I fortunately made trial of a 10 inch shell, whose weight was 961bs. or just |ths of that of the last solid ball of the same dimensions ; and I was not a little surprised to find, that I could observe no difference whatever between these results and the former. I then determined on a regular course of expe- riments with the shell, at the same distances, &c. as I had adopted with the ball ; and having com- pleted them, I found, on a comparison of the results that they tallied with each other throughout. In fact, it appeared that the power of attraction resided wholly on the surface, and was independent of the mass. 5 1 . Being, however, unwilling to leave any thing doubtful respecting a result which appeared so extremely novel and unexpected, I tried two other 10 inch shells, lest there should have been any thing peculiar in the one above referred to : I then employed other shells of different diameters and thicknesses, the whole of which still indicated the same law ;* viz. that, the tangents of the deviation are proportional to the cubes of the diameters, or to the f power of the surfaces, whatever may be the weight and thickness. Here * I shall not detain the reader by giving the detail of these experiments, as it would consist merely of a repetition of the same numbers as those stated in the preceding tables. IN* REFERENCE TO THE MASS, &C. 49 again, the magnetic force being as the surface, and the tangent of deviation as the I- power of the surface, it follows also, that the square of the tangent of deviation varies directly as the cube of the force, or the tangent of deviation directly as the * power of the force ; which is the same con- clusion that we have drawn from (art. 46). 52. This law, however, has its limits ; for having procured a 10 inch shell of tin, and another of iron, the weight of the former being 21bs. lloz., or 43oz. ; and of the latter, 21bs. 13oz., or45oz. ; I found the power not so great as in the solid ball of iron, although the approximation was very near, considering the great disparity in the weights ; the iron shell producing deviations, which were to those of the solid ball as 2 to 3, nearly. Now the thickness of the iron being here at a medium about TiVth of an inch, the conclusion which we may draw from this fact appears to be, that the magnetic fluid requires a certain thickness of metal, exceeding ^rVth of an inch, in order effectually to develope itself, and to act with its maximum of power. The tin shell produced a similar effect in some positions, and a greater in others, arising obviously from its having imbibed (probably in the operation of raising it, as is termed by workmen, to the globular form), a partial degree of magnetism, an effect from which the iron shell was not wholly E 50 LAW OF ATTRACTION free ; and to which we may probably, in part, attribute the discrepancy alluded to above. This is, indeed, rendered the more probable, from my having, . in the first instance, employed a tin vessel of a globular form, and of about the same dimen- sions as my 10 inch shell, but which had not been strained in the same degree by the workmanship, from which results were obtained fully equal to those of the solid ball. Upon the whole, therefore, I may venture to conclude, (although further experiments are neces- sary, fully to confirm the fact), that the magnetic power resides wholly on the surface of iron bodies, but that a certain thickness of metal is necessary for its complete developement ; a remarkable in- stance of the analogy which subsists between the magnetic and electric fluids.* 53. Since the publication of the first edition of this work, Captain Kater has made a short set of experiments, with a view of verifying the above deduction. For this purpose, he had three cylinders made of * The analogy between these two sciences, already known, had led Mr. Charles Bonnycastle to suggest to me, some time before, that it would be desirable to ascertain whether they resembled each other in this respect also ; but being myself decidedly of opinion that the power resided in the mass, I made no trial on the subject, till led to it acci- dentally, as above stated. IN REFERENCE TO THE MASS, &C. 51 soft iron, about 2 inches in diameter, and nearly the same in height. " One of the cylinders was of sheet iron, less than ^vth of an inch in thickness ; the second of that kind called chest plate, 0*185 inch thick ; and the third was of solid wrought iron. The first weighed 2760 grains, the second 9376, and the solid cylinder 22929 grains. Pre- vious to the experiments, they were all made red hot to destroy any accidental magnetism." The compass employed was of a very delicate construction, and the cylinder was so placed that its centre was in the direction of a tangent to the zero of the compass, and at the distance of 4 '85 inches from the southern extremity of the needle. The position of the cylinder was varied six times, and the following were the deviations of the needle : Sheet iron Cylinder. Chest plate Cylinder. Solid Cylinder. 2 1-5' 2 1-5 2 4-5 2 5 2 5 2 10 2 50' 3 4 3 20 3 45 3 10 3 30 2 55' 3 15 2 57 2 50 2 55 2 30 Mean.. 2 16 3 16 2 54 Suspecting an error in the experiment with the solid cylinder, from an accident which occurred, Captain Kater repeated the whole with the utmost 52 SUPPLEMENTARY EXPERIMENTS. attention. The position of each cylinder was now varied eight times, and the results were as follows i Sheet Iron Cylinder. Chest plate Cylinder. Solid Cylinder. 2 3' 2 55' 3 15' 2 22 2 50 3 12 2 32 3 20 3 15 2 20 3 40 3 O 1 50 3 40 3 15 2 45 3 28 2 50 2 45 3 10 ,2 45 1 55 3 5 2 58 Mean. . 2 19 3 16 3" 4 " The surfaces of the cylinders determined hy very careful measurement, were, the sheet iron 28*54 inches ; the chest plate 30'77 j and the solid cylinder 28 '94 inches." " Reducing the deviations to the same extent of surface ; viz. to that of the solid cylinder, they become respectively 141, 184 and 184 minutes.'* Philosophical Transactions for 1821. SECTION VIII. SUPPLEMENTARY EXPERIMENTS, RELATIVE TO THE QUANTITY OF ATTRACTION AS REGARDS THE THICKNESS OF METAL. 54. HAVING received permission, from my Lords Commissioners* of the Admiralty, to avail SUPPLEMENTARY EXPERIMENTS. 53 myself of any facilities which His Majesty's Dock Yard, at Woolwich, might afford in pursuing my inquiries, I ordered plates of iron, a foot square, to be formed of the various kinds that could be pro- cured from the stores ; and I thus obtained the specimens as stated in the following page, varying from 1 -50th of an inch to one fifth of an inch in thickness. These being prepared, I placed my compass so that it read very accurately zero at the north and south, and in a situation where I could set up in succession the several plates at ten inches distance from the pivot of the needle, and exactly parallel to its direction ; keeping the centre of the plate three inches above the point or pivot of suspension. Each plate was placed in four successive positions, viz. with each of its four sides downwards, the deviation taken in these respective positions, and then a mean of the four, as given in the table ; these precautions being rendered necessary in con- sequence of the partial magnetism which the plates all exhibited in a greater or less degree. The following are the results of these experiments : 55. Experiments on Plates of Iron, afoot square, of various Thicknesses. No. AVeight in ounces, voirdu poise Sickness in lecimals of an inch. Deviations. Mean deviations. DenoBMiiatiou of the iron in commerce. 1 14'5 0223 } 2 15' 2 30 2 1 30 V 2 4' Tin plate. 2 20-0 0308 < 2 3 2 45 2 V 2 26 Number 22 plate iron 3 20-5 0315 2 45 Number 20 ditto. 5 310 0477 < 4 30 5 4 30 4 > 4 30 Number 18 ditto. 6 42'0 0646 1 5 30 5 5 5 30 V 5 15 Number 16 ditto. 7 48-0 0738 J 4 O 4 4 4 3O }.. ;. Number 15 ditto. 8 48-0 0738 < 3 3O 4 15 4 30 4 }, * Ditto ditto. 9 900 1384 < 6 30 6 30 5 45 6 15 > 6 15 Chest iron. 10 122 1877 < 5 3O 5 45 5 5 > 5 18 Common plate. 11 122 1877 < 5 O 5 30 4 (5 4 O \4 37' ) Ditto. 12 130 2000 mounted on a platform which admitted of its being traversed through an entire circumference ; the trucks at the bottom running over a circle ten feet six inches in diameter. 69. After ascertaining the magnetic north point of this circle, I had it divided into 32 equal parts, corresponding to the points of the compass ; whereby I was enabled to carry the gun round, and set it in any required position. I then had a piece of wood formed to fit the bore of the gun inside, and pro- jecting beyond the muzzle above four feet. This projecting part was semi-cylindrical, the flat side exactly bisecting the bore horizontally ; and on this piece the compass was placed, at different distances, while the gun was traversed, point by point, from north to north again, as stated in the following tabulated results. 70. As my preceding experiments had shown that much depended upon the angle formed be- tween the compass and the plane of the circle of no attraction, and being unable, from the irregular nature of the mass, to compute the place of the centre of attraction, it was necessaiy to determine the situation of the above plane experimentally. In order to effect this, the compass was placed on the projecting piece above described, at 18 inches TWENTY -FOUR POUNDER. 63 distance from the muzzle, and the gun rendered, by means of the breech screw, truly horizontal ; being now pointed north and south, the needle also attained its true direction ; which was a proof that the compass was equally acted upon by the iron of the gun and carriage, to the right and left of the line to which it was adjusted. But on bringing the muzzle east or west, the needle was found to deviate about 15 from its true direction; the deviation being east with the muzzle at the west, and west with the muzzle at the east ; which indicated that the centre of attraction of the mass was below the horizontal plane passing through the pivot of the needle : the gun was therefore gradually depressed till the needle pointed due north and south. In performing this operation it was observed that every degree of depression caused a change of about 4 in the direction of the compass ; and having at length brought the needle due north and south, the angle of depression was found to be 3 58' : at greater distances this angle was a few minutes less, as ought obviously to be the case ; because, as the compass was carried farther from the muzzle, it descended below the plane of the above circle. This striking confirmation of the existence of the plane of no attraction in the most irregular masses of iron was highly gratifying to me, and equally so to those who witnessed the experiments. 71 . Having thus found the position of the gun 64 EXPERIMENTS ON A such, that the compass read correctly when the^ piece was placed at the four principal points, north, east, west, and south, I caused it to be traversed, as above stated, point by point, from north to north again ; and the following are the observed deviations. EXPERIMENTS 72. On an Iron Twenty-four Pounder Cannon. Length, 9 feet G inches ; the Distance of Trunnions from the Muzzle, 5 feet G inches ; Weight of the Mass, 58* cwt. Distance of Compass from the Muzzle, 2 feet 6 inches ; Depression, 3 45'. Position of the Trail of Deviation of the Position of the Deviation of the Position of the Deviation of the Position of the Deviation of the Mean Com- the Needle. Trail. Needle. Trail. Needle. Trail . Needle. puted Carriage. deviation East. 0' E. West. o 4 15 67! N. 4 30 67 S. 4 30 67 ! S. 4 30 4 37 78* N. 2 30 78* N. 2 30 78* S. 2 30 78* S. 2 30 2 30 North. O North. O South. t) OO South. OO OO * The weight of the gun itself, 51 cwt. 1 qr. 9lb. ; estimated weight of the wheels, trucks, and appendages, 6 cwt. 2 qrs. 19lb. ; making the entire mass 58 cwt. TWENTY-FOUR POUNDER. 65 73. The computed deviations in the last columns of the two preceding tables were obtained by first finding from the observed deviations the mean ratio , - . sin 2 X cos I , . or value ot A = ; . and then using: it as tan A a constant co-efficient, (A) in the expression sin2X cos Z m , . . ^ ... tan A = . The same might likewise be done, by saying, " As the rectangle of sin 2 \ cos / (correspond- ing to any position of the compass), To sin 2 X,' cos /' (answering to any other posi- tion), So is the tangent of the deviation in the first instance, To that in the second. 1 * For example ; the latitude and longitude cor- responding to 45orNE, is lat. 13 30'; long. 43 1 8'; and the same answering to one point from the east, is lat. 3 44', and long. 10 48': there- fore, As sin 27. cos 43 18': sin 7 28'. cos 10 48': tan 6 30' : tan 2 30', which latter is exactly the deviation found by observations in Table II. The former of the above methods, however, is to be preferred, because it is made to depend upon a mean result instead of adopting any one in parti- cular, as must be the case in the latter. As the reader may not find so close an agreement between the computed and observed results in the F 66 EXPERIMENTS ON A preceding table as he would probably have an- ticipated, it may be proper to observe, that some allowance must be made in this respect, on account of the nature of the division of the lower circle, by which the direction of the trail was ascertained : but, on the other hand, as the diameter of that circle was considerable, viz. 10 feet 6 inches, (Art. 69,) a trifling discrepancy in the length of the divisions is the less perceptible, although it is impossible to say that an angular error of a few minutes may not exist. 74. In all ships the compass is placed con- siderably above the common centre of attraction of the guns, and in most, perhaps, so much above it, that the line joining that centre and compass never intersects the plane of no attraction, in this or any higher latitude, although that intersection must necessarily take place in approaching towards the equator. In order to make some observations of this kind, I caused the gun to be brought truly horizontal, thereby raising the compass above the common centre of attraction ; then, placing the former at 30 inches distance from the muzzle, I caused it to be traversed round in the manner above described, and the following are the results of these experiments : TWENTY-FOUR POUNDER. 67 Trail of the Gun. Deviation. Trail of the Gun Deviation. S E / West. sow tf East, S 111 E 2 45 Do. S 111 W 2 45 Do. S 221 E 50 Do. S 221 W 4 30 Do. S 33| E 6 15 Do. S 33| W 6 15 Do. S 45 E 6 45 Do. S 45 W 6 30 Do. S 56 E 6 15 Do. S 56 W 6 Do. S 67| E 30 Do. S 671 W 2 45 Do. S 76 E 00 Do. S 78$ W 30 West. East. 4 30 East. West. 5 Do. E Hi N 7 45 Do. W llj N 8 Do. E 221 N 10 30 Do. W 221 N 11 Do. E 33| N 11 45 Do. W 33| N 12 Do. E 45 N 11 30 Do. W 45 N 11 45 Do. E 561 N 9 30 Do. W 56 N 10 15 Do. E 67! N 7O Do. W 67! N 7 15 Do. E 7Sf; N 3 45 Do. W 78| N 3 45 Do. North. North. 75. The gun being now elevated 7 45', the following observations were made w hile the trail was traversed through one half circle only, viz. from North to South : Trail. Deviation. Trail. Deviation. S E / E N 12 30' East. S ll E 1 45 West. E 11 N 15 45 Do. S 221 E i 30 DO. E 221 N 16 30 Do. S 33| E 2 15 Do. E 33| N 16 15 Do. S 45 E 10 Do. E 45 N 14 30 Do. S 56 E 1 45 East. E 56 N 11 45 Do. S 67| E 50 Do. E 67| N 8 30 Do. S 78f- E 8 15 Do. E 78$ N 5 15 Do. East. 12 30 Do. North. ' 68 EXPERIMENTS ON A 76. As in my former experiments the gun was depressed 3 45', in order to bring the pivot of the compass into the same horizontal plane with the centre of attraction, we may consider, that when the gun was laid horizontally, the compass was elevated about the same quantity above the centre of attraction ; and if we compute at what distance from the east or west points, a small circle parallel to the horizon would intersect a great circle inclining at an angle of 19 30', we shall find that distance to be very nearly 1U on the horizontal circle ; and exactly at this point, we find by the first of the preceding tables the deviation became zero ; it being 4 east at the east point, and 3 0' wesf, at ESE, and zero at E by S. 77. In the same manner, the gun being elevated 7 45' in the last experiments, and depressed 3 45' in the first, we may consider the compass as being elevated about 1 1| above the centre of attraction ; and therefore the deviation ought to become zero at that point, where a small circle parallel to the horizon, and distance from it 11, intersects the oblique circle of no attraction. Without entering into any computation on this head, it is obvious, by referring to our table of experiments page 37, that the latitude correspond- ing to 35 from the east, is 11 2', and to 40, from the same 12 33'; the point therefore at TWENTY-FOUR POUNDER. 69 which the deviation ought to vanish, must lie between the S E and S E by E ; which is pre- cisely what is shown by the last table of the foregoing observations : the deviation being 1 west at the former point, and 1 45' east at the latter. 78. These experiments will be, I trust, quite sufficient to satisfy every one, that the same laws which I first obtained from observation on regular masses of iron, are equally applicable to irregular masses, and that they furnish us with the means of computing the local attraction of a ship's guns upon her compass, under all circumstances, and in all parts of the world; at least if (as there is the strongest reason to believe) the plane of no attraction varies its position in different lati- tudes, so as to be every where inclined to the horizon, at an angle equal to the complement of the dip. 79. When the above article was written, the conjecture here advanced was attended with the highest degree of probability ; but it has been most satisfactorily confirmed, since the first edition of this work was published, by Mr. Lecount, of H. M. S. Conqueror, by a series of observations made in a voyage from the Cape of Good Hope to England. The experiments were made on bars, handspikes, mast-rings, and various other iron bodies ; from the whole of which the author con- cludes that "A plane or circle held east and west 70 EXPERIMENTS, &C. (magnetic) and at right angles to the direction of the dipping needle, divides the north from the south magnetic effluvia, each lying on that side to which the dipping needle points ; and by referring the position of all iron bodies to this plane, the plane of section shall divide the iron into north and south polarity, provided it be of uniform thick- ness. " If it be not of uniform thickness, the section must be drawn not through the centre of its length, but through its centre of (gravity) attraction. This plane will, therefore, be vertical at the magnetic equator, and horizontal when the dip is either 90 N or 90 S, and will be inclined proportionally to the dip between these situations." Lecount, on the Magnetic properties of Iron Bodies. Without examining here the particular illustrations and ideas of the author, the fact of the change above sug- gested, actually taking place in different latitudes is, I conceive, fully verified. It may be proper also to add, that these experi- ments were made without any knowledge of what had been published in the first edition of this work. ON THE LOCAL ATTRACTION, &C. 71 SECTION XI. ON THE LOCAL ATTRACTION OF VESSELS. 