For calculating it, we have from eq. (118), page 879: H' In this, H is the Earth's horizontal intensity; H' that of Ship and Earth combined; and ồ the deviation proper to the magnetic course: thus the factor.cos & expresses the procedure above described for obtaining λ. The numerical work will be illustrated by data relative to the steering compass of the U. S. S. SAN FRANCISCO before it was compensated. The Ship was swung and a Table of Deviations obtained; this showed a maximum of -29° 30' on compass course SE. by S. The table was analyzed on Form 10, and the coefficients obtained as follows: A = -0° 25′; A = .007; B = -11° 44′; B=-.233; C=+5° 46'; C=+.085; D=+16° 38'; D=+.29; E=+0°11′; &=+.005. While the ship's head was N. 38° 30′ W. magnetic, with a westerly deviation of d = 4° (whose cos=+.9976), a horizontal needle was oscillated, making ten oscillations in 26.36 = T'; on shore, it made the same number in 22o.5=T; (22.5)2 T2 H' hence 2 = (26.36) T2 H T'1⁄2=Ħ =.728; from the direction of the ship's head, 【=321° 30′, of which the sine is —.6225, and :+.7826; 25=643°, or 283°(+360°); the sine of this is .9744, and cosine +.2249. Substituting these values in (258) it becomes COS = λ=(.728)(+.9976) I 1+(−.233)(+.7826) −(+.085)(−.6225)+(+.29)(+.2249) (+.005)(-.9744) Hence = .772, which indicates considerable decrease of directive force by the ship. When oscillations are made with the ship heading successively on four or more equidistant magnetic courses, the quantities in eq. (258) containing functions of the courses will reduce to zero, as explained in Art. 296—[6], H' leaving only the factor .cos ; denoting this for the several headings by 0, 1, 2 ... n, eq. (258) becomes Table 76 is an example of this from experiments on the U. S. S. ALBATROSS, on eight magnetic courses. Although, on this ship, has a fairly good value-still the extremes in col. (6), Table 76, of which is the mean, show the compass to have indifferent surroundings. From the foregoing, it is seen that can be determined in two principal ways-1st, by oscillation experiments on one magnetic course, and ascertaining the deviation proper to that, and also the deviations on 8, 16, or 32 equidistant compass-courses, from which to deduce the coefficients; then computing by eq. (258): 2d, by oscillation experiments on four or more equidistant magnetic headings, and determining the deviations proper to them, when the computation is by eq. (259). The latter affords a view of the individual values of as the ship swings through 360°, and is the best mode of determining it; the first method gives no such view, and is delusive in so far that it may indicate a fairly good average, without showing those quarters in which the directive force may be very weak. CHAPTER XXIV. VARIOUS METHODS OF DETERMINING THE MAGNETIC COEFFICIENTS; THEIR FLUCTUATION WITH GEOGRAPHICAL CHANGE; AND COMPUTATION OF THE DEVIATIONS. Section One: B, C, and D from Observations for Deviation on Three Specific Points of a Quadrant. 321. Northeast quarter. The coefficients A and E being generally small, and D practically constant, it is desirable to have a short and speedy method for determining fluctuations in the coefficients that are most liable to change, viz., B and C: such is the method of this section. Furthermore, it is a means of determining B, C, and D ab initio from three very convenient points-the two cardinal and principal quadrantal points of any quadrant; and from them computing a table of deviations by equations to be given in Art. 327: in this case A and E are to be considered zero. The great advantage of acquiring at first a thorough knowledge of the ship's magnetic character by survey in dock, oscillation experiments with horizontal and vertical needles, and swinging on 32 points, should never be lost sight of or omitted: all short methods-such as those of this chapter-should be deemed a means of detecting change in original conditions, rather than replacing a complete investigation. The formulas for each quadrant, with numerical examples, will be given in this and the next three articles. From eq. (124), page 880, we have sin d=A.cos d+B.sin '+C.cos' +D. sin (25′+ d) +E. cos(25′+d). (260) Expanding sin (25′+d) and cos(25′+d) by means of (30) and (31), Art. 296, eq. (260) becomes sin d=A.cos d+B. sin '+C.cos +D.sin 2.cos d+D.cos 2.sin d (261) +.cos 2.cos d-E sin 2g'.sin d The quantities ò, S, and y' applicable to the points employed will receive the designations they have on Fig. 511; and it should be recalled that S,, S,, etc., may be used for both sines and cosines, and that their values are specific for 。° and 90°. For NORTH, NORTHEAST, and EAST, (261) becomes successively sin d=A.cos do + B. S2+C. S ̧ + D. S ̧ cos d。o 0 8 0 +D.S. sin o,+E.S, cos do-E.S, sin d。. (262) sin d1 = A.cos d1+B. S1 + C. S1 + D. S ̧ cos d 4 +D.S, sin d1+E. S1 cos d1-E. S, sin d1. (263) sin d.cos dg + B. S ̧ + C. S.-D.S, cos d 0 -D.S, sin d.-E.S, cos d.-E.S, sin d. (264) 8 8 From (264) we obtain the value of B, and from (262) that of C as follows, since S, o, and S, I: = B = (1+D) sin d. - (A - E) cos d = =(1+D) sin d,, if A and E = zero. (265) C = (1-D) sin d。 − (A+E) cos d = (1-D) sin do, if A and E = zero. (266) |