सिद्धान्तशिरोमणि: गणिताध्याय (भास्कराचार्य - ग्रहगणित, मध्यमाधिकार व स्पष्टाधिकार सटीक)

rate of 15° per hour or 6° per nadi or 10 Vinādis per degree or 60 asus per 60 minutes of arc or as many asus as there are minutes of arc in the right ascension of the mean Sun. So, what is stated by Bhāskara is the difference of the minutes of arc in the mean longitude of the Sun and the minutes of arc in his right ascension ie. (l—a) expressed in minutes. We know that the total equation of time arising out of unequal motion in the true longitude of the Sun ie. ☉ in comparision with the equal motion in his right ascension ie. a is measured by ☉—a which may be expressed as (☉—l) + (l—a) where l is his mean longi- tude, ☉—l = Equation of centre and so the time expressed by ☉—l is the equation of time due to obliquity. The difference l—a arises out of the obliquity of the ecliptic and so the time expressed by l—a is the equation of time due to obliquity. We have the modern formula Cos ω = tan a / tan l so that (1 — cos ω) / (1 + cos ω) = (tan a — tan l) / (tan a + tan l) = (sin a — l) / (sin a + l) ∴ Sin (a — l) = tan² ω/2 sin (a + l). As a is very nearly equal to l, we could write, when expressed in radiaus a—l = tan² ω/2 sin 2l. Thus the maximum difference between a and l arises when 2l = 90° ie. l = 45 degrees ie. at the mid-point of the first quadrant; the mini- mum difference is when 2l = 270 ie. l = 135 ie. at the middle point of the 2nd quadrant. Also the numerical magnitudes of the max. as well as the minimum value are each tan² ω/2 ie. they are equal. Since this is expressed in radiaus, converting into time the numerical value of the max. and minimum equation of time due to obliquity is 9.87′. Thus we can write l—a = 9.87′ sin 2l. Again where l = 225, 2l = 450 so that l—a will have a positive max.; and again when l = 315, 2l = 630 so that l—a will have a negative maximum value. Also when l has values 0, 90, 180, 270 it is zero. Thus the equation of time due to obliquity is zero at ♈, ie. the vernal equinox; +ve in the first quadrant