80. BEFORE I enter upon the laws of action in this case, it will be proper to offer a few remarks, and make some references to such works as have treated on the subject of local attraction. The first notice of such an effect, that I am aware of, occurs in the voyages of Captain Cook, it having been first observed by Mr. Wales, his astronomer ; the cause of the deviation of the needle, however, seems not to have been suspected, and the subject at that time attracted little attention. The next reference to the local attraction of vessels, and in which the cause is clearly pointed out, is found in Walker's Treatise on Magnetism, published in 1794 : it is contained in a report from Mr. Downie, master of H. M. S. Glory, where he says, " I am convinced that the quantity and vicinity of iron in most ships, has an effect in attracting the needle ; for it is found by experience that the needle will not always point in the same direction, when placed in different parts of the ship, also it is rarely found that two ships steering the same course, by their respective compasses, will go exactly parallel to each other, yet these compasses, when compared on board the same ship, will agree exactly." 72 ON THE LOCAL ATTRACTION A few years after this, the action of the iron of the vessel was more minutely noticed by Captain Flinders, who was the first to trace its connection with the dip of the needle, and through whose perseverance some attention was paid by Govern- ment to the subject, and several experiments were made, by order of the Admiralty, on various ships at the Nore, by which the general fact was esta- blished. The subject, however, seems to have been again lost sight of, till Mr. Bain published his valuable little Treatise on the Variation of the Compass ; in which the fatal consequences attend- ing this source of error are put in so clear a point of view, as to strike the most indifferent reader. And as at this time our Arctic Expeditions were in contemplation, the local attraction of the vessels was one of the objects to which the attention of the officers was particularly directed. The results of the experiments made in these instances are given by Captains Ross and Parry, in the accounts of their respective voyages, as also by Captain Sabine, in the Philosophical Transactions, Part I. 1819; another memoir on this subject is also published in the same volume, by Captain Scores - by. These statements all agree in establishing the existence of this source of error, and in showing the necessity of some method of correcting it par- ticularly in high latitudes. Let us then examine how far the principles established in the foregoing OF VESSELS. 73 sections are applicable to this case. Or how nearly the deviations observed on shipboard agree with our formula sin 2 X cos I tan A = . A I shall select, for making this comparison, the deviations observed by Captains Ross and Sabine, on board the Isabella, in Brassa Sound, Shetland, being those perhaps in which the greatest reliance can be placed, while, at the same time, they em- brace the entire circumference, whereby we are enabled to take a mean between every two corres- ponding deviations, viz. between every two points equally distant from the line of no attraction.* 81. As the above formula has reference to two circles, the one inclining to the horizon at an angle of 15 38i' (the dip being 74 211') and its vertical, as also to the position of the common centre of attraction of the vessel ; it is obvious that we must proceed by a method of approximation to deter- mine those values of x and /, and the constant co- efficient A, which best agree with the given devia- tions. In order to this, I begun by assuming different values for the inclination of that line which may be supposed to join the pivot of the needle with the common centre of attraction of all the ship's * I have, since the above was written, made several ex- periments of the kind, but I retain the above comparison, as it stood in the first edition of this work. 74 ON THE DEVIATIONS iron ; and after a few trials, I found its inclination to be about 65 with the horizon, or 25 with the vertical, and that the value of the constant co-efficient was A = 7.934 nearly * These being determined, the other part of the operation is precisely equivalent to the reduction of right ascension and declination to longitude and latitude. The constant declination being 65, the obliquity 15 38!', and the right ascension, the angles given by the direction of the line of no attraction in the vessel, with the magnetic east or west points of the horizon. 82. The following table exhibits the results of these operations, with the computed and mean observed deviations. * I do not profess to have found either the one or the other of these quantities to the greatest degree of accuracy; for my object being merely to show that the laws in question are applicable to the determination of the deviation on shipboard, I was satisfied with my approximation, when I had brought the errors between the observed and computed results within reasonable limits. OBSERVED ON BOARD THE ISABELLA, Comparison of the computed, with the observed Deviations, on board the Isabella, off Shetland. Dip, 74 2l'. m E g I t> Deviations ob- ! SHf? -1 1? II II g.1 served by Captain Sabine. r! 1 ill 15 g 8, a.i I'ff H o 2 O r* |" vj WpTn' ". ft | III M i ^~ I Eas . West. ? 5f P 0) o. " jfl' 1 ! 2 5' - P 1 89 41' 80 40 / 89 11' 2' 19' 19' 19 X o 1?' 77 53 79 47 59 54 1 16 1 19 26 52 24 65 43 78 13 35 59 2 5 2 9 1 26 1 47 18 53 30 74 40 18 9 3 29 3 4 2 26 2 45 43 41 30 71 29 4 29 4 19 3 34 3 26 3 30 49 29 30 68 15 6 52 5 4 4 4 26 4 15 45 17 38 65 8 16 44 5 15 4 34 5 11 4 52 23 5 35 62 30 24 35 5 22 5 34 5 46 5 40 18 5 40 59 28 33 58 5 14 5 34 5 46 5 40 26 16 52 57 5 41 51 4 54 5 34 5 41 5 37 43 27 35 55 3 49 9 4 26 4 59 5 11 5 5 41 38 2 53 20 56 6 3 51 4 24 4 11 4 17 26 48 45 51 53 63 10 3 10 3 34 3 56 3 45 35 59 15 50 46 70 2 2 25 3 4 2 56 3 35 69 7 49 50 76 29 1 40 2 4 1 11 1 37 3 79 45 49 29 83 21 50 1 34 26 1 10 83. The numbers in the first column of the preceding table are corrected for the mean observed deviation, so as to exhibit the true magnetic bearing of the line of no attraction, assuming (what Captain Sabine has not stated,) that the deviation was eastward while the ship's head was between the east and north, and the east and south, and western in the other semi-circle. The indication of plus and minus is not sufficient to determine this, as 6 ON THE DEVIATIONS these signs will change accordingly as the bearing of the object is to the west or east of the north ; and the name of the variation will also change, according as the principal centre of attraction is fore or aft of the compass. In most cases that centre is doubtless forward ; but in the Isabella, the compass being placed between the main and mizen mast, it is somewhat doubtful on which side that centre might fall : the circumstance also or its being elevated so much above the deck, and its peculiar situation in the vessel, will account for the great inclination that I have found, (65) for the line joining that centre with the pivot of the needle. The corrections I have made are on a supposition that the principal focus of attraction was forward : in the other case a different correction will be re- quired ; but the results will not be much affected, on account of the deviations being so very nearly equal at equal angular distances from the two extremities of the line of no attraction. 84. I have already observed in the preceding page, that the utmost accuracy has not been aimed at in the above approximations ; nor could it pro- bably have been attained, had such been my in- tention : it is indeed obvious, that as the corres- ponding observed deviations do not always agree with each other, it is in vain to expect to reconcile them completely with any law that gives the same OBSERVED ON BOARD THE ISABELLA. 77 deviation to each two positions, equally distant from the same extremity of the line of no attraction. What may be the cause of the discordance in the equi-distant observed deviations, it is difficult to say ; but that, in general, there is a tendency to equality, is obvious from the observations of Cap- tain Flinders, Mr. Bain, and those above reported : the aberrations, therefore, where they occur, must be considered as accidental, and due to some cause independent of the general law of the dis- turbing force. One cause may be the unavoidable inclination of the vessel during the observations, produced by the wind and tide in opposition to the cable and warp, which necessarily changes in a slight degree the latitude and longitude of the centre of attraction, as referred to the ideal sphere circumscribing the compass, and which will, according to the pre- ceding laws, make a corresponding change in the deviation. A second source of error will arise in the parallax caused by warping the vessel round ; which, however, is not likely to be very great. But, on the other hand, it is to be remarked, that the errors which embarrass the results are also, as to their actual magnitude, very inconsiderable ; and it is not improbable that the two causes alluded to above may be amply sufficient to account for all the observed irregularities. A third, however, may have some influence, viz. the difficulty of bringing 78 ON THE DEVIATIONS, &C. the ship's head exactly upon the point of the com- pass at which the observation is intended to be made.* It appears from what has now been stated, that whether we employ regular iron balls or shells, or an irregular formed body, as a gun with its car- riage, &c. or a ship in which the iron is distri- buted in almost every direction, yet the same laws of action are found to obtain ; provided, in the two latter cases, the mass and compass revolve together, so as to preserve the relative position of the latter, and the disturbing body constantly the same. * Since the above was written, viz. since the publication of the first edition, I have had myself considerable practice in experiments of this kind : first, on board H. M. S. Leven f prior to her former voyage ; and again very lately. I have likewise performed the same experiments on board H. M. S. Conway, in Portsmouth Harbour, and on board IT. M. S. Brig, Barracouta, which accompanies the Leven on her present voyage for surveying the Eastern coast of Africa 5 and although every possible precaution was taken, (which will be explained in a subsequent section) yet we never could produce a complete coincidence in the corresponding obser- vations : but as circumstances were more favourable, so our corresponding results approximated more nearly to equality. METHOD OF DETERMINING, &C. 79 SECTION XII. METHOD OF DETERMINING THE LOCAL ATTRAC- TION OF A VESSEL BY EXPERIMENT. 85 ALTHOUGH the rules given above cannot be considered as involving any great intricacy of calculation, yet they stand in need of one important datum, not easily obtained, viz. the dip of the needle, which renders them, generally speaking, of but little use to practical navigators ; I propose therefore to explain, in the present section, a method of reducing the above determination to a mere matter of observation. My first idea relative to this subject was, that since the guns of a vessel will produce exactly the same deviation of the needle as a smaller mass of iron placed in a similar situation, but so much nearer in proportion as its mass is smaller, that it would be possible to place such a body of iron aft of the compass, as should exactly balance the action of the guns forward, and thereby leave the needle to act in the same manner as if no iron were in its vicinity : but this, unfortunately, I found to be im- practicable, without shifting the position of the ball for every different position of the gun or vessel, which would of course render it nugatory. I there- fore abandoned this idea for the following, which is simple, and may be easily practised. 80 METHOD OF DETERMINING THE 86. Since, as I have observed above, the action of the guns is precisely the same as that of a ball of iron of given dimensions, placed in a correspond- ing situation with respect to latitude and longitude, as referred to the ideal sphere surrounding the compass, it is obvious, by placing such a ball in such a situation, the deviation, instead of being destroyed, will be doubled, and that this will con- tinue to be the case under all circumstances, and in every part of the world, while the ball remains in its place, and the centre of attraction of the guns continue to maintain the same relative position with respect to the compass. Instead, therefore, of fixing the ball, let only its proper place be assigned, and the ball itself laid aside : then, at any time when it is desirable to ascertain the effect of the guns on the needle, apply it in its assigned situation, and observe how many degrees, &c. it attracts the needle out of its prior direction ; and just so much will the guns have drawn the same from its true magnetic bearing before the experi- ment. This being ascertained, and the course of the vessel corrected accordingly, the ball is to be removed and laid aside, till some new circumstance renders its application again necessary. 87. It is to be observed that, strictly, it is not the angle of deviation which is doubled by this experiment, but the tangent of the angle ; but, as in small angles the tangents have nearly the same LOCAL ATTRACTION BY EXPERIMENT. 81 ratios as their arcs, it will be sufficiently correct to consider it as above stated. If greater accuracy should be thought desirable, let x be the angle of deviation produced by the guns, and a, the angle produced beyond the former by the ball ; then we shall have , x tan x + tan a . (tan t r + a) = = 2 tan x. 1 tan x tan a Mr, 1 + A/ (1 8tan 2 a). Whence tan x ~ 4 tan a This formula may, however, as I have before observed, in most cases be dispensed with. 88. In order to leave nothing doubtful in a case of so much practical importance, and as I had Sir William Congreve's authority to have such apparatus constructed as I should conceive requisite, I ordered a frame work to be affixed to the gun, which should project beyond the compass, whereby I could suspend a ten inch shell in any required po- sition with respect to the centre of the needle. This being prepared, and the ball fixed in the required situation, I repeated my first course of experiments with the ball attached, by traversing the piece through the entire circle. The following table shows the results ; in which I have distinguished the angles due to the gun and shell, in order that the reader may see how nearly they approach to equality. METHOD OF DETERMINING THE EXPERIMENTS 89. On an Iron Twenty- Four Pounder, with an attached shell 96lbs. Position of trail. Devia- ion due to the gun. Devia- iou pro- luced bv he shell. Whole deviation Position of trail. Devia- tion due to the gun. Devia- ion pro- duced by the shell. Whole deviation East. 0' & 0' West. 0' (X 0' E. by N. 4 15 3 45 S W. by S. 4 4 8 E. N. E. 7 30 7 14 30 W. S. W. 7 30 7 15 14 45 N.E.byE. 9 8 30 17 30 S.W. byW. 9 8 45 17 45 N.E. 9 45 9 18 45 S. W. 9 30 9 18 30 N. E. by N 8 45 8 15 17 S. W. by S. 8 15 8 16 15 N. N. E. 7 o 6 45 13 45 S. S. W. 6 5 45 11 45 N. byE. 4 15 4 8 15 S.byW. 3 45 3 45 7 30 North. O South. N. by W. 4 15 4 8 15 S. by E. 3 45 3 45 7 30 N. N. W. 7 6 30 13 30 S. S. E. 6 30 G 30 13 N.W.byN 9 8 45 17 45 S.E. byS. 8 15 8 15 16 30 N.W. 9 45 9 15 19 S. E. 9 30 9 18 30 N.W.byW 9 15 9 18 15 S. E.by E. 9 15 9 18 15 W. N. W. 7 30 7 14 30 E. S.E. 6 30 6 30 13 W. by N. 4 15 3 45 S E. by S. 3 45 3 45 7 30 These results, although they exhibit some small aberrations, are sufficient to show that the princi- ple itself is correct ; and that with greater preci- sion, and a more accurate method of suspending the shell, greater accuracy might have been at- tained. 90. The above experiments had been performed, and the preceding paragraphs written, before I had discovered that the power of an attracting body of iron resided in its surface ; and I therefore at that time foresaw an impediment to the practice of this LOCAL ATTRACTION BY EXPERIMENT. 83 method on shipboard, in consequence of the mass of iron which I thought would be necessary to produce the desired effect : but having since found, that surface is the principal thing to be attended to, this difficulty is avoided, as a mere globular iron shell, or a simple circular plate of the same metal, is amply sufficient for the purpose. I therefore ordered a double circular plate of iron to be made, 15 inches in diameter, which was found to weigh only 41b. 13oz., and with this I repeated the pre- ceding series of experiments, and made several others, the whole of which gave the most satisfac- tory results ; and by afterwards attaching the same plate to a ship's binnacle, obtained from his Majesty's dock-yard for the purpose^ I found that its power was far greater than would be requisite for doubling the effect of the guns of any vessel in the navy, although applied exterior of the binnacle, and nearly 15 inches distant from the' pivot of the needle.* 91. My project being thus far advanced, I presented a memorial to the Lords Commissioners of the Admiralty, soliciting permission to make a trial of my method on board any of his Majesty's ships ; to which solicitation I received a reply from the first Secretary, stating, that their lordships, * In the experiments I have since made on board the several ships mentioned in a preceding note, I have only used plates of one foot diameter. 84 METHOD OF DETERMINING THE having had my memorial under consideration, and and having also received a report upon it from the Secretary of the Board of Longitude, they were pleased to grant the permission I requested ; and it is in consequence of that permission, I have been enabled to make the experiments detailed in the following chapter. 92. After the communication above referred to had been made to me on the part of the Admiralty, Sir William Congreve very obligingly introduced me to Sir George Cockburn, J. W. Croker, Esq. and some other gentlemen connected with that board, who did me the honour of attending a re- petition of a few of my experiments on the twenty- four pounder above-mentioned ; and I take this opportunity of returning my best thanks to Sir George Cockburn for the attention he paid to the subject, and particularly for the assurance he made me, that every possible facility would at all times be afforded me by the Admiralty, and that whatever ship might be appointed for the trial, the officers should be instructed to give every possible attention to the subject, and to lose no opportunity of proving its accuracy, and reporting the results, which should be duly communicated to me. Mr. Croker also was certainly much interested in the experiments ; and, if I had no reason to flatter myself that he entered the Repository highly pre- possessed in their favour, I had the pleasure of LOCAL ATTRACTION BY EXPERIMENT. 85 receiving from him, before he left it, his unequi- vocal opinion, that they were justly entitled to a fair trial in other latitudes, and an acknowledgment of their importance, provided they should be found to succeed. I am also much indebted to him for the order which he afterwards forwarded to Wool- wich, permitting me to avail myself of any facili- ties His Majesty's Dock-yard might afford, in the further pursuit of my inquiries. Description of a model infended to illustrate the preceding method of correction. 