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vs.27-28 ] 55 the prime vertical shadow of the gnormon. When this condition is not satis fed, the Sun in the northern hemisphere would not cross the prime vertical and likewise the prime vertica1 shadow of the grommon would not exist When the Sun is in the southern hemisphere, the Sun does not cross the prime vertical above the horizon and so the prime vertical shadow of the grnommon does not exist A rule for the determination of the Sun's tropical longitude from the Sun's prime vertical altitude 24-25. The Rsine of the Sun's altitude (when the Sun is on the prime vertical), determined from the method of the shadow, should be multiplied by the Rsine of the latitude and divided by the Rsine of the (Sun's) greatest declination: the resulting Rsine, in minutes of arc, reduced to arc or that subtracted from half a circle (i.e., 180°) is known as the (tropical) longitude of the Sun determined from the shadow of the grommon when the Sun is on the prime vertical (according as the Sun is in the first or second quadrant, i.e. according as the prime vertical shadow or midday shadow of the grnommon is decreasing or increasing day to day).* This rule follows from the previous one combined with rule i. 16 A rule for finding the arc corresponding to a given Rsine : 26. The number of the tabulated Rsine-differences which can be subtracted from the given Rsine, as also the remainder (of that subtraction, if any) 'divided by the current (i.e., next) Rsine-difference, should be (severally) multiplied by 225: their sum is the (required) arc.* This rule is the converse of that given in i. 2(ii)-3(i) above. It has been stated here because it is required in the preceding rule for calculating the are corresponding to the Rsine of the Sun's longitude. A rule for finding the midday shadow of the grnommon with the help of the Sun's declination and the latitude of the place: 27-28. In case the Sun is situated on the meridian (1it. in