Spectroscopic orbital elements and/or related parameters have been determined for eight binary systems, using radial-velocity measurements that have a typical precision of about 15 ms⁻¹. The orbital periods of these systems range from about 10 days to 26 years, with a median of about 6 years. Orbital solutions were determined for the seven systems with shorter periods. The measurement of the mass ratio of the longest-period system, HD217166, demonstrates that this important astrophysical quantity can be estimated in a model-free manner with less than 10% of the orbital cycle observed spectroscopically.\\ Single-lined orbital solutions have been derived for five of the binaries. Two of these systems are astrometric binaries: β Ret and ν Oct. The other SB1 systems were 94 Aqr A, θ Ant, and the 10-day system, HD159656. The preliminary spectroscopic solution for θ Ant (P~18 years), is the first one derived for this system. The improvement to the precision achieved for the elements of the other four systems was typically between 1--2 orders of magnitude. The very high precision with which the spectroscopic solution for HD159656 has been measured should allow an investigation into possible apsidal motion in the near future. In addition to the variable radial velocity owing to its orbital motion, the K-giant, ν Oct, has been found to have an additional long-term irregular periodicity, attributed, for the time being, to the rotation of a large surface feature.\\ Double-lined solutions were obtained for HD206804 (K7V+K7V), which previously had two competing astrometric solutions but no spectroscopic solution, and a newly discovered seventh-magnitude system, HD181958 (F6V+F7V). This latter system has the distinction of having components and orbital characteristics whose study should be possible with present ground-based interferometers. All eight of the binary systems have had their mass ratio and the masses of their components estimated.\\ The following comments summarize the motivation for getting these results, and the manner in which the research was carried out. \\ The majority of stars exist in binary systems rather than singly as does the Sun. These systems provide astronomers with the most reliable and proven means to determine many of the fundamental properties of stars. One of these properties is the stellar mass, which is regarded as being the most important of all, since most other stellar characteristics are very sensitive to the mass. Therefore, empirical masses, combined with measurements of other stellar properties, such as radii and luminosities, are an excellent test for competing models of stellar structure and evolution.\\ Binary stars also provide opportunities to observe and investigate many extraordinary astrophysical processes that do not occur in isolated stars. These processes often arise as a result of direct and indirect interactions between the components, when they are sufficiently close to each other. Some of the interactions are relatively passive, such as the circularization of the mutual orbits, whilst others result from much more active processes, such as mass exchange leading to intense radiation emissions. \\ A complete understanding of a binary system's orbital characteristics, as well as the measurement of the all-important stellar masses, is almost always only achieved after the binary system has been studied using two or more complementary observing techniques. Two of the suitable techniques are astrometry and spectroscopy. In favourable circumstances, astrometry can deduce the angular dimensions of the orbit, the total mass of the system, and sometimes, its distance from us. Spectroscopy, on the other hand, can determine the linear scale of the orbit and the ratio of the stellar masses, based on the changing radial velocities of both stars. When a resolved astrometric orbital solution is also available, the velocities of both stars can allow the binary system's parallax to be determined, and the velocities of one star can provide a measure of the system mass ratio.\\ Unfortunately, relatively few binary systems are suited to these complementary studies. Underlying this difficulty are the facts that, typically, astrometrically-determined orbits favour those with periods of years or decades, whereas spectroscopic orbital solutions are more often measured for systems with periods of days to months. With the development of high-resolution astrometric and spectroscopic techniques in recent years, it is hoped that many more binary systems will be amenable to these complementary strategies.\\ Several months after this thesis began, a high-resolution spectrograph, HERCULES, commenced operations at the Mt John University Observatory, to be used in conjuction with the 1-metre McLellan telescope. For late-type stars, the anticipated velocity precision was ≲10 ms⁻¹. The primary goals of this thesis were: 1.~to assess the performance of HERCULES and the related reduction software that subsequently followed, 2.~to carry out an observational programme of 20 or so binary systems, and 3.~to determine the orbital and stellar parameters which characterize some of these systems. The particular focus was on those binaries that have resolved or unresolved astrometric orbital solutions, which therefore may be suited to complementary investigations.\\ HERCULES was used to acquire spectra of the programme stars, usually every few weeks, over a timespan of about three years. High-resolution spectra were acquired for the purpose of measuring precise radial velocities of the stars. When possible, orbital solutions were derived from these velocities, using the method of differential corrections.

