  This work presents the development and construction of the Heliometer of the
Observat\'orio Nacional/MCTI. This instrument is designed to monitor changes on
the solar diameter with the accuracy of the next-generation solar satellites. A
review of the heliometric method is made and the building and testing of 4
prototypes is described. The instrument has a mirror objective split in
dihedral, formed by the hemi-sections of a parabolic mirror. The materials that
form the instrument have thermal and mechanical stability to 10^(-7). The
number of optical parts is minimized and their quality is greater than
{\lambda}/12. An original software for the automated collection and analysis of
the images was developed. With its latest version fully developed, we conducted
an observational campaign of 9 days, deriving more than 70000 heliometric
images of the Sun. The measured solar diameter has a standard deviation of 0.5
arcseconds, with no instrumental bias, and limited only by the provisional
atmospheric modeling. Therefore, by improving the statistics, an accuracy at
milliarcseconds can be achieved. A study of the correlation between the solar
diameter and the geomagnetic field intensity was made. A correspondence between
the peaks of the series related to solar activity, namely, the semidiameter
variation, the flares index, and the sunspots counts, and the number of
negative peaks on the intensity of the geomagnetic field is found. It must be
cautioned though that it is a complex correspondence, requiring different modes
of response and phase dependence on the stage of the cycle of solar activity.
The straightforward interpretation of observational evidence indicates that the
semidiameter of the Sun seems to vary significantly prior to the corresponding
variations of the geomagnetic field. The effect is most evident in the downward
phase of the solar cycle.