93. Some readers will perhaps form a better idea of the method proposed in the preceding part of this section, by the representation and descrip- tion of a model I had the honour of presenting to the "Society of Arts,* &c." of which figures (4), (5), are an elevation and plan. T T is a board or table, in which is fixed an up- right spindle S s, which passes through the vessel, and about which it may be turned in any direction at pleasure. D is a brass plate fixed on the deck of the vessel, and divided according to the points * For this communication the Society in the most unani- mous and handsome manner, elected me a perpetual mem- ber, and presented me with their gold medal, and a com- plete set of their Transactions, in 38 volumes. 86 DESCRIPTION OF A MODEL, &C. of the compass, the north and south points being fore and aft. H is a hand, or index, movable on the spindle ; C is the compass, P the correcting plate, and B the rod by which it is attached to the pedestal of the compass. The dotted line passing obliquely downwards from C, is that in which the centre of attraction of all the guns, and of the other articles of iron contained in the model falls, and in this line the centre of attraction of the plate P is also situated, and at such a distance from C, that its power on the needle is equal to that of all other iron at a greater distance. Now, to illustrate the nature of the correction by the model, turn it about on its pivot, till the compass shows north, that is, till the lubber line in the brass compass box, and the north of the card coincide ; the vessel is then in the meridian, and the movable index on deck must be set also to the north point. Turn now the vessel on its spindle, till the hand is directed to any other point (as for example East) : then if there were no attraction from the iron on board, the compass would read East also ; but it will be found to point about E i N, which shows the attraction at that point to be about 5F ; and in the same way the attraction at any point may be observed, the plate during such time being re- moved ; and if at uny of those points the plate be DESCRIPTION OF A MODEL, &C, 87 applied, it will be found to double the quantity of the error. To illustrate its application in real practice; turn the vessel about (having first adjusted it), till the apparent course by compass, is East, or any other proposed point ; and now, to find the true course, apply the plate, and observe how many degrees, &c. it attracts the needle ; which, in the model, at East, will be found about half a point, so that the apparent course, by compass, will be now E 5 N ; the attraction of the plate having drawn the north end forward about 51 or half a point : the iron of the vessel had therefore done the same before the plate was applied ; consequently, the true course was E 5 S, and by looking to the index on deck, it will be found that this is actually the course shown. The same will be the case at any other point, except that the quantity of attraction will be different, being most towards the east and west, and less as we approach the meridian. In other parts of the world, however, the east and west will be the points of least attraction, and the greatest will be at the north-east, north-west, south-east and south-west ; but still the plate will always continue to give the same attraction as the vessel, and will, therefore, in all places furnish a ready method of correction. The accurate action of a model is seldom to be expected, and less perhaps in magnetical experi- 88 DESCRIPTION OF A MODEL, &C. ments than in any other. I was therefore very agreeably surprised to find how very correctly this model answered all the conditions which I had found to obtain in the largest vessel. According to the laws deduced in the preceding sections, it appears that the tangents of deviation are directly proportional to the cube of the linear dimensions of similar iron bodies, and that those tangents are also inversely proportional to the cubes of the distance, all other things being the same : consequently if (as in the model) the tanks, guns, Sec. are made proportional to the dimen- sions of the vessel represented, the linear mea- sures of these will be proportional to the distance of the compass ; and therefore the deviations ought to be the same in quantity, as in the vessel at large ; and certainly the agreement in this re- spect is much more perfect than could possibly have been anticipated. This model is deposited in the Society's rooms, and may be examined by any person introduced by a member. I have also since constructed a model of a 74 gun ship, which likewise exhibit the experiments in the most satisfactoiy manner. ON LOCAL ATTRACTION. 89 SECTION XIII. ON THE METHOD OF ASCERTAINING THE LOCAL ATTRACTION OF VESSELS. An Account of some Experiments made on board His Majesty's Ships Leven, Conway, and Barracouta. 94. THE first opportunity which presented itself of putting the orders of the Lords Commissioners of the Admiralty into effect, was on board the LEVEN, which was fitting at Woolwich, for a survey of some part of the western coast of Africa. The first object, in course, in all cases is to de- termine the quantity of the local attraction of the vessel ; and the method we adopted for this deter- mination in the present instance, will be easily un- derstood by the following extract from my report to the Admiralty : ' The Leven having dropped down to Northfleet on the loth of April, 1820, I went down on the 17th, for the purpose of making a series of experi- ments before the guns should be brought on board, these observations were conducted as below. First, * Finding that there would be great diffi- culty in warping the vessel round in the tide way of this place, I proposed, and it was agreed to pro- ceed in the following manner : 90 ON THE METHOD OF ASCERTAINING ' I took on shore an excellent azimuth compass, by Messrs. W. and T. Gilbert, which I had pro- cured for the purpose, as also a theodolite, by Schmalcalder. With the azimuth, the bearing of a distant object was taken, and found to be N. 35 50' E., and the theodolite was then adjusted to the same reading, viz. 35 50' from zero ; by means of which the zero of the theodolite was brought to the true magnetic north, and conse- quently the bearing of an object might now be de- termined without any further reference to the needle. It will of course be understood, that the theodolite was fixed immediately over the spot where the azimuth compass was first erected. The latter instrument was now taken on board, for the purpose of the experiments, while Lieutenant Mudge remained on shore to take the bearings of the pedestal,* or pillar, on board with the theo- dolite. ' The ship now beginning to swing to the tide, the w r ord was given "look out," at which signal Lieutenant Vidal, at the azimuth compass on board, kept Lieutenant Mudge on shore, in the line of the sights, while the latter gentleman kept in the same way, Lieutenant Vidal in the field of the telescope. Being thus prepared, the word * Captain Bartholomew had ordered a pedestal to be erected just before the mizen mast, as a fixed situation for taking his azimuths during the voyage. THE LOCAL ATTRACTION. 91 " stop', 5 was given, at which each registered the bearing of the other at the same instant. These bearings, independent of the local attraction of the vessel, ought to have been diametrically opposite, and consequently the difference between the two readings, was the error due to the attraction of the iron on board. * The first observation being registered, the word " look out," was again given, and then the word " stop," and the same was repeated as often as possible while the vessel was swinging; Lieutenant Baldey taking every time the bearing of the ship's head, by the ship's azimuth compass at the capstan. * The advantages of this method are, that both bearings, viz., on board and on shore, are made to depend on the same compass, and thus the errors arising from the use of different needles are avoided, as are also those arising from the parallax of a dis- tant object while the vessel is swinging ; a source of error which must have attended all former ob- servations of this kind. * * The only thing actually necessary in this case, is a fine free azimuth compass, those commonly served out to the navy are so sluggish, that it is impossible (while there is no motion in the vessel), * A reference to fig. 6 may render this description a little more intelligible, by supposing V the vessel in the river RR, and T the station of the theodolite on shore. 92 ON THE METHOD OF ASCERTAINING to depend upon their settling within 2 or 3 of the true magnetic north.* ' The experiments above referred to, were made before the guns were got on board, but the same were again repeated on the 1 9th of April, after they had been all shipped. The following are the re- sults of both series of observations : EXPERIMENTS 95. On board H. M. S. Lecen, at North-fleet, April 17 and 19, 1820. By Mr. BARLOW and the Officers of the above vessel. Dip, 70 30'. Guns not on board* Guns on board. INo. of Expe- rilnents. Bearing of Ship's Head. Difference in bearing or local at- traction. No. of Experi- ments. Bearing of Ship's Head. Difference of bearing or local at- Local attrac- tion shown by the plate. 1 N. 77 0' W + 2 22' 1 N. 71 W + 251 / 2 N. 68 30 W- + 2 25 2 N. 64 () W + 2 07 2 20 3 N. 57 W. + 1 37 3 N. 57 W + 1 39 4 N. 47 o W. + 1 54 4 N. 47 W + 1 45 5 N. 32 W. + 1 12 5 N. 31 W. + 1 39 1 30 6 N. 20 W. + 1 20 6 N. 24 W. + 1 10 1 7 N. 14 30 W. + 12 7 N. 15 W. + 1 19 8 North. 15 8 N. 6 O W. + 17 40 9 N. 5 E. 54 9 N. 4 W. 8 10 N. 16 E. 1 32 10 North. 24 11 N. 32 E. 1 43 11 N. 5 E. 11 12 N. 45 E. 225 12 N. 13 E. 29 40 13 N. 52 E. 226 13 N. 23 E. 46 1 14 N. 67 E. 3 15 14 N. 57 E. 1 27 1 30 15 N. 74 O E. 36 15 N. 59 E. 2 32 16 N. 83 E. 2 13 16 N. 72 E. 2 23 2 10 17 East. 17 N. 80 E. 2 51 18 S. 81 15 E. 234 IS S. 86 E. 2 11 2 30 19 S. 74 30 E. 230 19 S. 85 E. 2 34 2 30 THE LOCAL ATTRACTION. 93 Note 1. The rapidity and force of the tide at Xorthfleet, at the time of making the experiments on theLeven, would not admit of warping the vessel about point by point, which is doubtless the best way. This, however, is easily done in Portsmouth Harbour, and was the method adopted by Cap- tain Hall, in our experiments on the Conway : reported in the next page. All the numbers in the following Table marked thus * are those in which two or more observations were made at the same point, and the mean of the two taken. In the others we had not an opportunity of making more than one obser- vation. Where the apparent, or observed westerly bearing exceeds the true westerly bearing, the error or local attraction is marked -f (plus) ; and where the former is less than the latter, the error is marked (minus) . With the ship's head at west, the object on shore could not be seen. * Since this sheet has been set up, I am happy to find that the Navy Board has determined upon an improvement in the compasses for His Majesty's ships. I have received instructions for examining all those in store, and am required to make a report of such that are found defective. It is to be hoped therefore that these instruments will soon be placed upon a footing with the other excellent appointments of the British Navy. 94 ON THE METHOD OF ASCERTAINING bserved bear- g of the sta- n on shore CaptainHall. CK W H W 03 rfJ | .fl W W H ^ - ' t .0 a? o5 co cc K H W W * * C~HC* CO SC CO ii ring of com- on board, Mr. Foster shore. == fill =1 s* K 10 O 'X co m s^ M c o o< I-HWOW co c* *n =o i i co x C000,r-l x o >n M * oo ooxcocogocx) THE LOCAL ATTRACTION. 95 Experiments on board His Majesty a Ship Le- ven, (Captain OWEN), and on her consort, His Majesty s Brig Barracouta, (Captain CUT- FIELD), previous to the departure of these vessels for the Eastern Coast of Africa. 97. The Leven on her return from the western coast of Africa, having been ordered to survey the eastern coast of that continent, and the command of her given to Captain Owen, who deservedly en- joys the reputation of one of the most able scien- tific officers in the navy; I was very happy in having this new opportunity of submitting my method to the test of experiment, particularly, as the vessel was proceeding to a part of the globe, where the dip of the needle is south ; and where consequently the trial will be the most conclusive. Captain Owen had done me the honour of at- tending a few of my experiments, some time before his appointment, and had taken much interest in their success, he was now therefore anxious to have them made on board his vessel, under his own per- sonal inspection. I accordingly went down to Northfleet, on the 13th January of the present year (1822), for the purpose of superintending the ob- servations, which were made at the same time on board the Leven, and on her consort theBarracouta. We proceeded nearly as in the cases above, 96 ON THE METHOD, &C. except that our land station being at a greater dis- tance we used signals by flags, instead of calling to each other ; warps were also employed in this in- stance, and we were thus enabled to steady the vessel on any proposed point, and to take the ob- servation on board with more precision. A second situation was also taken for a compass, a little forward of the foremast, where a pillar was fixed, and the two compasses placed under like cir- cumstances, except their different situations in the vessel. Another compass was also placed on the gun-room table, with which the ship's head was registered every time it was taken with the other two. The following are the results of these experi- ments : EXPERIMENTS Made to ascertain the quantity of Local Attraction in H. M. S. Leven, on Two Compasses, one forward and one aft, under the direction of Captain OWEN, January 15, 1822, at Northfleet. After Compass. Fore-mast Compass. II ~-2$ *|i Hi 1 If i i It 1 Hi jjff Bearing of Vidal at ai pass from E tion. J! III Bearing of niel's at sh tion from f compass. Bearing of Boteleratf. compass frc station. i 1 I"" i , o / \. 4 00 E. 10 00 16 00 o / S.34 SOW. 30 30 30 30 o / N.34 23 E. 34 6 33 30 + 07 336 3 / N. 5 00 E. 18 30 21 30 S.33 3o'w. o / N.32 20 E. 33 30 32 40 - fi'o / N. 17 30 E. 20 00 29 30 34 3 4 33 28 30 33 30 25 30 22 00 30 00 34 23 423 29 30 "3 a 34 00 26 30 28 00 33 30 35 52 232 36 30 1-8 34 12 __ 33 00 40 30 29 30 34 43 5 13 51 00 " >2 34 47 ___ _ 50 00 29 00 34 40 540 __ __ -2 w 35 10 57 00 28 50 34 35 5 45 _ ** 35 17 67 00 29 00 34 19 5 19 78 43 15 35 54 + 7 21 72 00 82 00 26 00 33 47 747 84 30 43 15 35 45 + 7 30 N.89 00 E. 89 00 East. 26 30 27 20 33 25 34 11 655 651 83 00 43 35 26 + 7 34 S. 88 00 E. .80 00 E. 27 00 33 01 601 S. 67 30 E. 42 30 34 47 + 6 43 73 00 70 00 27 40 32 45 545 56 15 41 34 20 + 6 40 65 00 63 00 27 10 32 28 5 18 50 30 40 30 34 27 + 6 IS 58 30 56 00 27 32 25 526 47 15 39 30 34 12 + 4 48 52 30 49 00 26 20 31 57 5 37 39 30 38 45 33 45 + 5 00 45 30 44 00 28 00 31 56 356 38 30 37 30 33 40 + 3 50 41 30 40 00 28 00 31 45 345 33 15 37 00 33 23 + 3 37 37 30 27 00 27 00 30 57 357 20 00 27 00 South. 32 00 31 14 + 046 S. 5 00 E. 31 30 30 00 + 1 30 S. 6 OOW. .13 OOW. _ S. 7 00 W. 25 30 31 23 5 57 9 00 17 00 34 20 31 05 + 315 12 30 25 30 30 50 5 20 13 00 26 00 34 00 31 06 + 254 18 00 24 30 30 50 6 20 21 00 33 00 34 30 31 02 + 328 26 00 23 00 30 31 7 31 28 30 39 00 35 00 31 09 + 351 31 30 22 30 30 38 8 08 34 00 50 00 35 40 31 36 + 4 4 37 30 22 30 30 49 8 19 43 30 57 00 34 00 . 45 00 21 30 30 58 9 28 50 30 60 00 35 00 31 23 + 347 22 30 29 30 7 00 70 00 38 50 33 24 + 526 57 30 21 30 32 00 10 30 65 35 80 00 40 20 34 05 + 615 68 30 22 00 32 54 10 54 75 SO West. . 74 00 W. 40 00 41 10 34 36 35 00 + 524 + 610 77 30, N.87 OOW. 22 30 21 30 32 36 32 56 10 06 11 26 S. 87 30 W. N.76 OOW. 63 00 39 50 35 22 + 428 77 00 22 00 33 02 11 02 64 30 53 00 39 40 35 29 + 411 58 30 24 15 33 15 9 00 50 00 43 00 33 00 40 30 35 32 + 458 50 00 25 30 33 08 7 38 48 00 22 00 39 10 27 30 30 45 36 00 5 15 16 00 38 30 37 30 + 10 19 00 30 45 35 22 4 37 ' __ __ 12 00 38 00 37 57 + 03 15 00 31 30 35 43 4 13 10 30 (Signed) A. H. VIDAL, First Lieutenant of H, M, S, Leven, 98 ON THE METHOD OF ASCERTAINING I , sT I pjoj -tuna MJ^ 'UOIJBJS 3.101(8 uioajpiBoquo ssedaioa jo SVLUVSQ natq'pjeoq uo ssed ajoqs jo Suu'tag s,dRs 10 uorpajtQ; -BJS uiojj 'pJBoq uo ssedmoD jo 2utJ8ag -UIOD IUOJJ U01JB1S aioq? jo SutJBag S,dll{9 JO UOI^D3JI(I OOIOOO^OXI I 1 1 1 ^ o 1 Jf.o i-i a * ^ 1 1 1 1 I 00510000^2^^1 I 1 I 1 G ; Tt<- cold. \EndB, 2130/ m Ditto, white heat, zero ; blood-red - 62 O. Experiment II. Malleable Iron ( End A, deviation 37 0' \ , ft0 & cold. \EndB, 430/ m Ditto, white, zero 5 blood-red - - 55 0. POWER OF IRON AND STEEL. 139 These two experiments were repeated with exactly the same results. The positions of the bars were now changed, viz. they were raised about two inches, but the dip was still observed. Experiment III. Cast Iron /End A, deviation 24 2O / 1 ^ cold. \EndB, 24 2O / m Ditto, white heat, zero ; blood-red 78 3O Experiment IV. Malleable Iron ( End A, deviation 1 cold. \ End B, not observed. J Ditto, white heat, -zero; blood-red 70 SC/ These experiments were repeated with the same results. 142. I should observe here, that the great at- traction produced by the heat, did not subside with it, provided the bar remained in its place undis- turbed ; for after some days I found the power of the bar continue just the same as at the time of making the experiment, when it had not been dis- placed ; but then the bar upon trial was always found to possess a certain degree of fixed magne- tism, its other extremity producing an opposite effect upon the needle ; but if the bar was inverted, while it retained any visible colour from the heat, both ends produced exactly the same deflection : as to the magnetic effect to which I have alluded above, 140 ON THE RELATIVE MAGNETIC it was lost, or at least a great part of it, after leav- ing the bar for some time horizontal, or, after its being thrown about with other pieces of iron. 143. It is also proper to observe that the needle always begun to indicate the power of the iron upon it, as soon as it arrived at that state of tem- perature shown by a high blood-red heat, and its motion generally proceeded gradually till it had reached its maximum deviation, which it com- monly attained in about a minute or two. It will be remarked as very singular, that cast iron, which is so decidedly inferior in its action, when cold, should possess a superior power when hot, which happened uniformly in every experiment that was made, the two bars being placed under like circumstances : it is moreover to be remem- bered that the cast iron bar was 1 - 1 6th of an inch less in its lateral dimensions, which ought, and necessarily did, diminish its actual power of at- traction. Its comparative power is therefore greater than that stated above. Comparison of the Magnetic Power of soft Iron and shear Steel, when heated in a furnace. 144. The bars employed in these experiments were those, whose effects are recorded in our second table. The results were as follow : POWER OF IRON AND STEEL. 