COMMISSION 27 OF THE I.A.U.
               INFORMATION BULLETIN ON VARIABLE STARS
                            Number 1442

                                                      Konkoly Observatory
                                                      Budapest
                                                      1978 June 27


 TIME SHIFT-PERIOD-AMPLITUDE RELATION FOR PULSATION VARIABLES

1. Introduction

The phenomenon, that several pulsation variables show a delay in
time (time shift) between the instants of maximum light, as one
goes from shorter to longer wavelengths, is wellknown.
The effect has been observed in AI Velorum stars, Beta Canis Majoris
type pulsators, cepheids and long period Mira stars.
The aim of the present investigation is to find out, if there
exist a relation between the mean value of the time shift, the
period and the amplitude of a pulsation variable.

2. A linear time shift-period-amplitude relation
From our observations at the European Southern Observatory (ESO),
during 1970-1977, we have estimated by means of a cubic spline
fit procedure, the instants of maximum light for the pulsation
variables SX Phe, AI Vel, V703 Sco and BS Aqr (AI Velorum stars).
By comparing the values of the U and V filter, we were able to
deduce a mean value for the time shift between U and V maximum
light.
   Table 1 gives a review of some intrinsic properties of the 
investigated stars.


                                  Table 1

Star       Type   Period  Amplitude    P/DeltaV    Observed mean     Calc.time
                  (min)  DeltaV (mag)             time shift (sec)  shift (sec)

SX Phe    AI Vel    80      0.45        177.8        30     (47)*      30
AI Vel      "      160      0.41        390.2        47     (32)       50
V703 Sco    "      166      0.32        518.7        68     (12)       61
BS Aqr      "      288      0.44        654.5        70     (10)       73

*number of observed maxima

   Since we believe, that there exists a linear relation between time
shift, period and amplitude, we will write now this relation as
follows

   Time shift (seconds)= alpha x Period (minutes)/amplitude V (magnitudes)+beta

where alpha is the slope and beta the interception (least square solution).
   All observations of Table 1 could be assembled into the following 
particular TPA relation

           DeltaT = 0.09056 P/DeltaV + 14                  (1)

where DeltaT is the time shift, and the other symbols have their 
ordinary meaning. The last column of Table 1 shows the calculated
value of the time shift with the aid of eq. 1.


                                 ERIC W. ELST

                            Royal Observatory at Uccle