means of adjusting it north and south, if the centre of the card be made the pivot of a magnetic needle. In the mariner's compass, how ever, it is usual to affix the needle to the card, pointing towards its north and south point, so that the card travels with the needle; and if a pointer (fixed with respect to the ship) mark out the point on the edge of the card which lies in the line drawn through the pivot parallel to the plane which symmetrically bisects the ship, the bearing of the ship's head is shown by the part of the card to which the pointer directs for the time being. Instead, however, of a pointer being used on board ship, it is usual for a mark to be drawn upon the inner surface of the compass-bowl, a line between which and the centre of the compass being always parallel to the ship's keel. To ensure the horizontality of the compass-card, the cylindrical box or bowl in which it is enclosed, is supported in a hoop at opposite points, by pins pro-adding of a counterpoise to the ancient Chinese form of needle, renjecting from it, so as to allow the box to revolve inside the hoop. This hoop is supported in the same manner on pivots, the line of which is at right angles to the first pivots; so that between the rotation of the compass-box in the hoop, and the hoop itself, the former can always find its position of equilibrium, which is the horizontal position. The small oscillations of the apparatus are immediately destroyed by the friction. The apparatus is then said to be supported on gimbles, or gimbals. | as regards mere form. (We, for the present, leave intensity out of the question.) But it must be remembered, that steadiness might amount to sluggishness, and activity might merge into inconvenient oscillation. A modified form, therefore,-one combining both qualifications,—has, through many centuries, been the navigator's desideratum. It is curious to notice how varied have been the attempts to produce a good and unobjectionable compass. Still more are we astonished and humbled to see in the most recent (so-called) "improvement" the very principle of the floating compasses, as described in 1242 by Bailak Kibdjaki ! Scarcely any modification of form had occurred, certainly for the three centuries previous to the time of Richard Norman of Limehouse, in 1590. Norman appears to have introduced some change, in what, however, one would imagine his only improvement to have been, the dering it, by means of a weight sliding on the needle or bar, susceptible of adjustment in removing it from one part of the earth's surface to another. [DIP.] Probably few successful attempts had, till very recently, been made to examine the magnetic conditions and changes to which the needle was subject, or the advantages of one form of the needle itself over another. The only improvements seem to have been those which insured greater nicety of construction. Our countryman Michell subsequently increased the efficacy of the needle by his diffused the magnetic influence in the two arms of the needle; and early in the present century, Captain Kater directed his attention to the imparting of the greatest amount of directive intensity by experimenting largely on the form and temper of the metal of the bar. Several men of science, and among them Professors Barlow, Lloyd, Arago, Faraday, Wheatstone, Airy, &c., and also Messrs. Biot, Hauy, Coulombe, Dr. Gowan Knight, Dr. Scoresby, Sir Wm. Snow Harris, and others, from the delicacy, beauty, and success of their experiments, created an interest in the matter never before felt; but these researches were, with some exceptions, rather confined to the properties of the bar or needle than to the precise form of compass to be used on shipboard. It is however proposed to limit our considerations in this article rather to the mechanical form of compass than to abstract principles, which will be referred to in their proper place under the word MAGNETISM. By whom the suspension now generally used was invented, is alto-invention of what was called the double touch, which symmetrically gether unknown from any document or other evidence. The suspension of the whole machine itself on two circles, whose suspending diameters are at right angles to each other, is, however, on all hands admitted to have been English, though we are still ignorant both of the person who invented it or the period of the invention. It appears to be traditional evidence on which the opinion rests; but a tradition in which rival nations agree, bearing on an invention which would be honourable to any one to have a power to claim, can hardly be supposed an erroneous one. Voltaire, in his essay on 'Universal History,' seems to confirm the English claim, when he admits that "the first who certainly made use of the compass were the English, in the reign of Edward III." He speaks of a Carmelite friar of Oxford named Linna, an able astronomer of those days, having sailed as far as Iceland, when he drew charts of the North Seas, which were afterwards made use of in the reign of Henry VI. But Voltaire should have applied his assertion to an improved form of it, rather than to the circumstance of its use for the first time. Still, even in England, in the time of Queen Elizabeth, the construction was very rude in its execution. The mechanism of the compass is a subject affecting so largely the commercial interests of Great Britain, that not only does the safe transit of