141 Experiment V. Malleable Iron cold. f End A, deviation 16 30' 1 _ C0 ... lEmlB, 13 30 j mean15 1(/ Ditto, white heat, zero; blood-red - 41 1O Experiment VI. Soft shear f End A, deviation 1 1 3O 7 \ . n , steel, cold. I End B, 10 30 / m Ditto, white heat, zero j blood-red - 48 0. Experiment VII. Hard shear f End A, deviation 15 30' 1 00 , steel, cold. { End B! O 30 j mean 8 Ditto, white heat, zero ; blood-red - 47 30. 145. The only positive deduction which we are able to make from these experiments is, that soft iron, whose power is so far superior to every other kind of iron and steel when cold, is inferior to any of them when heated; and that cast iron, which has the least power cold, is equal, or supe- rior to any when hot. But there is certainly not so decided a scale of relation in this case, as in the experiments on the cold bars ; the principal reason for which may be the damage sustained by the iron by being repeatedly heated. I should, therefore, now have concluded my experiments on this subject, but for a circumstance which had been noticed, and which strongly at- tracted our attention. It had been observed both 142 ON THE ANOMALOUS by Mr. Bonnycastle and myself, in some of the preceding experiments, and others of which I have not given the results, that between the white heat of iron, when its power was actually zero, and the blood-red heat, at which its actiyn manifested itself so highly ; there was an intermediate state of the bar, during which it attracted the needle the contrary way to what it did when cold, viz. if the north end of the needle was attracted in the latter state ; the south end was attracted, while the heated iron passed through the shades of colour denoted by the workmen the bright red, and red heat. Our object was, therefore, now to examine this circumstance a little more minutely, than we had hitherto done. On the Anomalous Attraction of heated Iron, which takes place, while the metal retains the high red, and simple red heat. 146. In our first experiment the compass was placed nearly west of the bar, rather below its upper extremities, and distant from it about 61 inches. At the white heat, the attraction of the iron was lost ; and at the blood-red heat, we had more than 70 of deviation, but that intermediate action we were searching after, did not appear, at least it was by no means so obvious as we had noticed it in our preceding experiments. The po- ATTRACTION OF HEATED IRON, &C. 143 sition of the bar and compass, however, was not quite the same as before ; we therefore raised the stand for the bar about four inches, by which means its upper extremity was about the same height above the compass ; and on repeating the experi- ment with the bar thus placed, we obtained an obvious deviation of the south end of the needle to the bar of W ; which remained fixed for about two minutes. Having gained this by raising the bar 4 inches, we now raised its base 6 inches ; and on applying it in this place, we obtained a deviation of 1 OF , which remained fixed about the same time as before ; when the needle suddenly yielded to the natural magnetic power of the iron, and obtained almost instantaneously a deviation of 81 the opposite way. 147. It was thus rendered obvious that the quantity of negative attraction at the red heat, depended upon the height or depth of the centre of the bar ; and as the natural effect of the cold iron was changed by placing the compass below the centre of the bar, the next question was, will the character of the negative attraction change also ? To decide this point ; we lowered our compass to within six inches of the bottom of the bar ; in which position the cold iron attracted (of course) the south end of the needle, and produced a deviation of 21 ; and upon being heated, we found as usual 144 ON THE ANOMALOUS all its power upon the needle cease at the white heat ; but as this subsided into the bright red, the negative attraction begun to manifest itself, and it soon amounted to 10: the north end of the needle being attracted towards the iron : it remained stationary for a short interval, and then gradually returned, first to due north, and ultimately to 70 30' on the opposite side. 148. I now determined upon making a regular course of experiments, with a view, if possible, to trace this anomalous action to some fixed principle ; for it will have been noticed from what is stated above, that the negative attraction appeared to in- crease from each extremity of the bar towards its middle ; whereas the positive or natural action of the iron, decreases in the like cases, and, passing through zero in the plane of no attraction, has its quality of action different when placed towards the upper and lower extremity of the bar. But the negative attraction, which is also different in two opposite halves of the bar, seemed to pass through a maximum to arrive at this change of quality, which appeared wholly inexplicable ; and after all the experiments I have made, I must ac- knowledge that it still remains so. It is at all events certain, that the least change of position, when the compass is opposite the centre of the bar, will change altogether the quantity and quality of this negative action. ATTRACTION OF HEATED IRON, &C. 145 149. I should have been glad, in pursuing this inquiry, to have been able to use balls of iron in- stead of bars, and I made one experiment to see how far it was practicable, but the heat was so intense, that I found it inconvenient, and relin- quished this plan for that which I had hitherto pursued. The result of the ball experiment was as follows : attraction cold + 13 31': white heat 0': red heat 3 30'; blood-red heat + 19 30'. It may be proper also to observe, that having some doubt, whether the effect I had observed was due to any change in the attractive power of the iron during its change of colour, or whether it might not proceed merely from the heat, I pro- cured two copper bolts, of rather larger dimensions than the iron bars, and had them heated to the highest degree that metal would admit of; but upon placing them, when thus heated, in the same situation as the iron bars, no action whatever upon the needle could be detected. 150. In the experiments detailed in the follow- ing table, I used four different bars, each 25 inches long, \\ inch square, two of them of cast iron, denoted in the first column by C. B. No. 1, C. B. No. 2, and two of malleable iron, denoted by M. B. No. 1 ; M. B. No. 2 ; I had also two other bars, one of cast, and one of malleable iron, which were not heated, but kept as standards for L 146 ON THE ANOMALOUS determining the quantity of cold attraction ; as tins could not be safely done by the bars used in the experiments, after being repeatedly heated in the fire. The time occupied in each experiment was about a quarter of an hour ; the white heat commonly remained about three minutes, when the negative attraction commenced ; this lasted about two mi- nutes more, and then the usual attraction begun to indicate its presence ; this arrived at its maxi- mum sometimes very rapidly, but at others it proceeded increasing very gradually, and com- monly in a quarter of an hour from the beginning the needle had been found perfectly stationary. N. B. In the following table, to avoid confusion, that attraction which took place according to the usual manner, is marked plus +, which ever end of the needle was attracted ; and the opposite attraction is marked minus . For example, when the compass is above the centre of the bar, the north end should be drawn towards the bar j but when the compass is below the centre, the south end should be attracted j these, therefore, are both marked + in the table ; and the contrary attraction at the red heat is marked . 1; rf I; >> e >- i 2 ^ S3 12 |J| ^5 5-2 111* 1 ! s a*-- *-s ^ e - - Hi o -1 Il OOOOiCOOOOOOOO COCO ^GOSOCOCOOOCO ig 000 ooc O O O 0* CO tf5 1 I I I g I I I I I I I I I + 1 + 1 I I -022222 2 22|||2|22222 % O OOOOtlOOtlOOs^ OO CO 0> V CO CO V CO 10 >. 3 3 5 s . 3 5 o > jf ^W^ WW o o o o o in 2 o2i2^ g^& 00 CO CD CO 00^ 5 WS g S Tf s| ~S i~ j Sj^xOOOOO O CO^*OOiOO*OO Fi f ~^"n boo o I222J22 2 6 6 6 6 6666666666666 K ^ . . K ZZZZZZZZZZZZZ ffi 2 pq 2 P3 2 pq" pq pq PQ pq pq pq pq' pq pq" pq pq pq* pq" juara u 3 clx 3 jo -OM O> O -* O? CO 't 5 ^ o? CM T^ Or, which is the same, tan A' = o sin 2 X cos I - ^ cos 8 + (3 sin 2 X 1) cos S + sin2 X sin 3 sin I C r 3 2 Or making _ 3 (3 sin 2 X 1) cos o -\ sin 2 X sin S sin I = N (the lower sign applying to the case of i 7 90) we have more concisely sin 2 X cos I _._ T where x denotes the complement of the angle 0, or the latitude, and / the complement of the angle t, or the longitude, conformably with the notation employed in the preceding sections of this Essay. 164. This is a rigorous formula for all distances, and for a ball or shell of any radius, and of any description of iron ; but the value of the co-efficient Q is different for different species of iron. In the M 162 LAWS OF MAGNETISM case of cast iron, it will be seen in the following article, that it is very nearly equal to unity, and consequently in this case, when d exceeds two or three times r, as in my experiments ; the quantity denoted by N, which is made up with the sums and differences of products, of which each of the trigonometrical factors is less than unity, is small M 2d 3 in comparison with the other term -^r cos f and we shall, therefore, by rejecting the former, have as an approximate formula, which exhibits in one term, all the approximative laws deduced from the experiments ; that is, it follows from this formula, 1 . That although by the hypothesis the develope- ment of the magnetism of the ball or shell takes place only at its surface, yet the effect of it as shown by the tangent of deviation is proportional to the cube of the radius or diameter. 2. That the tangent of deviation is inversely as the cube of the distance. 3. That the tangent of deviation is proportional to the sine of tlie double latitude and cosine of the longitude, the latter being estimated from the magnetic east and west points, which are precisely the laws deduced from the experiments. 165. With reference to the numerical value of PECULIAR TO IRON BODIES. 163 C 3r 3 the constant co-efficient ^ y^r cos 8 it may be found by comparing it with the experimental value of the same as deduced from our experimental results, given in arts. 23, 24, 25, 26, or rather from the two latter ; because the distance in these are greater than in the two former, and it is obvi- ous from our formula, that the approximation will be nearer as the distance is greater, the rejected term N being in that case less considerable in re- spect to the constant part. Hence, since C 3 r 3 tan A' = . (sin 2 X cos I) M 2 d a cos S v we have, when cos / = 1, as in the experiments in question, sin 2X, _ M 2 d s cos 3 .,,] tan A' ~~ ^C " JT 3 The exact diameter of the ball is 12*8 inches, or radius 6*4 inches, and in one case the distance is 18 inches, and in the other 20 inches. Hence our tabular numbers give, x , . M 3 .18'.co_sTO-| The first of these gives ^ = 1 >0558 > ri and the second = 1>0513 Mean ^ = 1-0535 M2 164 LAWS OF MAGNETISM This number is constant for cast iron balls and shells of every diameter, and for all distances and positions ; our correct formula, (9) therefore, be- comes tan A' = sin 2 X cos I 1-0535 r or ~ 1 } COS * + sin2X sin B Sin l cot A' = (10) which is the most convenient form for com- putation. 166. As this formula is wholly theoretical, with the exception of the numerical co -efficient 1 . 0535 > it will be satisfactory to compare the results de- duced from it with those obtained from actual experiment, and we have an excellent opportunity of doing this by means of the table of experiments published by Mr. Christie in the first part of the Transactions of the Cambridge Philosophical So- ciety. These were made by that gentleman on the same apparatus which I had employed, but in different circles ; namely, in parallels of latitude corresponding to 30, 45, and 60, and at every 10th degree of longitude. They were made with a new and accurate compass constructed for the purpose, and every precaution was used to assure the greatest possible accuracy in the results. PECULIAR TO IRON BODIES. 165 The distance in all these experiments was 18 inches, or d = 18 ; the radius of the ball was 6*4 inches, or r 6*4 ; and dip * = 70 3CK ; whence the constant part of the above formula for each different parallel of latitude are, for cot A' = 5-360 sec I + tan I sin 70| cot A' = 4-8O9 sec / + tan I sin 7O c f cot A' = 5745 sec / + tan I sin 70'| lat. 30 - - lat. 45 - - lat. 60 - - 17. Table containing a comparison between MR. CHRISTII experiments, and the theoretical results computed by the precedii formula. f Latitude 30 Longitude. Latitude 45 1 Latitude 60 Com- puted. Dbscrvcd Error. Com- puted. Observed Error. Com- puted. Observed Erro o / o / / / o o / O / N 2 14 2 20 6 SON 2 34 2 33 + 1 SON 2 4 2 5 4 22 4 44 22 70 5 2 5 + 2 70 4 1 3 58 + 6 17 6 52 35 60 7 9 7 12 3 60 5 48 5 43 + 7 53 8 16 23 50 8 57 8 53 + 4 50 7 18 7 29 9 9 9 21 12 40 1O 2O 1O 1 + 19140 8 29 8 26 + 1O 2 9 58 + 4 30 11 18 10 54 + 24 BO 9 19 9 5 + 10 34;10 23 -f 11 20 11 56 11 29 + S1JHO 9 50 10 1 10 44 1O 33 + 6 10 11 58 11 45 + 13 1O 10 1 9 46 + 10 34 10 17 + 17 O 11 45 11 32 + 13 9 52 9 43 + g 10 7 9 56 + 11 10 S 11 13 11 8 + 5 1O S 9 27 9 21 + 9 23 9 8 '+ 15 20 10 22 1O 16 + 6 i! 20 8 48 8 38 + 8 27 8 16 + 11 3O 9 19 9 17 + 230 7 56 7 49 + 7 19 7 3 + 16 4O 8 3 7 58 + 5 ! 40 6 53 6 45 + 6 2 6 3 1 50 6 38 6 37 + 1 50 5 41 5 35 + 4 38 4 38 60 5 5 5 + 5'6O 4 21 5 25 3 8 3 9 1 70 3 27 3 20 + 770 2 58 2 54 + > 1 35 1 38 2 80 1 44 1 4O + 4JSO 1 29 1 166 LAWS OF MAGNETISM 168. It would be useless to expect a closer ap- proximation between theory and practice, in ex- periments of such a nature, which, notwithstanding all the care that can be used, are subject to errors which it is impossible to estimate ; the daily vari- ation alone, for example, may cause an error of 15', and very few of our errors in the preceding Table exceed this amount ; besides which, we have to allow for any trifling deviation in placing the meridian line on the table in the plane of the actual meridian, in the adjustment of the compass at each place of observation, and in measuring its distance from the centre of the table and its depth below the centre of the ball. When these sources of error are properly considered, it will be found that the agreements between the theory and experi- ment is as close as can be reasonably expected. It is to be farther observed, that we have assumed, for the sake of simplifying the computation, that the needle is indefinitely small, whereas it must pecessarily be of a determinate length ; but while this is less than one third of the distance, the errors thence arising, although of some amount, are very inconsiderable. Of the Dipping Needle. 161). Having completed our computation on the horizontal needle, let us next inquire what the PECULIAR TO IRON BODIES. 167 effect will be upon a dipping needle limited in its motion to the meridian. For this purpose we have only to project the arc A, determined in formula (7), upon the plane of the meridian, by drawing the arc S' E (fig. 14) perpendicular to the circle H Z H'; so will S E be the deviation sought. Since S' E S is a right angled triangle, we have immediately, tan S E = tan S S' cos i. But S S' = A, and by formula (7) 3 sin cos tan A = Whence denoting the arc S E by A" we have - + from which the angle A" may in any case be computed. But for the purposes of computation it will be best to convert the above expression into 3 sin cos cos t CO ' A "= {(||| |)sec 2 X in which it is only requisite to introduce the proper value of the several quantities, as determined in (art. 165). 168 LAWS OF MAGNETISM Comparison of this formula with the results of experiments on the Dipping Needle. 170. The experiments, of which the results are given in the following Table, were made on the same apparatus as that employed in my former experiments. The needle was placed only in the plane of the meridian, at such distances from the centre of the table, and the ball elevated so much above the centre of the needle, as to bring it into the several latitudes 73, 15, 22, &c. keeping, in all the experiments, the centre of the ball and centre of the needle at the constant distance of 20 inehes from each other. M l We have, therefore, -g = i^55g-(art 165) r = 4 '6 inches, d 20 inches, and cosee / = 1 . 171. Hence the above formula in numbers becomes cot A" = 18-639 cosee 2 X 4- tan X from which the column of computed deviations, in the first of the annexed Tables, has been cal- culated. 172. If we take r = 8'85, the radius of an 18 inch shell, then the above becomes cot A" = 6-6341 cosee 2 X + tan X which is the formula employed in Table 2. PECULIAR TO IRON BODIES. 169 173. Table showing the deviations produced in a Dipping Needle by an Iron Ball 13 inches in diameter ; and the computed deviations from the preceding formula. Distance 20 inches, mean detached dip 70 4(X. Latitude. Observed Dip. Observed deviation. Computed deviation. o / / o / / 70 40 7 30 69 40 1 48 15 68 55 1 45 1 31 22 30 68 20 2 20 2 9 30 O 68 10 2 30 2 36 37 30 67 4O 3 2 51 45 67 40 3 3 4 52 30 67 55 2 45 2 41 60 68 10 2 30 2 24 67 30 68 40 2 1 58 75 69 10 1 30 1 23 82 30 69 4O 1 43 9O O 7O 55 15 The above mean dip 70 40', was with one end of the needle only, without inverting the poles : the error of the instrument is not included. 170 LAWS OF MAGNETISM /4. Table showing the deviations produced in a Dipping Needle by an 18 inch Shelly and the computed deviations from the preceding formula. Distance 20 inches^ mean detached dip 70 11'. Latitude. Observed Dip. Observed deviation. Computed deviation. Time of making 40 vibrations. o / / / / // o o 70 11 125-3 15 66 7 4 4 4 14 124-44 30 63 49 6 22 6 56 121-3 33 30 120-3 45 62 43 7 28 7 28 116-5 6O 64 22 5 49 6 5 113-58 75 O 65 44 3 27 3 21 112-3 9O O 70 11 O O 110-2 The above experiments were made with a diffe- rent instrument from the former ; the needle was on Captain Kater's construction, viz. diamond formed ; 7 inches in length, the action of the needle remark- ably correct. The above is the dip with one end only. 175. The last column shows the number of seconds in which the needle made 40 vibrations in each position ; the object was to compare the computed with the observed intensity, as will be explained in a subsequent article. These obser- vations were made with great care, the time being counted by a machine which would register to 40ths of seconds. The face of the instrument PECULIAR TO IRON BODIES. 171 was first turned to the East and then to the West, the dip and vibrations being registered four times in each position, and the mean of the eight results taken, as they are given in the foregoing table. 1/6. Confining ourselves here only to notice the deviations, we think it must be admitted that the agreement is as near as can be reasonably ex- pected ; both the instruments employed were per- haps amongst the most perfect of their kind ; but every one who is acquainted with the dipping needle will be aware that it is not so constant in its action as we might desire ; the difference between any two dips, however, in the same position, never exceeded half a degree ; and as to the number of vibrations, they seldom differed from each other by half a second. General Results. 