Page:Encyclopædia Britannica, Ninth Edition, v. 15.djvu/269

Rh MAGNETISM magnet- ism Perma- iron), and on her position with respect to the magnetic nent and meridian during building. A considerable portion of it is manent w iafc &quot;^T ca ^ s ^permanent; i.e., it diminishes gradually as the s ^ip i s worked. This magnetic settling down will take place more rapidly in a steamer which is constantly agitated by the jarring of machinery than in a sailing ship, unless the latter be subjected to shocks from the impact of waves in rough weather. After a time the ship reaches a more or less stationary condition as to per manent magnetism. Along with the phenomenon of sub- permanent magnetism has to be classed what is sometimes Sluggish- called the sluggishness of ships magnetism; this arises ness. from the fact that all the temporary magnetism of a ship which has sailed for some time on any one magnetic course in any one latitude does not at once disappear when the course or the latitude is changed, so that to the permanent magnetism of the ship has to be added a subpermanent magnetism depending on her course and position several day.s before. It is evident that the cause of disturbance at pre sent under discussion is somewhat capricious, and can only ba controlled by constant attention on the part of the mariner. Tempo- The temporary induced magnetism depends on the ship s rary mag- position on the earth, and on her angular position relative sm &quot; to the magnetic meridian; but, so long as the iron in the ship or the position of the compass is not altered, the con stants which determine it remain the same; the disturbance can be foreseen, and either allowed for or mechanically corrected with much greater certainty than in the case of the permanent magnetism. Mathematical Formulas for the Deviation. Let the origin be at the centre of suspension of the compass card; and let the axes of x, y, and z be drawn in the direction from stern to head, in the per pendicular direction from port to starboard, and vertically down wards respectively, the ship for the present being supposed to be on even keel. Let P, Q, R be the components of the magnetic force parallel to these axes arising from the permanent magnetism of the ship; x, y, z the components of the earth s force; and x, y , z the components of the whole force at the centre of the compass card. Then x = x + ax + by + cz + P 1/ = y + dz + ey+fz+Q ..... (103) J-z+gx+hy+lz + R are, according to Poisson s general theory, the fundamental equations of the subject. P, Q, R are constants depending on the permanent, and a, b, c, d, e,f, g, h, k constants depending on the temporary induced magnetism. Nine By a synthetic process of great interest and importance we may rods to show that the nine constants a, I, c, d, e,f, g, h, k are all independ- repre- ent. For example, if we place a rod of practically infinite length sent the with its end before the binnacle, and stretching forward, or with its indue- end abaft the binnacle and stretching aft, it will give rise to the tion con- term ax in x. If a be negative the rod must be finite and it must stants. run under the binnacle, ending a little fore and aft; again, to represent dx, we must have a pair of infinite rods with their ends to starboard and port of the binnacle, and running fore and aft or aft and fore respectively, according as d is positive or negative; finally, to represent^*, a pair of infinite rods with ends above and below the binnacle, running fore and aft or aft and fore respectively. The reader will have no difficulty in completing the scheme, the rule being that the ends lie in the direction of a/, y, or z , and the lengths in the direction of x, y, or z. From equations (103) the deviation of the compass is expressed in terms of the magnetic or of the compass course as follows. Let H be the horizontal force of the earth; H the horizontal force of the earth and ship; -6 the dip; the &quot;magnetic course,&quot; i.e., the azimuth of the ship s head eastward from magnetic north; the &quot;compass course,&quot; i.e., the azimuth of the ship s head eastward from the direclion of the disturbed needle; 5 = -&quot; the easterly deviation of the compass. Then -77 sin 5 = Jt + sin + cos + 1 sin 2^+ cos Poisson .s equa tions. Devia tion in term of magnetic and com pass courses. whert TT/ -g cos 8 = 1 + i) cos - sin f + ) cos 2- &amp;lt;g sin 2( db, a-e . d+b (104), , A= 1 H 2A From (104) we get tan 8 = -? 