the goods of the merchant depend on its proper adaptation to the principles on which magnetism can be available to the sailor, but much of the safety of ships of war, in particular, will be involved in the accuracy of working shown by these instruments. Our unnautical readers will easily understand the importance of a correct manufacture of the compass when the following case is assumed in illustration: Let two ships of war, of equal size, shape, and fittings, and commanded respectively by pilots of equal skill, attempt, in hazy weather, to enter the Thames or some other estuary difficult of approach. Let their compasses be from the same maker and alike, and of ordinary construction, as now used in H.M. navy. It is quite possible that one ship may reach her port in safety, while the other may suffer total wreck; for the secret of the safety or loss of the ships may even have depended on the following simple circumstance: In the one case, the wary old quarter-master at the "con binnacle" shall have attached a piece of packthread to the compass-rim, by lightly jerking which occasionally the compass-card will have been kept more "alive" on its needle point, or have moved more freely on its pin; while the quartermaster in the other ship may have thought such precaution uncalled for, and the sluggishness of the compass have caused an erroneous impression as to her courses. Some remarks, therefore, as to form and manufacture are called for, having for their object the development of a compass system calculated to avert not only existing inconveniences, but those calamities which the introduction of iron into shipbuilding in the merchant service, and the increased armament with heavy ordnance (and especially the adoption of Armstrong's steel gun) into her Majesty's service afloat, would, if unheeded, entail upon the navies of the maritime kingdoms of the world. So much has been written and said upon the compass of late years, so many of our ablest philosophers have devoted their attention to the improvement of the mariner's compass, that, seeing the results of their labours in the complexity and variety of form which have still further complicated the question in the eyes of the unscientific, it will be well to review slightly the past, taking, however, the present condition of the compass as the best and most profitable subject for our consideration. A slight glance at the history of the compass will assist us in our conclusions, inasmuch as the experience of centuries will have its bearing upon and considerably influence them. The most simple and primitive form of the compass appears to have been either the magnetised needle thrust transversely through a cornstalk, and left floating in a screened basin of water [COMPASS, HISTORY OF THE], as used on the Syrian shore; or the small Chinese needle, resting, just below its centre of gravity, upon a needle-point fixed on a wooden stand. The greatest amount of steadiness on the one part, and activity of the needle on the other, seem to have been obtained, so far | While it is admitted by many (and among them by Sir Wm. Snow Harris) that the sensibility and delicacy of the primitive small needle of the Chinese are quite surprising, and while Michell and many others approve of the very light steel bars of the Chinese to be used as compass-needles (because magnetic power increases in a less degree than the friction arising from increase of weight), it is singular that those now in use are quite of opposite construction. As many as, or more than, four or five bars being now attached to the same card, and resting on the same needle-point, their weight, as might be expected, increasing friction to such a degree that even agate caps soon wear out and become useless. Mr. Stebbing, an eminent optician at Southampton, partially obviates the inconvenience of this by substituting the ruby. Few individuals gave more attention to magnetism and to the accuracy of form in the needle than the late Dr. Scoresby; but it appears that no improvement in shape resulted from his long continued labours. Dr. Gowan Knight, the first appointed principal librarian of the British Museum, a man of persevering research in science, who wrote a century since, described the form of compass-needle used in his day by the merchant service as formed of two steel plates bent at their centres and meeting at their ends, and forming the two poles, in this manner: In this he detected a capability of its having no less than six poles, while the greatest available directive force can only exist when there are two. His investigations of the question established the still admitted fact, that the form of needle best adapted to the mariner's compass was the regular parallelopiped, being a straight bar with its narrow dimension placed vertically. Dr. Knight also found that the mode of suspension adopted by the Chinese,-namely, the suspension of the needle at a point a little below its centre of gravity, was the best, as conducive to sensibility. He moreover recommended the use of such a needle without central perforation. Dr. Knight's form of needle was for a long time adopted in H.M. ships; and, as Sir Wm. Snow Harris, with undoubted propriety, in his excellent Manual of Rudimentary Magnetism,' suggests, "it is still worthy of serious attention." Perhaps in no one branch of science has more valuable time been bestowed in the construction of an instrument