1 77- If we now collect under one point of view our principal formula, (7), (9) and (10), and sub- stitute in them the proper values in x and /, instead of their complements and i, we shall have, after the requisite reductions, <"> sin 2 \ cos I _._ C050+ _ N 172 LAWS OF MAGNETISM s ' m 2 X sin I A// tanA = +2sm f AGNETIC attempted to register nearer than to quarter se- conds. (See art. 174). 186. Table showing the computed and observed intensities of a Dipping Needle in different positions, with respect to an 18 inch Shell. Value of R a or of 57288 sin 2 A- + -82582 Time of 40 vibrations Computed time of 40 vibrations Observed time in Latitude. Value of R 2 from Iron. Latitudes. Latitudes. o / // // O O 82582 120- 12578 125-3 15 86419 Ditto 124-46 124-44 30 96940 Ditto 120-95 121-3 33 30* 1-0000 Ditto 120-OO 120-3 45 1-11226 Ditto 116-85 116-5 60 1-25548 Ditto 113-36 113-58 75 1-36033 Ditto 111-12 112-3 90 1-39870 Ditto 110-35 110-25 * The proper value of A, when R = 1, that is, when 57288 X 2 = -17418 is X = 33 28'. 187- The remarkable approximation to equality in the computed and observed times of vibration, in the last two columns of the above table, is one of the best tests we have yet met with for compar- ing the hypothesis upon which our investigation is founded, with the interpretation usually given to the theory of Coulomb. According to the latter, eveiy ball or mass of iron becomes, by induction from the earth, a temporary magnet, having its north and south poles at its extremities, or at those INTENSITY OF A NEEDLE, &C. 181 of the line corresponding with the dip of the needle in the place of observation. Whereas, agreeably to the hypothesis I have advanced, the latent mag- netism* of the ball has merely polarity given to it ; but it is distributed over the surface, and has its centres of action indefinitely near to each other in the centre of the ball. 188. On discussing this question with a philo- sopher of eminence, he maintained an opinion that the ball which I had employed acted from two poles, at the extremities of that diameter which corresponds with the dip of the needle, and sug- gested an experiment that should demonstrate the fact. This was, to take a vessel of water, and to file a piece of soft iron with a new file, so that the dust of the iron should be distributed on the surface of the water ; I was then to bring the north pole of the ball nearly in contact with the surface of the water, and the motion of the filings was to indicate the existence of the pole in question. I performed this experiment in two or three different ways, but I could never distinguish the least motion in the filings. This, however, after all would be considered only a negative demon- stration of what I wished to establish ; but the preceding results are, I conceive, fully conclusive and satisfactory. 189. For the better illustration of the conclusion 182 CHANGE IN A NEEDLE, &C. I am desirous of drawing from the above tabulated experiments; I have given, in (fig. 16) a deline- ation to scale of the position of the needle n s, in respect to the ball N S in each of the situations noted in the preceding table ; by which it will be seen how closely the south end, s, of the needle approached (in its position lat. 90) what has been called the north pole of the ball ; consequently, the acceleration of the needle ought, in this posi- tion, to have been much greater than we have found it ; had the action taken place between N and s, or if N were a condensed centre of action, such as the hypothesis in question supposes. Whereas by referring the whole to a compound central action, we find the most accurate agree- ment between the observed and computed inten- sities. 190. I am the more anxious to establish this point, in consequence of its immediate connection with the method I have proposed for correcting the errors of a ship's compass, which has been ob- jected to, on the ground that according to the theory we have been controverting, the central action of all the iron on board would not remain constant under all dips and in all parts of the world ; but if the hypothesis I have advanced be correct, then the central action of any irregular mass of iron will be in the centre of attraction of its surface, whatever may be the magnetic direction, MAGNETIC ACTION, &C. 183 and must necessarily remain the same, while the iron and the point from which its action is esti- mated preserve the same relative situation ; as is the case with the iron of a vessel and its compass, at least, with the exception of those small changes of position which may, for the sake of convenience, take place in the course of the voyage ; but these will never materially affect the position of the general centre of the whole mass. SECTION III. ON THE MAGNETIC ACTION OF BARS OF IRON. 191. IT will be observed that we have hitherto confined our investigation to the laws of action of spherical bodies, which possess the singular quality of having their centre of attraction in the centre of the mass ; consequently the former remains fixed in position, at whatever distance the compass may be placed from the ball. This, however, is not the case with any other body; and I was therefore desirous of ascertaining, by experiment, how nearly the deduction I had already made from spherical bodies agreed with those of a different form. 192. These deductions, as we have already seen, amounted to this, that the magnetic attraction 184 ON THE MAGNETIC ACTION of any iron body, may be referred to the action of two centres indefinitely near to each other in the general centre of attraction of the surface of the body : viz. that point into which, if all the matter of the surface were collected, its action on a given point (the centre of the compass) would be the same as the action of the whole body in its natural form. In order, therefore, to compute the action of a bar of iron (considered as a line) on the compass, we must first determine the position and distance of the centre of attraction, or at least the amount of that attraction on a given- point. This part of the computation may be effected as follows : 193. Let A B, (fig. 17) denote the given bar, C the place of the compass, or the point to which the attraction is referred. Draw the perpendicular D C and join A C, B C. Make A D = b, D C = a, A C = c, and m D = x, any variable distance. Then, the attraction being inversely as the square of the distance, the attraction between m and c will vary as 1 i "g^ ~ 2 + x* Resolve this into the two directions D C, D m, and we shall have ( q a + x *\i = attraction in the line C D Or BARS OF IRON. 185 = attractlon m the nne (a* + consequently ./(a " + **)+ = ( DiUo 14375 PRECEDING FORMULA, &C. 199 vv ;, /No. 2. Baffin's Bay, dip 84 3(X . . . . 163 O I No. 3. Ditto 152-5 Needles / No - 2> Winter Harbour, dip 88 43'5',. . . 329-O 210. Comparing the results at the greatest of the above dips with the least, we ought to have, taking the means of the two needles, (3 + sec 2 69 55')* : (3 + sec 2 88 43'50* *. 8T5 2 : 3~23 7 5 U and we have in actual numbers for our fourth term 317*76, which is a very close approximation. In like manner we should have (3 + see 8 69 550* ". (3 + sec2 84 3f/)* *. ST*? 2 '. 15? -7 * and the last term is isTs^ 3 also (3 + sec 2 69 550* ". ( 3 + sec 2 83 O40* * &F&* '. 147'fi" but the computation gives the last term 138-29' 2 This is a greater aberration than in the preceding proportions, but still, a very slight error in taking the dip would be amply sufficient to account for it. 211. This relation between the dip and intensity of vibration has suggested to Captain Sabihe the idea of obtaining the former by means of the latter. For example, let D denote the dip in any place where it is known, and let n be the number of vibrations made by a finely suspended horizontal needle in the same place, in any given time. Let also N be the number of vibrations which the same 200 APPLICATION OF THE needle makes in the same time, in any other place where the dip (d) is required ; then (3 + see 2 D)* : (3 + see 2 d)* I : N 2 ' * or or 3 + see'd = T~J* (3 + see 2 D) whence seed= { -^- (3 + see s D) 3}* ...... (25) where n, N, and D, being given, d also becomes known. 212. It is to be observed that n and D, when once determined for any given place, as for ex- ample London, will be constant ; let therefore n* (3 + sec 2 D) = A, then the above becomes simply Or, if instead of counting the number of vibrations made in a given time, we take the time that the needle is in performing a given number of vibra- tions, (which is the best where we have a good stop-watch, or other instrument for marking shorter intervals of time) ; then denoting the times by T and /, the above formula is trans- formed into PRECEDING FORMULA, &C. 201 = { -L (3 + see 2 D) 3J* (27) which, like formula (25) is reducible to the simple form see d A/T 4 A' 3 .......... (28) after the dip D, and time t, have been ascertained in the first place of observation. 213. We may take as examples the numbers given in (art. 209), where it appears that with the dip, 69 55', the mean time of making ten oscilla- tions was 87'5" ; whence A = = .00000019584 87'5 Now at Winter Harbour, Melville Island, the mean time of making 10 vibrations was 323*5", whence we have for the dip at the latter place see d = J (323- 4 + -00000019584 3) = 88 46' In Baffin's Bay, see d = - ber 1821, a coincidence, or exceedingly close approximation, which could scarcely have been expected; and which will, I am persuaded, be duly estimated- by the candid philosophical in- quirer. Captain Sabine, by comparing the present dip with the dip 47 years back, finds the mean annual diminution to be about 3'. According to our hypothesis the dip has not an uniform decrease, but is changing now more rapidly than it has ever before done since magnetical observations have been made. Its decrease during tke last 5 years, 218 ON THE ANNUAL VARIATION. has been nearly half a degree ; and if our principles be correct it ought to decrease nearly the same during the next 5 years ; a short time therefore will either confirm or refute the hypothesis on which we have founded the preceding computations. Agreeably to which we ought to find in 1828, the variation 24 29' dip 69 43' 1833, 24 26 . . 69 21 The dip, therefore, is at present changing more rapidly than the variation ; and it will continue to decrease with the latter for about 260 years, when the longitude of the magnetic pole will be 1 80 ; the variation will therefore then be nothing, and the dip only 56, which will be its minimum, they will then both increase together for the next 260 years, when the needle will have its greatest easterly variation, and will then again return towards the north, the variation decreasing, but the dip still increasing, for 165 years longer; viz. till about the year 2510, when the magnetic pole will be again on the meridian of London ; the variation will be zero, and the dip being then at its maxi- mum will amount to 77 43'. Such at least are the results arising out of the hypothesis on which the preceding calculations are founded. They are unquestionably in some mea- sure speculative, and are only given as such ; but I may perhaps be permitted to say that as far as comparison could be made with well authenticated ON THE ANNUAL TARI ATI ON. 219 observation it has been done, and the approxima- tions towards coincidency have been throughout more favourable than, from the nature of the inquiry, we could have had any reason to expect. Further comparisons may also still be made, and a few years will be sufficient to confirm or refute the hypothesis, of an uniform motion of rotation in the terrestrial polarizing axis. It is however proper to state, that if we had carried our computations back to the 1 6th century, and compared them with observation, the agree- ment would not have been found so close as in the cases mentioned in the preceding table ; but I think it may be questioned how far these obser- vations may be depended upon ; one of which out of the only three we have recorded, being made previous to the time of the variation in the variation being known. At the same time I am by no means disposed to assert, that the elements of the motion we have assumed are perfect. It is to be observed that we have deduced them from two observations only ; viz. the dip as taken by Captain Kater in 1818, and the variation at that time; it is from these only we have determined the latitude and longitude of the magnetic pole, and thence by assuming the longitude to have been zero in 1660, we have determined the annual motion. I have little doubt that we should have found a nearer approximation by taking the polar distance of the 220 ON THE ANNUAL VARIATION. magnetic pole greater or less than we have done ; but my object has not been to find how nearly it was possible to approximate to observation, but how nearly the deductions, legitimately arising out of our first hypothesis, corresponded with the same. Churchman, in his Magnetic Atlas, has assumed a certain distance and movement of rotation, which give nearer approximations than those found above, but they are dependent upon no previous principle, and are inconsistent with every other magnetic law; whereas our distance and motion are drawn immediately from an inde- pendent hypothesis, and are perfectly consistent with every known principle of terrestrial mag- netism. ON ELECTRO MAGNETISM. 221 PART HI. On Electro Magnetism. SECTION I. SKETCH OF THE PRESENT STATE OF ELECTRO MAGNETISM. 230. IT \ras for many years suspected that there existed a strong analogy, if not a complete identity, between the electric and magnetic fluids, and va- rious attempts were made to establish such relation on satisfactory principles. It was known, for instance, that lightning destroyed and reversed the polarity of magnetized needles, and that it produced a magnetic power in pieces of steel which had not before any such action. Now lightning and electricity have been long known to be identi- cal ; consequently, electricity ought to produce similar effects to lightning on magnetic and simple steel bars ; but the attempts which were made to discover a satisfactory proof of this action by means of the electric apparatus were not at- tended with success ; at least all that was effected in this way amounted only to communicating the 222 PRESENT STATE OF magnetic property to steel bars, but without the experimenter being able to predict in what direc- tions the poles would lie, and therefore was little more than might be produced by a blow, by twist- ing, and various other means. It was indeed stated that the magnetism was more fully developed when the shock was passed through the needle transversely, than when it passed lengthwise ; but still no definite conclusions could be drawn from the experiments. 23 1 . Philosophers having thus failed of tracing the analogy between the electric and magnetic fluids, by means of the electrical apparatus, had next recourse to the Galvanic batteiy, which was known to possess electrical properties. Of these experiments those of Ritter are the only ones of any importance. He stated that he had succeeded, by placing a Louis d'or in contact with the extre- mities of a galvanic circuit, in giving to it a positive and negative electric pole, which remained after it had been in contact with other metals ; he also magnetised a gold needle by means of the galvanic battery, and seems to have had some obscure ideas of electric terrestrial poles at right angles to the magnetic poles. These experiments, however, were never much regarded, and the relation be- tween the two fluids seemed still to remain doubt- ful. 232. Soon after the time that Ritter made his ELECTRO MAGNETISM. 223 experiments, Professor CErsted, of Copenhagen, published a work in which some hints are thrown out respecting the analogy between the electric, galvanic, and magnetic fluids ; which were sup- posed to differ from each other only in their degree of tension. The galvanic fluid is there conceived to be more latent than the electric, and the mag- netic still more so than -the galvanic. The science, however, made no farther progress from this time (1807) till the year 1820, when the same learned Dane succeeded in establishing the reciprocal action of the galvanic and magnetic fluids upon each other by the most satisfactory experiments. These have been since repeated, and much ex- tended by Ampere, Biot, Arago, in France ; by Sir H. Davy, Professor Cummings, and Mr. Faraday, in England, and have thus led to the establish- ment of a new branch of philosophy designated electro-magnetism, of which it is proposed to give a concise view in the following pages. 233. CErstecCs experiments. As these leading experiments are veiy concisely and clearly stated by the author, we shall give them in his own words. The galvanic machine being charged, and its poles connected by a wire of any metal (which may be called the conductor or uniting wire), the following effects will be noticed : " Let the straight part of this wire be placed 224 PRESENT STATE OF horizontally above the magnetic needle properly suspended, and parallel to it. If necessary, the uniting wire is bent so as to assume a proper position for the experiment. Things being in this state the needle will be moved, and the end of it next the negative side of the battery will go west- ward. " If the distance of the uniting wire does not exceed three quarters of an inch from the needle, the declination of the needle makes an angle of about 45. If the distance is increased, the angle diminishes proportionally. The declination like- wise varies with the power of the battery. " The uniting wire may change its place, either towards the east or west, provided it continue parallel to the needle, without any other change of the effect than in respect to its quantity. Hence the effect cannot be ascribed to attraction ; for the same pole of the magnetic needle which approaches the uniting wire, while placed on its east side, ought to recede from it when on the west side, if these declinations depended on attraction and repulsions. The uniting conductor may consist of several wires or metallic ribbons connected together. The nature of the metal does not alter the effect, but merely the quantity. Wires of platinum, gold, silver, brass, iron, ribbons of lead and tin, a mass of mercury, were employed with equal success. The conductor does not lose its ELECTRO MAGNETISM. 