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An examination is made of Emiliani's curve (1961, Fig. 1) which shows the variations in temperature of the equatorial Atlantic Ocean water for the last 300000 years. In this curve seven large and twenty-three small oscillations are present. The period of the small oscillations (13000 years) almost equals the half precession period. This fact is explained with help of a slight improvement of Milankovitch's theory (section 1). Minimum equatorial temperatures are expected when Π = 90° or 270°, where Π denotes the perihelion length of the Earth's orbit. A search for the precise values of the periods in Emiliani's curve is carried out by means of Fourier analysis and periodogram analysis (section 2). The Fourier spectrum (Fig. 8) shows two significant main periods, P1 = 40000 years and P2 = 12825 years. The first period agrees well with the period of the oscillations of the obliquity ɛ of the ecliptic. The second period corresponds very well with the half precession period. Also the periodogram analysis and a probability consideration demonstrate significantly that Emiliani's curve shows an oscillation with the half precession period. From the two main periods of the curve a small increase in temperature is expected to occur for the equatorial Ocean water during the coming 3000 years. Still later a decrease in temperature is expected until in about 10000 years a new glaciation may occur.