than in the attempt to perfect the needle and mariner's compass. Sir William Snow Harris has, in a form of compass which bears his name, adopted the suggestions of Norman in 1590, as regards the compensating slides on the bar, and also the opinions of Dr. Knight in 1750, with reference to the form of needle; but its chief excellence is in the amount of directive force imparted to it. He also adopts the light form of needle, but not to the extent found in a Chinese instrument. Enough has been said to show that the precise form and arrangement of the mariner's compass has long been a question of public anxiety; and still more must its consideration press upon us when to the new armament of ships and the increased use of iron afloat (as already noticed), must be added the increased amount of iron carried as cargo, and the circumstance of increased speed of ships which brings them more suddenly into danger; these beset navigation with difficulties only to be surmounted by a well-founded confidence in the form, and simplicity in the mode of using a well-made compass, and this can only be attained by careful investigations and unfettered and disinterested conclusions. It is worthy of remark here that to such an extent has the public mind at times become embarrassed with this consideration, that in 1854 a panic on the Liverpool 'Change nearly excluded for several days the iron ships of the port from freight engagements. It arose from the following circumstance: The late Rev. Dr. Scoresby, with that honesty of purpose and plainness of elucidation for which he was remarkable, informed the merchants of Liverpool of various discoveries as to the causes of local disturbance in iron ships, such discoveries having however a tendency to cast doubt and distrust around that on which hitherto the sailor had relied as his faithful conductor through the pathless oceans of the globe. [LOCAL ATTRACTION.] The insidious workings of the magnetic influence, then for the first time made known to the commercial world, and this too under the sanction of a meeting of the British Association, naturally alarmed the 'ship-owner, appalled the merchant-captain, and lent its aid towards general confusion. Although the discoveries of Dr. Scoresby are of absorbing interest to the philosopher, and have assisted others in their laboratories, yet to the mariner or the ship-owner these subtle workings of the magnetic current ought to have presented very little real difficulty, as was promptly shown in a published address by Mr. Saxby to the ship-owners of Liverpool, and also by the judicious and timely appeals to them by Mr. Grantham, a very eminent marine engineer of that town. The effect of this on the compass question was, the almost immediate production of such a variety of forms of the instrument as were calculated, it was supposed, to pacify the ship-owners; but it actually left the ship-captain burdened and bewildered with novelties and perplexities which even now, in a great measure, render the correction and use of the compass, notwithstanding its importance, the least satisfactory, the most anxious, and the most tiresome of all his work at sea. This competition, however painful in its early operation, had, in a national point of view, a salutary effect. It loudly evoked the hidden talent of officers in the mercantile marine. It aroused their energies, and demanded of them something beyond attention to the mere routine in which they had been trained. Ship-captains soon found among their numbers many men of sufficient talent to grapple with the compass question, and that large and respectable body, relying on themselves rather than on men of reputed science, began to judge for themselves as to the merits of the various toys placed into their binnacles by credulous owners; and many an absurd, though presumptuous and specious form of compass has already been by them consigned to oblivion; many ingeniously contrived instruments, good in themselves but totally unfit for sailors' use, have gradually sunk or are yet gliding visibly into disrepute. With that promptitude, however, which characterises Liverpool merchants, soon after the announcement made by Dr. Scoresby, a Compass Committee, seconded by the authorities at the Board of Trade, was formed, and a vast collection of facts speedily poured in from those who were interested, and measures were taken to assist navigators, which will be clearly and more properly detailed under the head of LOCAL ATTRACTION in this work. nothing resulted from their really praiseworthy and indefatigable But investigations, calculated to modify the generally existing form of mariner's compass: nothing new appears to have been suggested by that body indicative of real improvement in the instrument. Although we must not in this article enter far into the question of local attraction, yet as its causes have led to some modifications in the form of compasses to facilitate corrections for deviation, &c., it is necessary to notice that the Astronomer Royal, having long turned his powerful mind to the question, announced to the world a theory of local attraction which involves the necessity for soft iron as a part of the compass-correcting arrangement. No greater proof of the difficulties which surround the mariner's compass as a nautical instrument COMPASS, THE MARINER'S. 106 with suggestions thereupon, as to somewhat blunt the intelligence, and thereby