Certain aspects of the Sun and resulting geomagnetic disturbances can be studied better on the source surface, an imaginary spherical surface of 3.5 solar radii, than on the photospheric surface. This paper presents evidence that the Sun exhibits one of the most fundamental aspects of activities most clearly during the late-declining phase of the sunspot cycle. It is the period when 27-day average values of the solar wind speed and of geomagnetic disturbances tend to be highest during the sunspot cycle.Important findings of this study on the late-declining phase of the sunspot cycle are the following:1. By introducing a new coordinate system, modifying the Carrington coordinates, it is shown that various solar activity phenomena, solar flares, the brightest coronal regions, and also the lowest solar wind speed region, tend to concentrate in two quadrants, one around 90 • in longitude in the northern hemisphere (NE) and the other around 270 • in longitude in the southern hemisphere (SW). For this reason, the new coordinate system is referred to as the NESW coordinate system. 2. It is shown that the above results are closely related to the fact that the neutral line exhibits a single wave (sinusoidal or rectangular) in both the Carrington coordinates and the NESW coordinate system during the late-declining phase. The shift of the neutral line configuration during successive solar rotations during the late-declining phase causes longitudinal scatter of the location of solar flares with respect to the neutral line in a statistical study. The NESW coordinate system is designed to suppress the shift, so that the single wave location is fixed and thus a 'nest' of solar flares emerges in the NE and SW quadrants. 3. It is also shown that the single wave is the source of the double peak of the solar wind speed and two series of recurrent geomagnetic disturbances in each solar rotation, making the 27-day average solar wind and geomagnetic disturbances highest during the sunspot cycle. The double peak is a basic feature during the late-declining phase, but is obscured by several complexities which we identified in this paper; see item 8. 4. The single wave of the neutral line configuration can be approximated by three dipole fields, one which can be represented by a central dipole (parallel or anti-parallel to the rotation axis) and two hypothetical dipoles on the photosphere. This configuration is referred to as the triple dipole model. 5. The location of the two hypothetical photospheric dipoles coincide with the two active regions (solar flares, the brightest coronal region) and also the lowest solar wind speed region in the NESW coordinate system; the lowest solar wind regions are the cause of the valleys of the double peak of the solar wind speed.Space Science Reviews (2005) 120: 27-65