I found a discussion on My Life Blog which offers a formula for finding the coordinates of a PD Theodolite,which I though might be helpful to a surveyor using this type of instrument.

Calculation of measurement with measurement theodolite.melakukan with Theodolite would be more time consuming calculations Dlm coordinates and elevation data let alone done manually using a calculator without the help of software ms excel at this pc.berikut calculation formulas with manual measurement involves counting theodolite.Perhitungan flat distance (D) skewed distance (S) and height difference (△ H). and after that we calculated would begin to calculate the coordinates X, Y, Z.
The formula: 
D = ((ba-bb) -100) * (sin V) ^ 2

S = ((ba-bb) -100) * sin V
△ H = tan (90-V) * D + IH-TH
Coordinate

Kor.X = SIN AZ * D + X ST

Kor.Y = COS AZ * D + Y ST 

EL .= △ H + EL ST where the vertical angle V = AZ = Azimuth ST = Station tool tool TH IH = high high = target / beacon meters

Has anyone ever used this formula or this instrument?  Have anything to add or change in this formula?