Coefficients of the Equation of the Diurnal Curve of the Northerly (170) If we transform the equations of the diurnal inequality in the usual manner, by grouping together the corresponding terms, we obtain the following expressions for the diurnal inequality of the northerly force at Dublin for the three divisions of the year, as well as the mean for the entire year, expressed in thousandths of the whole. The time is reckoned from midnight. Summer Months. = 1.40 sin (x + 152°) + 0.65 sin (2x + 301°) Equinoctial Months. E = 0.85 sin (x + 136°) + 0.59 sin (2x + 300°) Winter Months. = 0.13 sin(x + 140°) + 0.35 sin (2x + 290°) Whole Year. E = 0.79 sin (x + 146°) + 0.53 sin (2x + 299°) (171) The following are the calculated values of the force corresponding to the several hours. The general characters of the diurnal change, inferred from these numbers, are the following: I. About 6 A. M., the time varying slightly with the season, the northerly force begins to decrease rapidly; and reaches its minimum value about 10 A. M. or soon after. II. After 10 A. M. the northerly force increases; and the increase continues until about 6 P. M., when the force is a maximum. III. The magnitude of this change is considerably greater in summer than in winter. It is greatest in June, and least in December. IV. In winter there is a second but much smaller variation in the magnitude of the force during the night and morning, the force diminishing until about 1 A. m., when there is a secondary minimum, and afterwards increasing until about 6 A. M., when there is a secondary maximum. This secondary oscillation disappears in the summer months, in which the force decreases continuously throughout the night and morning. The epoch of the least force is the most constant of the critical hours. Its mean time is 10 A. M. in summer, and 10.30 A. M. in winter. On the other hand, the epoch of greatest force varies considerably, being earliest in winter, and latest in summer. The mean time for the summer months is 6.30 P. M.; and, for the winter months, 4.25 P. M. The range of the force is greatest in June, and least in December; and the ratio of the extremes is nearly that of 6 to 1. (172) It will be useful and instructive to combine the two horizontal forces into one. The values of the whole force in the horizontal plane, so obtained, exhibit some features of the phenomenon, which are not readily perceived when its two components are studied separately. This combination is effected by the ordinary rules for the composition of forces. Let p denote the intensity of the whole horizontal force, and the angle which its direction makes with the magnetic meridian, measured to the east of north; then ୧ ୧ The following are the mean yearly values of p and so obtained: Diurnal Inequality of the whole Force in the Horizontal Plane. (173) The numbers of the preceding table are graphically represented in the annexed diagram, the radius-vector of the curve measuring the intensity of the force, and the angle which it makes with the magnetic meridian its azimuth. The corresponding hours are indicated on the perimeter of the curve. It will be seen that in the early hours of the morning,namely, from 1 A. M. to 6 A. M., inclusive, the direction of the force changes little, being for the whole period nearly cast (magnetic). At 6 A. M. the azimuth begins to increase; and it becomes 180°, or the direction of the force is south, between 9 A. M. and 10 A. M. At 1.30 P. M. the azimuth be comes 270°, or the direction of the force is west; and at 6 P. M. it is north. Finally, after midnight, it reaches its stationary position in the east. The intensity of the force is greatest at 1 P. M., and its direction is then nearly west. There is a secondary maximum between 6 P. M. and 7 P. M. preceded by a secondary minimum an hour or two earlier. (174) If we form a similar construction for the separate months, we shall observe, in a very striking manner, the changes in the character of the diurnal inequality dependent upon season. The winter curves differ widely, both in form and magnitude, from those of summer; while the curves for the mouths nearest to the equinoxes are intermediate in both respects. It will be seen that the months resolve themselves naturally into the three groups already selected, viz., the four months nearest to the summer solstice; the four months nearest to the winter solstice; and the four months nearest to |