Let us use the formulas given in Table 9. Formula of artha sahama is: 2nd house – 2nd lord + Lagna. Because the chart is cast for the night time, we should reverse the formula. However, as the note in parantheses after the formula says, this formula should be used for both day & night. Lagna is at 10 Cp 50, i.e. 28050'. The 2nd house is at 10 Aq 50, i.e. 31050'. Lord of the 2nd house is Saturn and he is at 19 Ar 10, i.e. 1910'. So artha sahama = 31050' – 1910' + 28050' = 57230'. We can add or subtract multiples of 360º from a longitude to reduce it to the range 0º to 360º. By subtracting 360º, we get 21230'. This means that artha sahama is at 21230'. This means 230' in Sc or simply 2 Sc 30. Now we have to check whether the C is between B and A in A – B + C. We have to check whether lagna (28050') is between 2nd lord (1910') and 2nd house (31050'). It is – if we start from 1910' and go till 31050', we do encounter 28050' on the way. So we don’t have to add 30º.
Formula of samartha sahama is: Mars – Lagna Lord + Lagna. Because this chart is cast for night time, we should make it Lagna Lord – Mars + Lagna. Lagna lord Saturn is at 19 Ar 10, i.e. 1910'. Mars is at 24 Pi 58, i.e. 35458'. Lagna is at 28050'. So samartha sahama = 1910' – 35458' + 28050' + 360º. We added 360º to make the result positive. We can always add and subtract multiples of 360º from any longitude. So samartha sahama is 3052'. If we start from 35458' and go zodiacally till we reach 1910' (when we reach the end of Pisces, we go to Aries), we do not encounter 28050'. So lagna is not between Mars and lagna lord. So we add 30º. Samartha sahama is finally at 3352', i.e. at 52' in Pi or simply 5 Pi 02.
Formula of vanik sahama is: Moon – Mercury + Lagna. Because this chart is cast for night time, we should make it Mercury – Moon + Lagna. Moon is at 15 Pi 14, i.e. 34514'. Mercury is at 11 Aq 28, i.e. 31128'. Lagna is at 28050'. So samartha sahama = 31128' – 34514' + 28050'. So vanik sahama is 2474'. If we start from 34514' and go zodiacally till we reach 31128' (when we reach the end of Pisces, we go to Aries), we cover a large arc of about 330º. On the way, we do encounter 28050'. So lagna is between Moon and Mercury. So we don’t have to add 30º. Vanik sahama is at 2474', i.e. at 74' in Sg or simply 7 Sg 04.