1 Introduction

HR 5437 is a 6.24 magnitude star situated at $\alpha = 14^{\rm h}30\hbox{$.\!\!^{\rm m}$}4$,$\delta = + 60^{\circ}26\hbox{$.\mkern-4mu^\prime$}7$ (1950 coordinates). The photoelectric observations of HR 5437 were carried out between 1986 and 1988 at the Piszkéstetö Station of Konkoly Observatory of Hungary and the Xinglong Station of Beijing Astronomical Observatory of China. From the data obtained at the Xinglong Station in 1988 Jiang & Li (1988) discovered HR 5437 to be a $\delta$ Scuti variable star. But they did not give the values of frequency. From the 1988 data set obtained at the Piszkéstetö Station and the Xinglong Station, Paparó et al. (1990) gave two frequencies. The first frequency is 8.437 cd^-1, the second is 12.362 cd^-1. Joining the 1988 data set and the data obtained at the Piszkéstetö Station in 1986-1987, Paparó et al. (1990) gave two other frequencies. The first is 8.537 cd^-1 and the second is 11.376 cd^-1. Paparó et al. pointed out that due to the poor quality of the data distribution and the complex structure of the spectral window the precise values of frequencies were not found. Li & Jiang (1992) obtained only one frequency of 11.390 cd^-1 from their data obtained in 1991. However, comparing with the results given by Paparó et al. (1990), Li & Jiang (1992) thought that the frequency of 8.537 cd^-1 given by Paparó et al. (1990) was the fundamental frequency, the frequency of 11.390 cd^-1 was the first overtone frequency. The situation is quite confused.

In this paper we wish to make period analyses not only for present data, but also for the data obtained by Li & Jiang (1992), and also for the joint data of the two data sets to obtain more accurate frequency solution and investigate the pulsation modes of this star.