225 effect though interrupted by water, unless the interruption amounts to several inches in length. " The effect of the uniting wire passes to the needle through glass, metals, wood, water, resin, stone ware, stones, for it is not taken away by interposing plates of glass, metal, or wood. Even glass, metal, and wood, interposed at once, do not destroy, and indeed scarcely diminish the effect. The disc of the electrophorus, plates of porphyry, a stone-ware vessel, even filled with water, were interposed with the same result. We found the effects unchanged when the needle was included in a brass box filled with water. It is needless to observe that the transmission of effects through all these matters has never before been observed in electricity and galvanism. If the uniting wire be placed in a horizontal plane under the magnetic needle, all the effects are the same as when it is above the needle, only they are in opposite direc- tions ; for the pole of the magnetic needle next the negative end of the battery declines to the east. " That these facts may be more easily retained, we may use this formula, the pole above which the negative electricity enters is turned to the west ; under which, to the east. " If the uniting wire be so turned in a horizontal plane as to form a gradually increasing angle with the magnetic meridian, the declination of the needle increases, if the motion of the wire be 226 PRESENT STATE OF towards the place of the disturbed needle ; but it diminishes if the wire moves further from that place. " When the uniting wire is situated in the same horizontal plane in which the needle moves, and parallel to it, no declination is produced either to the east or west ; but an inclination takes place, so that the pole next which the negative electricity enters the wire is depressed when the wire is situated on the west side, and elevated when situ- ated on the east side. " If the uniting wire be placed perpendicularly to the plane of the magnetic meridian, whether above or below it, the needle remains at rest, un- less it be very near the pole ; in that case the pole is elevated when the entrance is from the west side of the wire, and depressed when from the east side. " When the uniting wire is placed perpendicularly opposite to the pole of the magnetic needle, and the upper extremity of the wire receives the nega- tive electricity, the pole is moved towards the east ; but when the wire is opposite to a point between the pole and the middle of the needle, the pole is moved towards the west. When the upper end of the wire receives positive electricity, the pheno- mena are reversed. " If the uniting wire be bent so as to form two legs parallel to each other, it repels or attracts the BLECTRO MAGNETISM. 227 magnetic poles according to the different conditions of the case. Suppose the wire placed opposite to either pole of the needle, so that the plane of the parallel legs is perpendicular to the magnetic meridian, and let the eastern leg be united with the negative end, the western leg with the positive end of the battery, and in that case the nearest pole will be repelled either to the east or west, accord- ing to the position of the plane of the leg. The eastmost leg being united with the positive, and westward with the negative side of the battery, the nearest pole will be attracted. When the plane of the legs is placed perpendicular to the place between the pole and the middle of the needle, the same effects recur, but reversed. " A brass needle, suspended like a magnetic needle, is not moved by the effect of the uniting wire. Needles of glass and of gum lac, jemain likewise quiescent." 233. These facts having laid the foundation of the present interesting science of electro mag- netism, I have thought it best to give the state- ment in the author's own words; but in what follows, it will be necessary to be more concise. The experiments of Mr. CErsted were no sooner promulgated, than they were repeated and considera- bly extended by M. M. Ampere, Arago, and Biot ; by Sir H. Davy, Mr. Faraday, and Professor Cum- mings, as well as by several celebrated German 228 PRESENT STATE OF philosophers ; and many curious and interesting facts and phenomenas were thus elicited. 234. M. Ampere, for instance, discovered that not only there is a reciprocal action between the galvanic wire and the magnetic needle, but that two such wires act upon each other, by attraction, when they both proceed from the same extremity of the battery, and by repulsion when they proceed from opposite extremities ; that is, two conducting wires, free to move, being placed parallel to each other, and the corresponding extremities proceed- ing to the like poles of two different galvanic machines, the wires will be attracted to each other ; but if the corresponding extremities of the wire proceed from contrary poles of the batteries, then the wires will indicate a mutual repulsion between them. 235. Again, it was shown by M. Arago that the connecting wire of a galvanic battery had an obvi- ous action upon iron filings, and that it would hold them suspended like an artificial magnet, but that they fell the moment the contact with the battery was broken. The same thing was discovered by Sir H. Davy, who also showed that the filings on the opposite sides of two parallel wires attracted each other, and that those on the same sides repelled. 236. The latter experiments naturally led to an attempt to magnetize steel wires by the galvanic ELECTRO MAGNETISM. 229 battery, in which the first successful attempt was made by Sir H. Davy, although it was effected at nearly the same time by M: Arago. In the first instance the needle was simply laid transverse of the single wire, and the operation required a certain time ; but M. Arago afterwards made use of a spiral wire, and was thus enabled to produce the maximum effect almost instantaneously. Sir H. Davy also succeeded in magnetizing steel needles with the electrical battery at- very consi- derable distances, and thus demonstrated that the magnetic power was not peculiar to the galvanic apparatus. 237. The next question was, since there is so obvious a connection between the freely suspended galvanic wire and a magnet, has the former a directive quality from the influence of the terrestrial magnetism ? This led M. Ampere to the construction of a simple apparatus, which will be described in a sub- sequent section, and by which he proved that if a part of the galvanic wire, bent into the form of a rectangle nearly shut, and free to move, be left to the action of the terrestrial magnetism, it will adjust its plane to one perpendicular to the mag- netic meridian, and that by giving to a similarly formed wire a freedom of motion on a horizontal axis, it will conform itself to that plane which in our first part has been called the plane of no at- 230 PRESENT STATE OF traction ; that is, the plane of the wire will in all cases have a tendency to place itself at right angles with the plane of the magnetic meridian, and to the line of direction of the dipping needle. These experiments are more fully illustrated in our last section. 238. At this stage of the enquiry Mr. Faraday, of the Royal Institution, commenced his enquiries. He proved that the action which had hitherto heen noticed between the magnetic and the galvanic wire, was neither attraction nor repulsion, but was of such a nature as to give to the magnetic needle a tendency to revolve about the wire, and he at length succeeded in producing this rotation ; viz. he was enabled by a very simple apparatus, which we have described in our third section, to cause either pole of a magnet to revolve about a fixed galvanic wire, and conversely, by fixing the magnet, he caused the wire to revolve about the former, and by the same apparatus also, the wire and magnet being both free, may be made to revolve about each other ; and he subsequently was en- abled to produce a rotation of the wire by the mere influence of the terrestrial magnetism upon it. These beautiful experiments threw an entire new light upon the science of electro magnetism. 239. M. Ampere having been informed of Mr. Faraday's experiments, succeeded in causing the magnet to revolve on its own axis, by introducing ELECTRO MAGNETISM. 231 it as a part of the galvanic circuit ; an experiment attempted by Mr. Faraday, but which he had not been able to perform ; and Sir H. Davy by his experiments on the mercurial vortices, proved also the rotation of the wire on its axis, which is effected in another manner in our 10th experiment. See section iii. 240. Such was the state of this science when I undertook the experiments reported in the fol- lowing section, and by which, if I have not deceived myself, the whole of the apparently anomalous actions hitherto observed, may not only be ex- plained, as to the general effects, but the disturb- ance on the needle computed for any determinate position of the compass and wire, in a manner very similar, but more simple, than that which has been illustrated in reference to the iron ball and magnetic needle. It may be proper to observe that several experi- ments, besides those alluded to above, had already been made by other philosophers, and which led to many curious facts, but as they do not appear to have had any influence in advancing the theory of the science they have not been referred to in the preceding sketch ; but some of them are given in our third section. 232 MATHEMATICAL LAWS OF SECTION II. ON THE MATHEMATICAL LAWS OF ELECTRO MAGNETISM.* 24 1 . ALL the experiments that have been made on the subject of electro magnetism, since the first discovery of that power by Mr. GErsted, seem to indicate a strong affinity, although not a complete identity, between the simply magnetic and the electro magnetic fluids ; or, if the identity be ad- mitted, still a certain difference must be conceived to have place in the modes of action. In the preceding parts of this work I have at- tempted to reduce the laws of induced magnetism to mathematical principles, and to render the results susceptible of numerical computation, the mass of iron, and its position with respect to the com- pass, being given ; and as soon as I heard of Mr. (Ersted's discovery, I was desirous to establish, on similar principles, the law of electro magnetism ; but it was some time before I was able to construct an apparatus convenient for the purpose. Having, however, at length effected this necessary prelimi- * The substance of this section was placed in the hands of Sir H. Davy by Major Colby, last March, and was read before the Royal Society, May 23. I am sorry I have been obliged to publish it before the council has decided respecting its appearance in the Transactions. ELECTRO MAGNETISM. 233 nary to my satisfaction, I proceeded to make the course of experiments, and to undertake the inves- tigations which form the subject of the present section. 242. My first object was to repeat veiy carefully all the experiments of Mr. CErsted, M. M. Ampere, and Arago ; of Sir H. Davy and Mr. Faraday, with some others suggested by the results thus obtained ; and having attentively considered all the peculi- arities of action thus developed, I was led to con- sider that all the apparently anomalous effects produced on a magnetized needle by the action of a galvanic wire, might be explained by the ad- mission of one simple principle ; viz. that every particle of the galvanic fluid in the conducting wire acts on every particle of the magnetic fluid in a magnetized needle, with a force varying in- versely as the square of the distance ; but that the action of the particles of the fluid in the wire is neither to attract nor to repel either poles of a magnetic particle, but a tangential force which has a tendency to place the poles of either fluids at right angles to those of the other ; whereby a magnetic particle, supposing it under the influence of the wire only, would always place itself at right angles to the line let fall from it perpen- dicular to the wire, and to the direction of the wire itself at that point. I pretend not to illustrate the mechanical princi- 234 MATHEMATICAL LAWS OF pies by which such an action can be produced ; I propose only to show, that if such a force be ad- mitted, all the results obtained from the reciprocal action of a galvanic wire and a magnetized needle may not only be explained, but computed, and that the results agree numerically with experiments. 243. The galvanic machine which I have em- ployed, is constructed after the principle of Dr. Hare's colorimoter, differing from his only in the mechanical contrivance for lowering and raising it out of the fluid; it consists of 20 zinc and 20 copper plates, each ten inches square ; but it possesses a power far beyond what is requisite for repeating all the experiments alluded to in the commencement of this paper. 244. That part of the apparatus which pecu- liarly appertains to the experiments I am about to detail, is represented in (fig. 1. pi. 4). A B is an upright stand, placed near the poles of the battery ; a b, cd, are two staples of stout copper wire, driven into the upright, the two ends at b and c passing quite through, as shown at C and Z; and on which two wires are fastened by spiral turns, and with which the communication is made with the poles of the battery ; ef,gh, are two copper wires of the same dimension as the staples, each four feet long, having their ends flattened and drilled so as just to enable them to slide freely upon the wires ab, c d, and the vertical wire fh, also 4 feet ELKCTRO MAGNETISM. 235 in length, which passes through a bole in the top of the table F G H I, and so tight as to render it perfectly fixed. On the plane of the table, which is two feet in square, the circle N E S W is de- scribed about the centre o, and divided into the points of the compass and smaller divisions ; N S, is an index or box ruler, through which the wire fh passes, so that the former may be turned freely about the latter, and set to any proposed azimuth. On this ruler is placed the small compass c', by means of which the deviation at any time may be taken ; c" is another compass placed on the top of the support L c", and is intended to remain fixed in its place, in order to serve as a standard for estimating and comparing the power of the battery at different times. For the principal experiments this apparatus is placed so that the plane of the rectangle of wires is perpendicular to the magnetic meridian ; because in this position the horizontal wires being east and west, they have no effect in deflection the needle from its direction, (at least there is only one ex- ception to this, which will be noticed hereafter,) and consequently all the effect produced upon the needle during the rotation of the index in the circle N E S W, is due to the vertical wire only, except so far as the horizontal wires may increase or diminish the directive power of the needle. 236 MATHEMATICAL LAWS OF This, however, in the cases to which we shall refer is very inconsiderable. 245. But in order that we may know precisely what part of the change of deviation between one situation of the compass and another is actually due to that change of position, recourse must be had to the standard compass, which, always re- maining fixed in its position, may be used as a constant indicator of the strength of the battery. But as the application of this measure to compu- tation is involved in principles not at present ex- plained, it will be proper first to inform the reader of the means which I employ in the first instance to preserve an uniformity of action during every separate course of experiments. These were as follow : 246. The vessel which contains the dilute acid, into which the plates are immersed, holds nearly twenty gallons ; and I begin the experiments with little more than twelve gallons ; moreover' the plates are not, in the first instance, let down to their lowest point. The intensity shown by the standard compass after the connection has been made, some minutes is noted ; and by breaking off and making the contact anew, this same in- tensity occurs again, the power being always strongest when the contact is first made; then when the standard compass returns to its former ELECTRO MAGNETISM. . 237 bearing, the observation with the other compass is taken ; the contact broken, and renewed, and so on as long as the battery retains sufficient power. When this fails, the plates are lowered a little more, the power thus increased, and the observa- tions resumed, till at length the plates being wholly down, and the power too weak, recourse is had to a supply of more dilute acid ; by which means a tolerably steady action is kept up longer than is necessary for any series of experiments of this kind. It will be observed here, that in this case the only use made of the standard compass is to indicate the same intensity of action, and consequently involves no theoretical principle that will be ob- jected to by the most scrupulous theorist or observer, but it will be seen in a subsequent article that this indicator is susceptible of a more extensive application. 247. Having thus made the reader acquainted with the means employed and the precautions adopted, to ensure accuracy, I shall proceed now to explain the principles of computation, and to compare the numerical results thus obtained, with those derived from experiments. According to the hypothesis (art. 242) if we conceive the wire in the first instance to be verti- cal, and the compass placed to the north or south of it, and opposite its middle point, the centre of 238 MATHEMATICAL LAWS OF action will lie in the horizontal plane, and at right angles to the natural horizontal direction of the needle. The latter, therefore, (which for simplicity sake we shall at present consider as indefinitely short with regard to the distance), will at either of those points, be acted upon by two rectangular forces ; viz. the galvanic force in an east and west direction, and which we may denote by/j and the natural magnetic or directive force m ; consequently, according to the principle of forces, the resultant will be expressed by V(/'a + m*) and the angle which it makes with the natural direction of the needle, being called A, we shall have tan A = J- . (1) m Hence the magnetic force being constant, the tangent of the needle s deviation at the north or south will be a correct measure of the galvanic power. 248. We have thus a principle by means of which we may verify a part at least of our theory by experiments. For example; since by the supposition every particle of the galvanic vertical wire acts inversely as the square of its distance from a given point, we ought to find a determined relation between the tangent of deviation, and the length of the wire ; or the length of the wire remaining constant, ELECTRO MAGNETISM. 239 between the tangent of deviation and the distance, provided always that the intensity of the battery remain constant. The apparatus already explained furnishes us with the opportunity of making both these compa- risons. For by means of the sliding horizontal rods, the vertical conducting part of the wire may be shortened in an instant; and in the second case, it is only necessary to slide up the compass to different distances, which may likewise be done so quickly, that it will not be necessary even to have recourse to the standard compass. It is fortunate also that the calculation here alluded to is of the simplest kind. For denoting the length of the wire by 2 /, and the distance of the compass by d ; assuming also x as any variable length, the corresponding elementary action at this distance will be J . and the sum of these actions n u ^ + x ' will be X dMFV which vanishes when x vanishes ; and which there- fore when x = /, and the two lengths are included, becomes arc. tan d d consequently if we denote the deviation, as we have done above by A, we ought to find this force vary inversely as tan A, or co t A [ arc. tan _i } = a constant quantity, t d d J 240 MATHEMATICAL LAWS OF The following are a few out of numerous experi- ments of this kind which I have made, and which have been all found equally satisfactory. 