obscure the truth, even when offered by the AstronomerRoyal himself. It must also be remembered, and indeed it is a fact well-known to the writer, that many merchant-captains who have had their compasses corrected in port by the use of fixed magnets, have found such error and inconvenience arising therefrom (on account of subsequent changes in the magnetic condition of the ship), that sequent on their use, they have pitched their correcting magnets overboard altogether; preferring to encounter the magnetic dangers of the rather than endure the annoying discrepancies and perplexities contampering with changeable and vacillating agents and appliances which were above their comprehension. Such may account for the voyage with a single well-made compass which they did understand, to authorities at the Admiralty rejecting the use of correcting magnets altogether. and soft iron as an instance, how few merchant-captains, unaided by Taking even Professor Airy's theory of moveable adjusting magnets valuable in itself); much less could they use the mathematical formulæ a mechanically convenient correcting apparatus, could follow a learned necessary for its application to the mariner's compass. It remains to discussion on so intricate a science as that of magnetism (however state that a practised compass-maker, a Mr. John Gray, of Liverpool, after study and experiment on an extended scale in which he believed he could corroborate physically the theoretical assumptions of Proan optician of talent well known in all the principal ports of Europe, fessor Airy, contrived a compass arrangement which, apart from all invidious selection, and from a sense of public duty, finds an illustration in this article. compass-needle exist, and each has its advocates, but the following sketches of Gray's compass arrangement give an idea of the form in Several other forms for correction of the which the Astronomer-Royal's suggestions are being carried out. can be adduced than the fact, that, although now some few years have B, Outer bowl, containing fluid, in which, в 2, inner bowl is floated; R and passed since Professor Airy first gave to the world his really simple and elegant theory for correcting by magnets and soft iron, his opinion remains unseconded and unadopted by the Admiralty, by whom correcting magnets are rejected altogether, from extreme and irreprehensible, but possibly overstrained, prudence. It is not improbable that a number of the fallacious methods of correction of the compass produced of late, have so deluged the authorities at the Admiralty R 2, Rims of outer and inner bowls; v s, Springs to keep the bowls in The above has, moreover, an interest from being the form of apparatus independence of thought and rigid impartiality which ought to characterise this work, we may remark that it is said by the Astronomer Fig. 3. 1, Cylinder containing vertical magnet; 2, Keys to raise and lower the magnets; 3, Frame in which the magnets are placed; 4, Magnets; 5, Vertical screws for raising and lowering the magnet frame; 6, Screws to prevent the vertical screws altering their position; 7, Guides to the magnet frame. tions, that no man of experience should rely on any mere system of instrumental correction, independent of actual observation of a heavenly body, much less will he rely solely on a correcting card, or correcting magnets. It may here be well to explain so clearly the present state of things, that the difficulties which have hitherto clouded the brow of the master mariner, plunged him into uncertainties and unnecessary labour, depriving many a weather-beaten and storm-tossed mariner of his nightly rest, may, in those whose intelligence really befits them for their duties, be totally set aside; and that ships may henceforth be navigated with a confidence and security profitable alike to their owners, their crews, and the public. The system of correction at present adopted in Her Majesty's navy is the following: A line-of-battle ship, having on board nearly 500 tons weight of iron guns, shot, and shell, being moreover a screw steamer, with all her massive machinery, an immense iron funnel, iron water tanks, iron anchors, iron cables, &c., is fitting for sea, off one of Her Majesty's dockyards, say for example, Sheerness, either before or after the usual trial trip (generally before), and it is thought necessary to swing her for compass correction. Where no distant and conspicuous object is in sight, this is done by sending a trusty officer on shore at an assumed station, say at the Isle of Grain, with an azimuth compass. The ship is then turned about, so as to bring her head to every point of the compass, and by comparing simultaneous observations (made during the time of swinging) between the ship and the station, and the station and the ship, some notion can be formed of the local attraction on board: thus, if the officer on board at a certain moment sees (for example) his assistant at the station on shore bearing due west by ship's compass, and the assistant on shore at the same time sees the officer on board bearing, not east, the opposite point, but E.S.E., there must be, in one or both instruments, a total deviation of two points, or 22° 30'; but as the compass on shore is carefully placed, so as to be beyond the influence of any local attraction, the deviation is always attributed to some magnetic disturbance on board. These deviations, as found on each