1 + $ cos f - C sin C+ 5 cos2 - (E sin 2 which gives the deviation on any given magnetic course. From (105) we get by substitution 251 (105), + 8)(]06), an equation connecting the deviation with the compass course. When the deviation is not greater than 20 or so, then (106) may be replaced with sufficient accuracy by S-A + Bsinf + Gcosf +Dsin2f +Ecos2f . . (107), where 21, $, C, g), &amp;lt;, are nearly the natural sines of A, B, C, D, E. In the above it is supposed that the ship is on even keel. Strictly we ought to take into account both the pitch and the heel of the ship; in practice the pitch is always so small as to be of no conse quence, but the heel, especially in a ship under sail, maybe very considerable. When the ship heels through an angle i, the deviation is obtained from the above formula} by writing ,-, b i} &c., in place of a, b, &c., where Effect of heeling. c; = ccosi + isini, = e--(f+h)cosismi-(e-k)sin*i, hi = h + (e-k) cos i sin i-(f+ h) sin 2? , ki = Tc + (/+ h) cos i sin i + (e- k) sin 2 i, If the soft iron be symmetrical with respect to the fore and aft central line, and if i Ije so small that its square maybe neglected, then C,- = C + c - k -- A V & and if 8,- represent the deviation for the given compass course &quot; when the ship heels i to starboard, 8 the deviation on the same course on even keel, then Si = S + ^+JicosC -^cos2C. . . (108). The part of the deviation which depends mainly on 2J, is called the &quot;constant deviation&quot;; it can only arise from horizontal in duction on soft iron unsymmetrically placed. The part depending mainly on U and tf, viz., Bcos + Csin , is called the &quot;semicircular deviation&quot; because it vanishes and changes sign on two diametrically opposite compass courses, or neutral points. The principal coefficient of the semicircular devia tion is $5 = (ctan0 + P/H)/A; ctan0/A arises from vertical induc tion in soft iron before or abaft the compass; P/AH arises from the permanent magnetism of the ship. The second coefficient C = (/tan + Q/H)/ consists of /tan 0/A, arising from soft iron unsym metrically placed, and therefore in general very small, and Q/AH arising from permanent magnetism. $3 can be reduced to zero by a magnet placed fore and aft with its centre in a transverse vertical plane passing through the compass, C by means of a transverse magnet in a fore and aft plane through the compass. In wooden ships the courses for which the semicircular deviation vanishes are nearly north and south; but in iron ships they approximate to those points of the compass towards which the stem and stern lay in building. The terms Dsin2 + Ecos2, depending mainly on the constants Jl and &amp;lt;g, are called the &quot;quadrantal deviation.&quot; This part is alternately easterly and westerly in the four quadrants, vanishing on four compass courses. J) = (a - e)/2A is the principal coefficient of the quadrantal deviation; it depends on horizontal induction in symmetrically placed fore and aft or transverse soft iron. It is in general positive, and in that case can be reduced to zero by two transverse rods with their ends symmetrically placed to starboard and port of the compass. In practice two hollow spheres an inch or so thick are used instead of the rods. The other coefficient &amp;lt; = (d + b)/2 is in general small, as it depends on horizontal induc tion in soft iron unsymmetrically placed. It is only when the ship heels that this coefficient is in general of any importance. . Whereas the semicircular deviation depends both on the geo graphical position of the ship and on the state of its subpermaneut magnetism, the quadrantal deviation is independent of both, and can be corrected mechanically once for all, or allowed for by means of tables constructed from observations made in any one place. The amount of the semicircular deviation in England does not exceed 10 for wooden ships of war, but in iron-built ships it fre quently exceeds 30 even at the standard compass. The quadrantal deviation in wooden ships does not often exceed 1 or 2; in ordi nary iron ships it ranges from 3 to 7, but in some armour-plated iron ships of war it has reached as much as 8 at the standard compass, and 15 for compasses less favourably placed. Constant devia tion. Semicir cular de viation. Quad rantal devia tion.