249. Experiments to determine the magnetic, deviation caused by a galvanic vertical wire at different distances. Length of vertical wire 36 inches. Deviation by standard compass. Distance of the other compass from the wire. Mean- observed deviation. A Value of 2 I arc. tan a a = A Constant product. A cot A / 25 O Ditto Ditto Ditto 12 inches 8 ditto 6 ditto 4 ditto 5 37 11 15 16 30 26 30 1877* 34-1OO 47-712 77-500 Mean 190880 171432 161O62 154440 164728 250. When it is considered that these observa- tions were made on a compass needle only one inch in length, and that the divisions extended only to quarter points, it is impossible to expect a closer approximation. The needle and card, however, being delicately suspended, and the latter very distinctly divided, I could depend upon my obser- vations to the nearest degree ; for by means of a strong magnifying power I could always bisect and trisect the quarter points without any very sensible error. * That is, the mean of two observations at each station of the compass ; the contact being changed. The same is to be understood of the deviation with the standard compass. ELECTRO MAGNETISM. 241 EXPERIMENTS 251. To determine the magnetic deviation caused by a vertical galvanic wire ; the length being varied, but the distance constantly 9 inches. Value of Deviation Observed 2 I Constant by standard compass. length of vertical wire. deviation. = A - arc. tan d d = A product. A cot A o / 36 inches 22 30 63-450 15318 24 ditto 18 16 53133 16097 . 16 ditto 12 O 41-633 19557 12 ditto 8 25 33-683 22764 Mean 18220 252. These results (except the last) although not so uniform as the above will be found, not- withstanding as nearly so as we have any reason to expect, particularly as we were not able in these to avail ourselves of the use of the standard compass. I am, however, inclined to attribute the discre- pance between the observed deviation and the com- puted, as the vertical wire shortens, to the approach * The standard compass cannot be used in these experi- ments, because the wire by which it is deflected is neces- sarily shortened with that on which the observations are made. 242 MATHEMATICAL LAWS OF of the horizontal wire, which has a tendency to increase or decrease the directive power of the needle, according to the pole with which the wire is connected, (as will be seen as we proceed) and thereby rendering the action of the vertical wire more or less effective, according to the circum- stances of the connection. (See art. 262.) 253. Having thus far versified our hypothesis by experiment, let us now proceed to the consideration of the deviation in different azimuths. Let Z (fig. 2.) represent the horizontal section of a vertical wire proceeding from the zinc end of the battery downwards, o a particle of the mag- netic fluid whose natural direction is in n s, join Z o, and draw r t, perpendicular to Z o ; then, according to the hypothesis, the direction of the force excited by the wire Z, will be in the line r t. Now the intensity of this force to turn the par- ticle about o, will vary as sin z t o w, or as cos S Z o, and its intensity in the line n s, will vary as sin S Z o, which latter force will be additive to the directive power of the terrestrial magnetism. Let the latter force on the horizontal needle be called m t and the galvanic force in r t f, also the angle S Z o 0, S being the south point of the horizon. Then the particle o, will be urged by the two rectangular forces. ELECTRO MAGNETISM. 243 m + /sin in the direction n s /cos in the direction perpendicular to n s, consequently, denoting the angle of the resultant, or the deviation of the particle from the line n s by , we shall have from the known principle of forces /COS0 tan c = ^ . (e a light hollow copper or brass cylinder having a steel point passing downwards into the agate cup f, fixed to the upper end of the magnet, and let e be a small tube or quill fixed on the wire passing through the top of the cylinder, holding a little quicksilver, and receiving into it the descending conducting wire Z. A B is a piece of wood turned to fit on the cylindrical magnet N S, which has a hollow groove on its upper surface to receive a quantity of quicksilver, into which the lower edge of the cylinder a d is slightly immersed, the sur- face being covered with weak dilute nitric acid. A C is a wire passing into the quicksilver. It is obvious that thus (the contact being made at Z and C) the galvanic circuit is carried from Z through the cylinder a b c d, thence to the quick- silver, and hence again through the wire A C to the other extremity of the battery, whereby the cylinder a b c d is made to become a part of the conducting wire, and it will be found to revolve on its axis with a great velocity, fully equal to that of the magnet in the last experiment ; the direction of the motion, with the arrangement shown in the figure, being from left to right, to a person coinciding in position with the magnet. If we conceive the cylinder to consist of an infinite number of wires, the explanation of this motion is the same as in Experiment VII. T2 276 A COURSE OF EXPERIMENT XI. To exhibit a quicksilver vortex by means of a galvanic wire and magnet. 278. To perform this experiment it is only necessary to take any shallow non-conducting vessel and put into it a quantity of pure mercury, into which is to be inserted the conducting wires Z y C, proceeding respectively from the zinc and cop- per sides of the battery. And if now the north end of a strong magnet be brought under the vessel, the quicksilver round the wire C will begin to revolve about the same, forming a beautiful vortex, the direction of the motion being from left to right. If the magnet be removed under the other wire the same kind of motion will be produced, but its direction will be reversed, and the same change of motion will take place, of course, in each case, by changing the end of the magnet. The explanation here is precisely the same as in the last experiment ; the moveable part of the con- ductor in this case, owing its mobility to its fluid nature, whereas in the former it is due to the peculiar mode of suspension. This very elegant experiment was first made by Sir H. Davy, and although it is referred to in this place for the sake of arrangement and concate- nation, it was made prior to the two former, the ELECTRO MAGNETIC EXPERIMENTS. 277 last of which I was led to institute from the hints furnished by this. EXPERIMENT XII. To exhibit the rotation of the galvanic wire inde- pendently of the galvanic battery. 2/9. For this purpose we must employ the ap- paratus exhibited in (fig. 16) where A B C D is a small copper vessel about 21 inches high, and the same in diameter ; a b c d is another small cylin- der of copper, of the same height, soldered to the former vessel at its lower end d c, a hole being left in the bottom of the former to receive it. The cylinder a If c d is therefore open, and will admit a cylindrical magnet to be passed up, and it will at the same time hold a quantity of dilute acid within the space ADdabcHC: z z' is a zinc cylinder, very light, of rather less altitude than the copper one. To the cylinders a b and z z' are soldered two copper wires, as shown in the figure, the upper one having a steel point proceeding from E downwards and resting in a small metal hole at F, and consequently the cylinder z z' will be free to move upon its point of suspension at F. Things being thus prepared, and the acid placed in the cell as above described, insert through the interior cylinder the north end of a strong cylin- drical magnet, and balance the whole apparatus 27$ A COURSE OF upon it ; when immediately the zinc cylinder will begin to revolve, with a greater or less velocity, according to the strength of the acid, the freedom of motion, and the power of the magnet. I have frequently with this simple apparatus produced a motion amounting to 120 rotations per minute. The only difference between this and the other rotations we have described is, that the galvanic power is here produced by the apparatus itself, instead of having recourse to the battery. For it is obvious that the wire from z %' to E, may be considered as a conductor proceeding from the zinc, and the wire from a b to F, as one from the copper side of the battery ; and consequently, the same effect is to be expected here as in the preceding cases. It is unnecessary to add, that with the north end of the magnet upwards, the motion is from left to right, and the contrary with the magnet reversed. This experiment is due to M. Ampere. The same otherwise. 280. A very pleasing addition has been made to this apparatus by Mr. J. Marsh. It consists in having a second point descending from F, which is made to rest in an agate cup, fixed on the top of the magnet, (fig. 17) and upon which the whole machine is balanced, having a perfect freedom of motion ; and to preserve this balance, the magnet ELECTRO MAGNETIC EXPERIMENTS. 2/9 is placed vertically in a foot. The machine being now charged with acid, a compound motion takes place, the zinc cylinder revolving in one direction and the copper vessel in another, producing thus a very pleasing effect ; the latter however is by no means so rapid as the other, in consequence of the weight of the acid, and in fact that of the whole machine being supported on the lower point. This young man, to whose ingenuity and indus- try I am much indebted for the success of my experiments, is at present employed in an inferior situation in the laboratory of the royal arsenal ; but his dexterity as a workman, his practical chemical knowledge, and his regular conduct, are qualifi- cations which render him deserving of a more respectable and profitable occupation. EXPERIMENT XIII. To show the effect of a horse-shoe magnet on a freely suspended galvanic wire. 281 . Let Z s (fig. 18) denote a part of the galvanic wire, freely suspended by the chain connection at o 9 proceeding from the zinc end of a battery, its lower extremity being amalgamated and slightly im- mersed in a reservoir of pure mercury, having a connection at C with the other extremity of the battery. N S is a horse-shoe magnet, posited as shown in the figure. The contact being now made at C and Z, the 280 A COURSE OF hanging part of the wire o z will be thrown out of the mercury into the position o z f ; the contact being thus broken, it falls by its own gravity into the mercury, by which means the contact being renewed it is again projected, and so on with an extraordinary rapidity ; and if the position of the magnet be reversed, or the contact be changed, the direction of the motion will be changed also, but the effect will be the same. This singular motion may be still explained by the hypothesis that has been advanced; for the wire having a tendency to pass round the north end of the magnet to the right hand, and round the south end to the left hand, is urged by equal forces directly in a line with the open space of the magnet, the equality of the two forces preventing the rotatory motion about either, but both con- spiring to give to the wire the rectilineal motion which has been described. This experiment is also due to Mr. J. Marsh. EXPERIMENT XIV. To exhibit a wheel and axle rotation by means of a horse-shoe magnet. 282. The machine by which this motion is produced is represented in (fig. 19), where A B is a rectangular piece of hard wood, C D an upright wooden pillar, D E a piece of stout brass or ELECTRO MAGNETIC EXPERIMENTS. 281 copper wire, and a b a somewhat smaller wire, soldered upon it at E, on the lower side of which the wheel W, of thin copper, turns freely; Ay is a small reservoir for mercury, sunk in the wood, and g i a narrow channel running into it : H H is a strong horse-shoe magnet. Mercury being now poured into the reservoir f g, till the tips of the wheel are slightly immersed in it, and the surface covered with weak dilute nitric acid, let the connection with the battery be made at i and D, and the wheel W will immediately begin to rotate with a great velocity. If the contact be changed, or if the mag- net be inverted, the motion of the wheel will be reversed ; but in general, the best effect is pro- duced when the wheel revolves inwards. The suspension of the wheel, which I find to answer the best, is shown in (fig. 20). This is a neces- sary consequence of the motion described in the last experiment, by which it was suggested, and is explained on the same principles. EXPERIMENT XV. To exhibit a compound wheel and axle rotation with two horse-shoe magnets. 283. The machine for producing this motion is shown in (fig. 21); AB G D is a rectangular piece of board, having two grooves, about half an inch deep, cut in it parallel to its length. C p, Z q, are two wires having cups for connection 282 $J A COURSE OF at Z and C, and each passing into its respective groove a b, c d, filled with mercury ; into which are slightly immersed the points of the wheels W, W 7 ; these being fixed on an axle W W, and resting upon the two supports m n, r s, brought to a fine edge at n and s, in order to reduce the friction as much as possible, and to give the greater freedom of motion. N S are two horse-shoe magnets, posited as in the figure, with the like poles interior and exterior of the wheels. The apparatus being thus prepared, and the con- tact made at Z and C, the wheels will begin to rotate, and in a very short time will acquire a velocity exceeding very considerably any of the motions hitherto described. It is unnecessary to say that by changing the contact, or by inverting the magnets, the direction of the rotation will be also changed. The usual precaution of covering the surface of the mercury with weak dilute nitric acid, will increase the rapidity of rotation, but it is not actually necessary in this case. EXPERIMENT XVI. To exhibit the terrestrial directive quality of a galvanic wire. 284. It was not long after the first experiments of Mr. CErsted, that the question naturally sug- gested itself, " Has the galvanic wire a directive, ELECTRO MAGNETIC EXPERIMENTS. 283 as well as a general, magnetic power ?" This question was soon answered in the affirmative by M. Ampere, who made use of the following inge- nious construction : A B (fig. 22) represents a piece of wood fixed to any convenient support, through which pass the two wires G, E, and where they remain fixed. At their upper and lower extremities are soldered the small metal cups a, b,c, d. D H I K, &c. is a part of the conducting wire, bent into the form shown in the figure, having small steel points soldered upon it at c and d. These points are inserted into the cups c, d, the upper one only resting on the base of its cup, the other being merely brought into contact with d, by a little quicksilver placed in it for that purpose, by which means the rectangle has a great freedom of motion given to it, the only solid contact being on the point c. Mercury is also poured into the other cups, for the sake of a more perfect and certain communication than that afforded by the mere juxtaposition of the wires. The apparatus being thus prepared, the two wires proceeding from the copper and zinc sides of the battery are inserted into the cups a, b, and thus the- connection is established ; first by means of the wire G with the cup c, thence by means of the contact of the point with the cup and mercury, it is carried forward from c through the 284 A COURSE OF rectangle, to the cup d, whence it proceeds to the cup a. We have already seen that of this connecting wire, the part from c to d has a perfect freedom of motion upon the point at c, and will therefore obey any exciting force. This force, in the experiment in question, is the magnetic influence of the earth, and in consequence of which the rectangle, imme- diately the contact is made, places its plane per- pendicularly to the plane of the magnetic meridian, and to which position it will always return after a few vibrations, if it be drawn out of it by the hand, or otherwise. This arrangement of the moveable conductor is perfectly consistent with our hypothesis, as is obvious without any farther illustration than what has been given in several preceding experi- ments. 285. A differently formed wire, and a more simple mode of suspension, is shown in (fig. 24.) Here a brass or copper wire A C, rests at its bent end A, in a cup containing a little mercury, and is very moveable in azimuth round this point. The other end passes through the centre of a circular piece of pasteboard, and then forms spiral turn- ings in the plane of this circular piece. The wire is attached by thread or silk to the pasteboard disc, and at the point B it turns and descends till its extremity reaches the quicksilver in the cup D. ELECTRO MAGNETIC EXPERIMENTS. 285 The communication being now made at A and D with the battery, the spiral will immediately arrange itself, as in the last case, in a plane perpendicular to the magnetic meridian. This experiment is originally due to M. Ampere, but the mode of suspension described is that of Professor Van den Boss. See Edin. Journ. of Science ', No. XII. A needle upon a different construction, also due to M. Ampere, is shown in (fig. 23.) The same otherwise. 286. The directive quality of the galvanic wire has been since exhibited in a variety of ways, much more simple than that above described, of which we shall only state the following : M* de la Rives apparatus. This consists of a small galvanic combination attached to a cork ; the plate of zinc is nearly half an inch wide, and extends about one and a half or two inches below its cork, its upper end passing through the same ; the slip of copper is of equal width to the zinc, but passes round it, being thus opposed to both its surfaces, as in Dr. Wollaston's construction ; its upper end also appears through the cork. A piece of copper wire, covered with silk thread, is coiled five or six times, and tied together so as to form a ring about an inch in diameter, and the ends of the wire are connected, by solder, one with 286 A COURSE OF the zinc, and the other with the copper slip above the cork. See (fig. 25). When this small apparatus is placed in water, slightly acidulated with sulphuric or nitric acid, the ring becomes highly magnetic, and will arrange itself in a plane perpendicular to the magnetic meridian, or it will at least indicate a tendency to take up that position, but the escape of the bubbles, arising from the decomposition of the water, pre- vents it from preserving a fixed direction. Its magnetic qualities, however, are more ob- viously shown by bringing to it a strong magnet. The one I made use of is cylindrical, about three quarters in diameter, and 18 inches in length. This being applied at the distance of several inches, the ring was immediately attracted, or repelled, accordingly as one or the other of the poles of the magnet was presented, or accordingly as one or the other side of the wire was opposed to the latter. When the result of the application is attraction, the cork will advance towards the extremity of the magnet, and if the latter be held horizontally, and in a line with the centre of the former, this will continue to advance till the pole of the magnet is within the ring, and then proceed with considerable velocity till it reaches the middle of the magnet, where it remains perfectly stationary. If now the magnet be withdrawn, and changed end for end, ELECTRO MAGNETIC EXPERIMENTS. 