point, are carefully noted and collected, and form what is generally called a correcting card. Various methods have been proposed for the registering of these deviations; perhaps nothing more simple and ingenious has been offered than the one by Sir Archibald Smith, in the form issued by the Admiralty to each of Her Majesty's ships. The swinging of a ship, then, is nothing more than a mode of finding the error of her compass at a certain moment; but as there are other methods of ascertaining this so important a fact, it is necessary to consider which of the many is the most accurate, simple, and convenient in application and practice. The swinging of a line-of-battle ship is a work of labour, time, and expense; it often occupies three or four days, the employment of about 300 men, the wear and tear of two, three, or four hawsers, the letting go and weighing two or three heavy kedge anchors;-all this is necessary in swinging a ship of the line. But the advantage of ascertaining precisely the state of such ship is paramount, and we should spare no time, labour, or money, if a permanent result could thus be obtained. It unfortunately happens, however, that any change which may occur in the magnetic condition, or even position of the iron on board, such as the training of a gun, the firing of a broadside, lighting the fires of the engine, moving the ponderous funnel up or down, and various other unavoidable operations on shipboard, may so affect the compass as to render a correcting-card, obtained at one time with so much labour, totally useless at another. It is true that some ships have been found to undergo very little changes during long periods; but, on the other hand, it is equally well known that steamers which have preserved a remarkably equable state of magnetic condition for years, have suddenly shown disastrous changes. To mention only one case out of hundreds, in support of this assertion-an iron steamer, belonging to one of the principal companies of Liverpool, which had shown great uniformity as to local attraction for several years, was, in 1857, proceeding down Channel, under the command of a distinguished officer, who was on his 73rd voyage past that coast. It was a pleasant, calm, hazy evening, and the commander supposed, from her standard compass, that the ship was heading fairly for the Longship's light. But just after sunset a cry suddenly arose from the look-out man, of "Rocks ahead!" and to his amazement the experienced commander found himself running stem-on to the Stones in St. Ive's Bay. It was afterwards found by the writer of this, that the local attraction on board must have varied 16 degrees after leaving Liverpool. The ship and crew were barely saved from destruction; an instance of the high importance of the subject now under our consideration; for we have no means of ascertaining the amount of liability in any particular ship to vary her condition, hence the doubtful value of any correcting-cards whatever. The subtle disturbing element may at any moment, from unforeseen causes, accumu late in this gun, or that range of shot, or in some particular iron knee, or chain, or iron stanchion; so that the wary master or commander may suddenly, and at any time, be deprived of that in his so-called correcting-card, the loss of which would necessarily entail much anxiety, until opportunity presented itself of checking the state of the compass by a celestial observation. Royal publicly to be "perfectly correct," as to the principles under which it is constructed, and "entirely satisfactory" to him. The one property which (while there might seem to be some complexity in the mode of suspension) distinguishes this apparatus from others, is the facility with which the adjusting magnet can, under very simple printed instructions from the maker, be altered in position, so as to compensate the changes produced from alteration in the magnetic condition of the ship. Nothing is intended herein to disparage the beautifully constructed and excellent compasses made by those whose names have been mentioned as some of the principal makers of this country. A very elegant form of compass, in which the magnet is attached to a vertical metallic zone, and the whole inclosed in a glass globe, has been invented recently by a Mr. Gowland, of Liverpool. It is for practical men to satisfy themselves thoroughly if the three grand desiderata of the compass be fulfilled in any one instrument; these are:1. Steadiness, without sluggishness. 2. Activity and sensibility, without oscillation. 3. Facility for correction under local attraction, without complication. COMPASS CORRECTION. Under the word BEARING, some notice has been taken of the most recent improvements in the method of using the compass for nautical purposes. It is ordinarily supposed by landsmen, that with a well-made compass, and a knowledge of the variation thereof, as depending on terrestrial changes [VARIATION], and this to be applied on either hand of any given point, according as the magnetic needle deflects towards the east or west from the true pole of the world, or the meridian, a navigator might find his way to distant parts of the earth; but the need of correction from other causes, daily or hourly in some ships, gave rise to and constitutes what has been so long called and agitated as the compass question. The navigator's desire at sea is simply to know on what angle from a meridian, or