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First Kendra	Sin ( Lj – 2 Ls ) -14.66 )*418
Second Kendra	Sin ( 2 Lj – 4 Ls + 56.90 )* 667
Third Kendra	Sin ( 3Ls – Lj + 77.38 )* 48

These values are to be added if the Kendra is Thuladi ( after the First Point of Libra ) and deducted if it is Meshadi ( after the First Point of Aries ). In Sanskrit it is called Meshadi Rinam & Thuladi Dhanam.  Meshadi is the beginning of the Northern Celestial Hemisphere and Thuladi the begining of the Southern Celestial Hemisphere. 

There are other minor perturbations which may affect only the Vikala ( second ) of the planet’s longitude and hence can be ignored.   

First Kendra	(Sin ( Lj – Ls ) – 1. 15)* 81
Second Kendra	Sin (( Lj – 2 Ls) – 13.08  )* 132
Third Kendra	Sin ( 2 Lj – 2 Ls –  0.58 )* 200
Fourth Kendra	Sin ( 2 Lj – 3 Ls –  61.57 )* 83
Fifth Kendra	Sin ( 3 Lj – 5 Ls – 56.38 )* 162

The Great Jupiter Saturn Perturbation. ( Amplitude 2783 sec, Duration, Laplace Period = 918 years ) 

The English Era + 3102 gives the Kali Era, the Era of the Vedic Calender.  Add 3102 to the Year of Birth to get the Kali Year of Birth.  From that value 4660 is deducted and the value is divided by 918. This gives the Beeja Kendra. Find out the Sin ( Bhuja ) of that, multiply it with 2783 seconds and add it to Saturn’s  longitude if the Kendra is in NCH and subtract it  if it  is in SCH. 

The differential equation for that is

If  Kali Year of birth is xyear  

m = 2783 secs*( Sin ( xyear -4660) * 360/918) 

If m is in SCH, M = M – m

If m is in NCH, M = M +m , where M is the Mean Longitude of Saturn 

The English Era + 3102 gives the Kali Era, the Era of the Hindu Calender. Add 3102 to the Year of Birth to get the Kali Year of Birth.  From that value 4660 is deducted and the value is divided by 918. This gives the Beeja Kendra. Find out the Sin ( Bhuja ) of that, multiply it with 1187 seconds and add it to Jupiter’s longitude if the Kendra is in NCH and subtract it  if it  is in SCH. 

The differential equation for that is

If  Kali Year of birth is xyear  

m = 1187 secs*( Sin ( xyear – 4660) * 360/918) 

If m is in SCH, M = M – m

If m is in NCH, M = M +m , where M is the Mean Longitude of Jupiter

There are other minor perturbations which can be ignored.  

( Lj = Mean Longitude of Jupiter; Ls – Mean Longitude of Saturn. These longitudes are Tropical or Sayana. ).