ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

302 BRAHMAGUPTA'S ASTRONOMY : ITS HIGHLIGHTS
K. S. Shukla has provided the following rationale to the
rule cited above :
The fraction of the intercalary month (obtained in the
rule) = (adhimāsaśeṣa) / (solar days in a yuga), in mean lunar months.
= (adhimāsaśeṣa) / (lunar days in a yuga), in mean solar months. (i)
The fraction of the omitted lunar day (obtained in the
rule)
= (avamaśeṣa or āhnika) / (lunar days in a yuga), in mean civil days.
= (avamaśeṣa) / (civil days in a yuga), in mean lunar days.
= (avmaśeṣa × 60) / (civil days in a yuga), in mean lunar ghaṭīs. (ii)
The fraction of the intercalary month corresponding to the
above fraction of the omitted lunar day
= [(intercalary months in a yuga) × (avamaśeṣa)] / [(lunar days in a yuga) × (civil days in a yuga)]
in mean solar months. (iii)
Adding (i) and (iii) and multiplying by 30, the total
fraction of the intercalary month
= { (adhimāsaśeṣa) / (lunar months in a yuga)

• [(intercalary months in a yuga) × (avamaśeṣa)] / [(lunar months in a yuga) × (civil days in a yuga)] }
  in mean solar days. (iv)
  Suppose that m lunar months and d lunar days have
  elapsed since the beginning of Caitra. Then, treating them as
  mean lunar months and mean lunar days, m months and d days
  denote the time elapsed since the beginning of mean Caitra up
  to the beginning of the current lunar day (treated as mean lunar
  day). As (ii) is the interval, in mean lunar ghaṭīs, between the
  beginning of the current lunar day and the mean sunrise on that
  day, therefore
  m months + d days + (ii)
  denotes the time in mean lunar months, days, ghaṭīs¹ elapsed

1. 1 hour = 2½ ghaṭīs; 1 ghaṭī = 60 vighaṭīs; 1 vighaṭī = 60 pravighaṭīs.