true north and south line, his ship is sailing. But before he can arrive at a satisfactory conclusion as to his correct course, the various channels through which local attraction affects his compass have to be estimated; in other words, he must free his compass bearing from all casual local magnetic influences; and this constitutes the work of compass correction. If such were easily performed, on merely knowing the deviation [DEVIATION], an ordinary additive or subtractive operation would suffice; but it unfortunately happens that the quantity of iron used about a ship, and especially in a steamer, presents a combination of disturbing forces so intricate in their rela As an important public question is deeply involved in this scrutiny of the practice of swinging a ship, an operation shown to be not only expensive and troublesome, but absolutely dangerous if too much reliance be placed upon it, it may reasonably be asked why we permit fallacies to exist in our system. In such a cause, it behoves every man of science who would assist the navigator to cast aside all prejudices and mere "customs," and, taking the simple facts of the case, attempt a total revision of the subject of compass correction. But what of the check referred to, as deduced from celestial observation? The question of correction must be viewed under two aspects, namely, the accuracy and labour in the means employed. As a question of spherical trigonometry, its accuracy is mathematically sufficient; and, as regards labour, there are two ways of working, namely, by logarithmic calculation and by construction. The calculation of an azimuth is the resolution of a spheric triangle, in which certain things are given to find others: as in the following example, in which it was possible to use the horizon. Suppose a ship to be in latitude 51° 30′ N., when the altitude of the sun's centre was 40° 25', the sun's declination at the same moment being 20° 2' N.: required the sun's true bearing and the error of the compass, the bearing of the sun by compass being S. 79° 39′ W.: Sun's declination 20° 2' 90 0 Such are the calculations in each case, and they are shortened when altitude and time are both known. Better even would it be to use in this manner a few extra logarithms daily, than to depend on a correctingcard. But there is another and more simple method, not generally known, of solving a spheric triangle with sufficient accuracy for an azimuth, where the nearest degree is enough, because one cannot steer a ship to within less than a degree or two: it is by construction of the spheric triangle. This process, however, would have its inconveniences, although it requires only a plane scale and a pair of dividers or compasses. But these inconveniences have of late been totally obviated by the invention of the spherograph [SPHEROGRAPH], in which, having any three elements of a spheric triangle, the others are found without any calculation, and in a very few seconds; indeed, the Astronomer-Royal has given his written opinion that "for the special purpose of determining azimuths to correct a compass, he thinks the spherograph is excellent." In anticipation of the word SPHEROGRAPH, a sketch of the instrument as it appears when finding an azimuth will in this place be sufficiently illustrative. In the annexed figure the sun is represented as being just on the horizon, the dark lines of the drawing represent the upper sphere, and the dotted ones those of the under sphere as seen through the upper transparent one, both spheres being moveable on the centre c. the horizon), and the oblique circle Pos to represent the hour circle for 7 P.M., and the small circle D o M to represent the sun in its distance from the equator (EQ), or, as it is called, the declination. For the heavens for that day. Now, the part of the circle R must have been all nautical purposes the line Doм may be called the sun's path in from P: on the under sphere no other movement is required: but we see moved on its centre c so as to place it 50° (the required latitude) at a glance that the sun would be at M at midnight, at o when rising or setting, and at D when on its meridian. Hence, the degrees being all printed on the spherograph so as to enable all distances to be read off, no further measure or construction could be required, and we should in this instance find that co on the horizon would measure the rising amplitude and OR the rising azimuth; and c being the east and R the north part of the horizon of the instrument, the sun would rise at about N.E. by E. Suppose it were required to correct the compass at any time of the day, say at 9 A.M., I should select the 9 A.M. hour circle Ps, as drawn on the under sphere of the spherograph, and notice where it crosses the parallel of declination DM at ; and any vertical circle (suppose zN) which, passing through the intersection, cuts the horizon (as at x), would show the bearing in azimuth as measured at HX; and as H is at the south part of the horizon and c is at the east, cx would be very nearly east by south: if the compass showed by it that the sun was at the same time (for instance) E.S.E., the compass would have an error of one point. It seems then that a possibility exists of totally avoiding accidents dependent on compass errors, and by a means sanctioned and approved by the Astronomer Royal; and although changes in magnetic condition cannot be foreseen and prevented, we