Nilakantha's Annual Horoscopy

...the days, ghatis Ghati: a traditional Indian unit of time equal to 24 minutes, and palas Pala: a unit of time equal to 24 seconds of the birth time should be added. Then, divide the topmost figure by seven; the remainder indicates the day of the week. In this book, one should declare the "Year Entrance" original: "Abda-pravesha" or "Annual Return" based on the resulting weekday, ghati, and pala. This should be known as the current weekday of the return. ॥ 16 ॥

The "Years Elapsed" original: "Abda," referring to the number of years since birth should be multiplied by eleven original: "Shivaghna," where Shiva represents the number 11, then increased by its own one hundred and seventieth part original: "Svakhadrimdulavadhya": Sva (self) + Kha (0) + Adri (7) + Indu (1). To this, add the lunar day of birth original: "Janma-tithi", counting from the first day of the waxing moon. Then, subtract or divide by thirty original: "Svagnishodhita": Agni represents the number 3, here meaning 30. The remainder indicates the lunar day on which the Year Entrance occurs. There is no absolute rule that the Year Entrance must fall on this exact lunar day; sometimes it occurs on the preceding or following lunar day. In this matter, the calculated weekday is the true authority. Among the three possible lunar days, the one that coincides with the previously calculated weekday is to be known as the true date of the Year Entrance. Where a remainder is found after division, the quotient is discarded and only the remainder is taken by the learned scholars. ॥ Now the sequence for a practical example is written. First:

Now the method for determining the Lunar Day (Tithi) is stated: The years elapsed, multiplied by eleven, increased by their one hundred and seventieth part, and reduced by thirty, then added to the birth lunar day; on that lunar day, the Year Entrance occurs. ॥ 17 ॥

An example of a birth is now written: In the year 1648 of the Vikrami Era Samvat 1648, approx. 1591 CE, 1513 of the Shaka Era, in the month of Magha, during the waxing fortnight, on the 1st lunar day, a Wednesday. The time was 36 ghatis into the day, under the Shravana star (nakshatra) which lasted 54 ghatis, with the Vajra yoga lasting 6 ghatis. On this auspicious day, the time elapsed from sunrise was 37 ghatis and 53 palas. The elapsed night time was 12 ghatis and 31 palas. The local latitude Akshama was 7;30 and the longitudinal correction Deshantara was 30. The Sun’s position was 9 signs, 7 degrees, 30 minutes, and 6 seconds. The rising sign Lagna at birth was Capricorn at 5 degrees, 10 minutes, 53 seconds, and 50 thirds.

Now, the example for the Year Entrance: The Shaka year at birth was 1513. Subtracting this from the current Shaka year of 1550 approx. 1628 CE, the remainder is 37, which is the number of elapsed years. This is increased by its fourth part (9;15;0), making the total 46. The 37 elapsed years are also multiplied by twenty-one, resulting in 777. This is divided by forty, giving a result in ghatis and palas of 19;25;30. Adding this to the previous calculation of 46;15;50 results in 46 ghatis, 34 palas, 25 vipalas, and 30 thirds. When added to the birth weekday and time (4 days, 37 ghatis, 52 palas), the sum is 51;12;18;30. Dividing the total days by seven, the remainder is 2 Monday, at 12 ghatis, 18 palas, and 30 vipalas—this is the moment of the Year Entrance.

Now, he states another method for bringing about the Year Entrance: The constant for the year Varsha-dhruvanka is 36;15;13;30. This is multiplied by the 37 elapsed years, resulting in 135;14;34;25;30. To this, add the birth weekday and time of 4;37;52...