Spectroscopic orbital elements and/or related parameters have been determined for eight binary systems, using radial-velocity measurements that have a typical precision of about 15 ms⁻¹. The orbital periods of these systems range from about 10 days to 26 years, with a median of about 6 years. Orbital solutions were determined for the seven systems with shorter periods. The measurement of the mass ratio of the longest-period system, HD217166, demonstrates that this important astrophysical quantity can be estimated in a model-free manner with less than 10% of the orbital cycle observed spectroscopically.\\ Single-lined orbital solutions have been derived for five of the binaries. Two of these systems are astrometric binaries: β Ret and ν Oct. The other SB1 systems were 94 Aqr A, θ Ant, and the 10-day system, HD159656. The preliminary spectroscopic solution for θ Ant (P~18 years), is the first one derived for this system. The improvement to the precision achieved for the elements of the other four systems was typically between 1--2 orders of magnitude. The very high precision with which the spectroscopic solution for HD159656 has been measured should allow an investigation into possible apsidal motion in the near future. In addition to the variable radial velocity owing to its orbital motion, the K-giant, ν Oct, has been found to have an additional long-term irregular periodicity, attributed, for the time being, to the rotation of a large surface feature.\\ Double-lined solutions were obtained for HD206804 (K7V+K7V), which previously had two competing astrometric solutions but no spectroscopic solution, and a newly discovered seventh-magnitude system, HD181958 (F6V+F7V). This latter system has the distinction of having components and orbital characteristics whose study should be possible with present ground-based interferometers. All eight of the binary systems have had their mass ratio and the masses of their components estimated.\\ The following comments summarize the motivation for getting these results, and the manner in which the research was carried out. \\ The majority of stars exist in binary systems rather than singly as does the Sun. These systems provide astronomers with the most reliable and proven means to determine many of the fundamental properties of stars. One of these properties is the stellar mass, which is regarded as being the most important of all, since most other stellar characteristics are very sensitive to the mass. Therefore, empirical masses, combined with measurements of other stellar properties, such as radii and luminosities, are an excellent test for competing models of stellar structure and evolution.\\ Binary stars also provide opportunities to observe and investigate many extraordinary astrophysical processes that do not occur in isolated stars. These processes often arise as a result of direct and indirect interactions between the components, when they are sufficiently close to each other. Some of the interactions are relatively passive, such as the circularization of the mutual orbits, whilst others result from much more active processes, such as mass exchange leading to intense radiation emissions. \\ A complete understanding of a binary system's orbital characteristics, as well as the measurement of the all-important stellar masses, is almost always only achieved after the binary system has been studied using two or more complementary observing techniques. Two of the suitable techniques are astrometry and spectroscopy. In favourable circumstances, astrometry can deduce the angular dimensions of the orbit, the total mass of the system, and sometimes, its distance from us. Spectroscopy, on the other hand, can determine the linear scale of the orbit and the ratio of the stellar masses, based on the changing radial velocities of both stars. When a resolved astrometric orbital solution is also available, the velocities of both stars can allow the binary system's parallax to be determined, and the velocities of one star can provide a measure of the system mass ratio.\\ Unfortunately, relatively few binary systems are suited to these complementary studies. Underlying this difficulty are the facts that, typically, astrometrically-determined orbits favour those with periods of years or decades, whereas spectroscopic orbital solutions are more often measured for systems with periods of days to months. With the development of high-resolution astrometric and spectroscopic techniques in recent years, it is hoped that many more binary systems will be amenable to these complementary strategies.\\ Several months after this thesis began, a high-resolution spectrograph, HERCULES, commenced operations at the Mt John University Observatory, to be used in conjuction with the 1-metre McLellan telescope. For late-type stars, the anticipated velocity precision was ≲10 ms⁻¹. The primary goals of this thesis were: 1.~to assess the performance of HERCULES and the related reduction software that subsequently followed, 2.~to carry out an observational programme of 20 or so binary systems, and 3.~to determine the orbital and stellar parameters which characterize some of these systems. The particular focus was on those binaries that have resolved or unresolved astrometric orbital solutions, which therefore may be suited to complementary investigations.\\ HERCULES was used to acquire spectra of the programme stars, usually every few weeks, over a timespan of about three years. High-resolution spectra were acquired for the purpose of measuring precise radial velocities of the stars. When possible, orbital solutions were derived from these velocities, using the method of differential corrections.