in reality seem to be able, by merely turning a transparent card on its centre, and at any time, or at any part of the world, and by a process which occupies about ten seconds of time, when any heavenly body is visible, and without requiring any observation for altitude, to place an effectual check upon a compass. In order therefore to put the question in a plain and available form for mariners, the following is proposed as a system applicable at all times to any compass, and on board any ship, be her magnetic condition whatsoever it may: and as this method of ascertaining a true azimuth from celestial observation is totally independent of the horizon, it is available in a few seconds whenever any heavenly body is visible, even in hazy weather, and is therefore much more convenient and expeditious, as it must be more accurate, than any swinging of a ship:: 1. As a mariner always knows his latitude and declination to the nearest degree, and his apparent time to the nearest minute or two, let him, when desirous of merely checking his compass, find at once the sun's true azimuth [BEARING] by the spherograph (or by construction or calculation, at pleasure), and compare the result with his compass bearing of the sun's centre. If his ship be at anchor, and he wishes to examine into her general local attraction, let him, while she is swinging with the tide, take the bearings of the ship's head as she comes to the several points of the compass, noting against each observation the apparent time at which it was taken: then let him seek against each of those times in the spherograph the corresponding true azimuth of the sun (the whole is done by one movement of the upper card of the spherograph on its centre), and by comparison the whole condition of the ship for that day or period is shown, and that too without the usual labour and expense and detention of the vessel during compass correction. As many as 300 bearings have been taken by the late secretary of the Compass Committee at Liverpool, while a ship has been swinging with the tide even in so quick and strong a river as the Mersey. 2. Either register the error so found in one of the admiralty forms of graphic delineation (Sir A. Smith's), or adjust the shifting magnets and soft iron by the astronomer royal's method, by the assistance of Gray's or any other apparatus for effecting this object. [COMPASS, THE MARINER'S.] 3. Let the ship occasionally yaw a few points from her course at least once a day, using the spherograph, and in case of suspected bad weather, up to the last moment at which a heavenly body is visible. By following the above plan the compass need no longer be a source of anxiety to an officer of a ship; for instead of his having, as at present, to depend on an erroneous system of adjustment made in port perhaps many months before, or by the working of an azimuth, for which he cannot always get an altitude, he can dispense with both these methods, and avoid all calculations or complexities whatsoever, whenever any heavenly body is visible. If by night, he would use the star's distance in time from the meridian of the place as if it were in the spherograph apparent time. From the extreme simplicity, infallibility, and rapidity of the above method, it may be suggested that, in passenger over sea steamers, the compass ought to be checked once in every watch; for this purpose a common compass, fitted with Captain Robertson's patent "deviation detector" [BEARING], would, with the spherograph, be all sufficient. COMPASS, NOTATION OF. The notation of the mariner's compass is very simple. If we divide a circle into four equal parts, each of the points which separate those parts may be called cardinal. Pliny called one of these the cardo mundi, or the pole of the world, meaning the north pole. Another ancient author speaks of the cardo cæli, or the pole of the heavens, meaning also the north pole; while Quintilian speaks of the four as the quatuor cardines mundi. Hence, by cominon consent, the north, east, south, and west are called "cardinal points." The formation of the compass card will be easily understood by the following: Let N.E.S.W. represent the cardinal points. The point midway between them is formed by combining the letters; thus, taking the quadrant or quarter of a circle which lies between N. and E., the intermediate point will be called N.E. If we halve this distance, N. and N.E., we call the middle point N.N.E. If we halve now the distance, N. and N.N.E., we call it N. b. E. (or north by east, or north towards east, for any further combining of letters would be inconvenient). In like manner we divide N.E. and E., and the intermediate point will of course be E.N.E. (the nearest cardinal point always stands first when we combine the letters); and again, halfway between E.N.E. and E. would be E. b. N. (or east towards north). It need only to be remembered that the cardinal points, and the midway points between them, such as N.E., S.E., N.W., S. W., always have the word "by" or "b." in the points next to them. The other three quadrants are formed in precisely a similar manner. We thus find the circle divided into 32 parts or points; and as the whole circumference of a circle is divided into 360 degrees, 360 divided by 32 will give 11° 15′, or 111 degrees, as the angle which each point makes at the centre of the compass. When using a compass card, the observer should always consider himself as at the centre of it, and not outside the circle; for the centre of the compass card represents the point of the earth on which he is standing, and the visible horizon may be considered to be represented by the outer rim of the card, on which the degrees are generally marked. The direction in which an object lies is called its bearing. [BEARING.] COMPASSES. This term we suppose to be synonymous with com passers, instruments by which we compass or go round a space. shall here only give such a general notion of differenf kinds of constructions as will perhaps suggest the most convenient for any particular purpose. We 1. Common Compasses, or Dividers.