287 and re-introduced into the ring, the latter will go off from the magnet, turn itself round when quite free from it, again advance, and settle itself as before in the centre. This very simple apparatus, which may be made at the expense of about a shilling, throws great light upon the nature of the electro magnetic action, and proves most satisfactorily that, not- withstanding the intimate relation between the electro magnetic and simple magnetic fluids, they are not identical ; for no possible arrangement of simple magnets can be made that would lead one of them beyond the pole of another to find its state of equilibrium in the middle of the latter. At the same time all the above facts will be found per- fectly consistent with the hypothesis that has been advanced ; for it will be seen, when the wire and cork are in equilibrio, as above stated, that an observer, conceiving himself situated as in (art. 258), will have the north end of the magnet to his left hand, and the south to his right, at equal distances, and acting therefore with equal and opposite powers ; consequently the wire itself ought to be in equilibrio, and when disturbed from it will have a tendency to regain it, and hence be subject to all the conditions of motions that have been described. This is in fact very similar to experi- ment 4, the difference only consisting in this, that in the present case the wire is moveable and the 288 A COURSE OF magnet fixed, whereas in the former the wire was fixed and the magnet free ; the explanation is of course the same in both. Another form of this apparatus is shown in (fig. 26.) Both the above apparatuses are much improved by fixing to the cork a light glass cylinder A B to contain the acid, instead of floating them in it ; the apparatus may then be floated on common water, and all the factg exhibited as above de- scribed. This appendage to the original construction is due to Mr. James Marsh,* already mentioned. 287. Apparatus of Prof. Van den Boss. Here C D (fig. 27) is a copper plate, E G a similar one of zinc, about an inch square, kept from touch- ing each other by the interposition of some small piece of wood : both plates are attached and sus- pended to slender brass wires P and R. The wire P enters at P, in the hollow space formed by a case of veiy thin quills inserted into each other, about 6 or 7 inches long. The end of the wire comes out of the quill at the extremity T, and * This ingenious workman has just completed a portable electro galvanic apparatus j which within the space of little more than a cubic foot, contains not only the necessary galvanic combination, but also all the instruments necessary for repeating nearly the whole of the experiments detailed in this Section. ELECTRO MAGNETIC EXPERIMENTS. 289 returns, being wound as a spiral about it to tbe other extremity V, where it again enters the quill, and proceeds in a right line to R, where coming out it descends, and is attached to the other plate. The whole is suspended in equilibrio to a piece of untwisted silk X. The plates are now dipped into dilute acid, and the whole is suspended at X, when immediately the magnetic quality of the wire becomes manifest ; but, like the former instrument, it is not so sensible to the terrestrial as to the action of a strong artificial magnet, with which its extremities T and V may be attracted or repelled, according as the one or the other pole of the magnet is applied ; and which ought necessarily to be the case agreeably to the explanation given in the preceding case. EXPERIMENT XVII. To examine the inclination of a freely suspended galvanic wire as affected by the terrestrial magnetism. 288. This is an experiment of M. Ampere, in which he employs the apparatus exhibited in (fig. 28), where the galvanic circuit is carried on from the extremity of the battery towards V, passes by V S, through the steel pivot k, placed on the metallic plate N, and thence through the rectangle A B C D ; whence, passing through the tube W. t-W.|N. = 18 37 J Greatest difference 1 40 When Mr. Barlow's plate was attached. /-S.W.byW. = 1732' Ship's head 32' 42 ll 57 J Greatest difference 50 The greatest difference being when the plate was not fixed. (14) Sept. 1, lat. 18N., long. 24| W. ship's head by compass S. W. by W. (dr) = 1710'W. (ddv)= 18 8 W. (c) = 58 Westerly deviation. (dc) - 17 10 W. (v) = 16 12 West. (16) Sept. 9, lat. 8 51' N., long. 19 W. ship's head by compass S. E. by S. (dv) - 1437'W. (ddv) = 14 26 W. (c) =011 Easterly deviation. (d v) = 14 37 W. (v) = 14 48 West. (18) Sept. 17, lat. 1 24' S., long. 25 W. ship's head by compass S. W. (dv) = 1125'W. (ddv) = 11 23 W. (c) - 2 Easterly deviation, (dr) = 11 25 W. (T) - 11 27 West. (15) Sept. 3, lat. 15f N., long. 25 40' W. ship's head by compass S. (dv) = 14 2'W. (ddv) = 13 56 W. (c) = (dv) = 14 6 Easterly deviation. 2 W. (v) = 14 8 West. (17) Sept. 16, lat. 30' S., long. 24 W. ship's head by compass S. W. (dv) = 123l'W. (ddv)= 12 31 W. (c) =00 (d v) = 12 31 W. (v) = 12 31 West. (19) Sept. 20, lat. 9 50' S., long. 31| W. ship's head by compass S. by W. W. (dv) = 613'W. (d d v) = 5 57 W. (c) = 16 Easterly deviation, (d v) = 6 13 W. (v) = 6 29 Wst. MADE ON BOARD H. M. S. CONWAY. 323 (20) Sept. 22, lat. 14 S., long. 33i W. ship's head by compass S. by W. f W. (dv) = 428'W. (ddv) = 4 6 W. (c) = 22 Easterly deviation, (dv) = 4 28 W. (v) = 4 50 West. (22) Sept. 25 , lat. 1 8 40' S., long. 36 40 7 W. ship's head by compass S. W. S. (dv) = 046'W. (d d v) = 26 W. (c) = 20 Easterly deviation, (d v) =0 46 W. (v) =16 West. (24) Oct. 15, lat 23 IVS., long. 43 12' W. ship's head by compass S. S. E. (d v) = 40' E. (ddv) = 4 E. (c) =00 Westerly deviation, (d v) = 4 E. (v) =40 East. (26) Oct. 17, lat. 27 S., long. 46 W W. ship's head by compass S. S. W. $ W. (d v) = 540'E. (d d v) = 5 31 E, (c) =09 Westerly deviation, (d v) =5 40 E. (v) = 5 49 East. (21) Sept. 23, lat 15 52' S. long. 34<"W ship's head by compass S. by W. W. (dv) =347'W. (ddv) = 3 17 W. (c) = 30 Easterly deviation, (d v) =3 47 W. (v) = 4 17 West (23) Oct. 11 , lat 22 55' S., long. 43| W. ship's head by compass W. S. W. (dv) = 42'E. (ddv) = 4 E. - (c) =02 Westerly deviation. (d v) = 4 2 E. (v) 44 East (25) Oct. 18, lat 25 35' S.,long. 44 W. ship's head by compass S.S. W. W. (dv) =459'E. (ddv) = 4 52 E. (c) =07 Westerly deviation. (d v) = 4 59 E. (v) =56 East (27) Oct. 18,lat2841'S.,long.4640'W. ship's head by compass S. S. W. (dv) = 724'E. (ddv) = 7 20 E. (c) =04 Westerly deviation. (dv) = 7 24 E. (v) = 7 28 East. October 24, at anchor off the town of Buenos Ayres. The variation was observed to be 14 3(V easterly. The plate being affixed, no difference could be observed, ship's head by compass N. W. v2 324 A REPORT OF THE EXPERIMENTS (28) Nov. 23, lat. 52J S., long. 64 40' W. ship's head by compass S. by E. (dv) = 2117'E. (ddv) = 21 16 E. (c) =01 Westerly deviation. M. S. GRIPER. 335 attracting matter on board the Griper might be ascertained. To determine this with the ship's head at all the various points of the compass, would have required more time, than could conveniently be bestowed on this occasion. The nature of the service on which we were about to be employed, rendering it neces- sary, that our departure should be as early as possible. Mr. Barlow then considered, that if the amount of the deviation were ascertained at the four cardinal points, it would be sufficient for the present, until opportunities offered for making more numerous and consequently more satisfactory observations hereafter. At the above-mentioned points this amount could be readily obtained, as the ship swung, with her head from east to west, via south, every change of tide, so that it only became necessary to lay a kedge out, by which her head could be brought to the northward at slack water, and to select some remote object, whose bearing could be observed when the ship's head was on those different points of the compass : in this instance, the western end of a clump of trees, situated on the high land, about twelve miles to the S. W. of Sheerness, was fixed upon, so that the consideration of parallax in the bearings taken, arising from a change of position of the ship, during the operation, might be safely neglected. 336 A REPORT OF THE EXPERIMENTS The following is a detailed statement of the experiments made on the local attraction of H. M. S. Griper, at the Little Nore ; in performing which two methods were adopted. First, by carefully observing the bearing of the object selected, with the ship's head in opposite directions, (as for example east and west,) the mean of the difference of the bearings so observed being accounted the local attraction at those points. Secondly, by taking an astronomical bearing of the object chosen, and from thence finding its cor- rect magnetic bearing, by the application of the va- riation of the compass ; the difference between the correct magnetic bearing so found, and that actually observed on board, when the ship's head was at the various points specified, being the angular aberration in the position of the needle caused by the local attraction of the ship, which, for distinc- tion, is designated by the sign , minus, when the observed bearing was less than the correct mag- netic bearing of the object, and +, plus, when it was greater. The former of course taking place when the north end of the needle was drawn towards the east, and the latter when it was drawn toward the west, by the local attraction of the ship. The following table exhibits the amount of the effect produced, when the ship's head was at the various points therein specified. MADE ON BOARD H. M. S. GRIPER. 337 hip's Head. I* ic bearing ject. ~ - ~ r.~ ili = 3 '=^ 2 i Ii tic bearing ject. en N. end WHH drawn d 5 when n to the E. 1 e s if n If * = \ 1 s J-a ^ = *$|i ^| =S = i + i x T 3 + 2 'S-c 'S 4" o S'S 2 ~ S * 11 c %M o '5 J J - s ^ t = ^ - - c S" < J5J U *" *^ "*" ^ .s .s U -" _ ,^ i i | %t2-3 5 c a ^^3"-S f North S66 OW S64545W + 14 South S63 OW S&56W - 1 56 3 6 -! 30 NE 54 30 ditto 10 26 *sw ditto ENE 52 ditto 12 56 wsw 76 ditto + 11 4 24 + 12 East 51 20 ditto 13 36 West 78 30 ditto + 13 34 2710 + 13 35 ESE 52 ditto 12 56 ViXW 77 20 ditto + 12 24 2520 + 12 40 SE 55 20 ditto 9 36 NW 75 ditto + 10 4 1940 + 9 54 From the above table, it is obvious that the north end of the needle was always drawn forward, or towards the body of the ship lying before the compass, by the local attraction, so that when her head was to the eastward, the north end of the needle was drawn to the eastward, or the observed bearing of the object on shore, was lessened ; and vice versa. The object of swinging the ship round from point to point being to enable us to fix a circular iron plate in such a position, with respect to the * With the ship's head at S. W. the object on shore could not he seen. 338 A REPORT OF THE EXPERIMENTS needle of the card used in the foregoing experi- ments, as will produce at the different points a similar set of deviations with those already obtained in the preceding table, which position was found, after numerous trials, when the centre of the plate was 7-r inches below the horizontal plane of the compass card, and 8i inches from the perpen- dicular line passing through its point of support. When this iron plate, which is 44 inches in circumference, is fixed in the above position abaft the compass, in the line passing through the ver- tical line of support of the card, and the point where all the various local attraction of the ship may be supposed united; Mr. Barlow conceives that it will annihilate those deviations arising from the attractive mass lying before the compass, and consequently leave, the needle in its correct mag- netic position ; how far this may obtain will be seen in the cases that follow; where the variation ascertained with the plate so fixed, will be the true variation of the compass ; and that obtained without the plate will be the variation affected by the amount of the local attraction at that point on which the ship's head might happen to be during the observation, and may be termed the deviated variation. It may save trouble to assign the following letters to the different elements in these experi- ments, viz. MADE ON BOARD H. M. S. GRIPER. 339 (d v) Deviated variation, or that observed with- out the plate. (v) Variation of the compass, or that freed from local attraction by fixing the plate. (1.) Sunday, May 18, 1833, when in latitude 65 6' N. and longitude 6 54' E. at 5h 30m P. M. Azimuths of the sun were observed, with and without the plate, when the ship's head was N. and N. E. by compass. Ship's head North, (d v) = 26 1' Westerly. (v) = 24 23 W. Difference = 1 38 or local attraction. Ship's head N. E. (dv) = 11 28' Westerly, (d) =25 2 W. Difference = 13 34 or local attraction. It will be seen that the variations obtained with the plate fixed, differ but little from each other, whilst those ascertained without the plate differ 14 33'. (2-) May 20, A. M. ship's head North by compass, in latitude 66 57' N., longitude 7 20" E. the following variations were obtained, with and without the plate, (d v) = 24 53' Westerly, (v) = 25 30 W. Difference = O 37 z2 340 A REPORT OF THE EXPERIMENTS (3.) May 20, P. M. 1823, ship's head E. \ N. by compass, in latitude 66 15' N. longitude 8 Of E. the following varia- tions were obtained. (d v) = 2 14' Westerly, (v) = 21 15 W. Difference =19 1 (4.) May 21, P. M. 1823, ship's head N. E. f E. by compass, in latitude 66 35' N. and longitude 9 12' E. the following variations were ascertained from azimuths taken with and without the plate. (d v) = 11 58' Westerly, (v) = 22 43 W. Difference = 1O 45 (5.) May 23, A.M. 1823, in latitude 67 21' N. and longitude 94 r E. the following variations were .obtained when the ship's head was N. E. \ E. and West by compass, with and without the plate. First ship's head N. by E. \ E. by compass, (d v) = 18 4' Westerly, (v) = 22 12 W. Difference =48 Second ship's head West by compass, (d v) = 43 5' Westerly, (v) =20 O W. Difference =23 5 MADE ON BOARD H. M. S. GRIPER. 341 (6.) From the near agreement of the variations with each other when the plate was fixed, and the discordances in those ascertained without the plate, it was thought neces- sary permanently to fix a compass with the centre of its card in the same relative situation with respect to the centre of the plate, as that used in these experiments, by which the winds, courses steered, and bearings taken, might be hereafter registered in the ship's log. The following is an extract from the log board of H. M. S. Griper, given as an example of the efficacy of this mode of fixing the plate in these latitudes, and may also serve to explain what in other vessels might be ascribed to currents, or other cajzses. The day's run is between two places ascertained by observation, one in latitude 69 16% r N., longitude by chro- nometer 7 54' E. ; the other in latitude 69 12' 1O" N. and longitude by chronometer 10 14%' E. The first column in the following table contains the hour; the second, knots ; and the third, fathoms ; the fourth shows the courses steered by the compass having the plate fixed; and the fifth, the courses steered by the compass without the plate; the sixth contains the magnetic direction of the wind ; and the seventh is the leeway allowed on the courses steered; in the eighth column are the officers of the watches' initials. 342 A REPORT OF THE EXPERIMENTS H. M. S. Griper at Sea, 25 th May, 1823. Lat. 69 16J' N., Long, by Ch'. 7 54' E. H. K. *. Courses with Plate Compass. Courses by Compass without Plate. Winds by Plate Compass. Lee- way. Officers nitials REMARKS, &c. 1 3 .. ESE EbyN 2 P ts. P.M. 2 3 t NE Fresh breezes and cloudy weather. 3 3 4 P.O. 4. Fresh breezes with a head swell. 4 3 4 5 3 .. 6 3 EbySjS EbyNJN ditto T. D. Variation 2 points west. 7 3 8 3 EbyS ENE NEbyN ditto H. F. 8. Squally weather. 9 3 2 EbySJS EbyNJN Ipt. More moderate set top- gallant sails. 10 3 2 EbyS ENE ditto 11 3 ES ENE ditto P. G. Midnight, moderate, and fine. 12 2 6 , 3 EbyS EbyNJN ipt. A. M. May 26, moderate NEbyN and fine. 2 3 ESE EbyN ditto 3 3 .. 4 3 T. D. 4. Tine clear weather set royals. 5 2 6 6 2 1 4 SEbyEJE E ditto 6 h 30 m tacked. 7 8 1 1 6 NbyE NbyEJE EbyN None H.F. 8. Moderate and fine. 9 1 6 10 1 6 Got spare sails up to dry. 11 2 NJW NJE ENE P. G. Variation 23 westerly. 12 2 Noon moderate and clear. Lat. observed at noon 69 12 7 10" N., Long, by Ch'. 10 14' 15" E. MADE ON BOARD H. M. S. GRIPER. 343 (The annexed diagram shows the apparent course of the vessel by both compasses, P. B.) True North. May 26th, by unconecud Coin pan. Ship's Place hj Observation, May 25th, at Noon. The numerical results stand as follows : Course and distance made good between the observations on the 25th and 26th of May, 1823. Course = S. 85 E., distance 50 miles. By the plate compass course = E., distance 51 miles. By the compass , without the Plate / Latitude observed May 26, = 69 12' 1O" N., longitude by chronometer 10 14' E. Latitude by the plate compass = 69 16' 00" N., lon- gitude 10 17' E. 344 A REPORT OF THE EXPERIMENTS Latitude by the } compass without !> = 69 4?' N., longitude 10 11' E. the plate ) Making a difference in the latitude of 35 miles. May 28, 1823, in latitude 69 8' N. and longitude 14 3(X E. the ship's head being N. E. and afterwards West, by compass ; azimuths of the sun were observed, from which the following variations were obtained. First ship's head N. E. (v) = 1719'W. (dv) = 13 35 W. Second ship's head W. (v) = 1428'W. (d v) = 40 37 W. Difference of variations obtained j first, With the plate fixed .... 2 51' Secondly, without the plate 27 2 (8.) Hammerfest, June 7, 1823. To determine the amount of the effect of the local attraction produced here, the Griper was swung, by means of warps, so arranged as to admit of her head being turned round the compass from point to point successively, and there steadied whilst the bearing of the most distant object seen was taken, whose correct magnetic bearing had been, or could afterwards be obtained, the differ- MADE ON BOARD H. M. S. GRIPER. 345 ence between which and that observed when the ship's head was at the various points of the com- pass, being accounted the local attraction at those points, and is, as before explained, designated by the signs +, plus, and , minus, according as the compass or deviated bearing of the object was greater or less than the correct magnetic bearing of the same. The following table exhibits the amount of the effect produced, in which the first column shows the position of the ship's head as indicated by the compass, with which the bearings were observed ; the second column contains the compass or deviated bearing of the object selected ; and the third, is the correct magnetic bearing of the same ; the fourth column is made up of the differences between the second and third columns, which is the local attraction of the ship at those points where her head was during the observation. 346 A REPORT OF THE EXPERIMENTS I, III , "S 14 ' i SO O O O * 00 oooooooooooocm 1 + + + + + + OOOOGO OOOOOOOCO Oi i <