-These are simply two pointed legs on a common pivot, for transferring distances. For drawing a circle the lower end of one of the legs is removed, and its place supplied by a holder for a pencil, or by a steel pen. 2. Hair Compasses.-One of the legs has a part attached to the upper part by a spring, so that by means of a screw a very small motion may be given to the lower end. It is convenient for very accurate dividing, but must be used with care. that the three points of a triangle can be at once transferred. This is 3. Triangular Compasses.-These have three legs and two pivots, so useful only in rough work, as the instrument is difficult to handle. 4. Proportional Compasses.-These consist of two dividing compasses with a common pivot, which, when open, present vertically opposite angles; consequently, the intervals between the points of one and the other are in the same proportion as the legs of one to the legs of the other. The pivot is a clamping screw, which can be transferred along the interval between the pairs of points, and a scale points out how to adjust the instrument so as to alter any line, or surface, or solid, in a given proportion. These compasses sometimes have an apparatus for slight adjustment; but on the whole we consider it as an instrument for rough work. cular to which, with clamping screws, slide a point and a pencil. The 5. Beam Compasses.-This instrument is a cylindrical bar, perpendiuse of it is to describe large circles, or to measure large distances, the It is a safe and sure construction. common compasses being very liable to slip when opened very wide. 6. There is a method of describing a small arc of a very large circle, which it can be drawn up by screws, so that the rod shall form an arc, as follows: An elastic rod of metal is furnished with a rigid bar, on the chord of which is a part of the bar. This may be adjusted so as to pass through three given points nearly in the same straight line, and though the curve then described by guiding the point of a pencil along the rod be not exactly an arc of a circle, yet, for all small flexures, it will come sufficiently near for practical purposes. 7. Caliper Compasses, or callipers, are compasses intended to measure the calibre or diameter of round bodies, and are formed with curved legs, knobbed instead of pointed. Being opened until the body to be measured can only just pass through them, the distance between the two internal extremities of the knobs is of course the diameter of the body. Many other species of compasses have been constructed, but the above are the principal ones in common use. [ELLIPTIC COMPASSES.] COMPLEMENT, that magnitude which, with another, makes up a given magnitude. This is the general meaning of the term; but the most usual specific uses are as follows: Complements of the parallelograms about the diagonal of a parallelogram: through a point in the diagonal draw parallels to the sides; the whole is then divided into two parallelograms on the diagonal, and two which only touch the diagonal at one angle. The latter pair are called by Euclid complements to the former. The complement of an arc or angle is the arc or angle by which it falls short of a quadrant or a right angle. The complement of a logarithm is the number by which a logarithm falls short of 10 thus comp. log. 2 is 10-30103 or 9-69897. The arithmetical complement of a number is the number by which it falls short of the next higher decimal denomination. Thus, ar. co. 936 is 1000-936, or 64; arith. comp. of 83 is 100 - 83, or 17. Beginning from the left, subtract every figure from 9, up to the last significant figure, which subtract from 10. For the complement of life, see DE MOIVRE'S HYPOTHESIS. COMPOSITION. In the gradual progress of mathematical language, this word has acquired a general meaning, as follows: Any one magnitude is said to be compounded of two others, when it produces the same effect as the other two put together. For instance, if we increase a length in the proportion of 3 to 7, and then increase the result in the proportion of 2 to 5, the original line is increased in the proportion of 3 x 2 to 7 x 5, or of 6 to 35. Hence the proportion of 6 to 35 is said to be the proportion compounded of (out of) the proportions of 3 to 7 and 2 to 5. The effects of which it is in our power to form a distinct conception are of two kinds: 1. Those in which there are only two kinds imaginable, and those two diametrically opposite, with one neutral intermediate state. 2. Those in which the diametrically opposites have an infinite number of intermediate gradations. Loss or gain of money is an instance of the first; change of direction of the second. If, at the rate of an inch to a shilling, gains were measured northward from a |