Eva tries a Penny-farthing in the Otago Museum.  The design came from a Frenchman, Eugene Meyer, in 1869 and it remained in fashion for about another 20 years until the practical design we know today replaced it.

According to Wikipedia:

The penny-farthing used a larger wheel than the velocipede, thus giving higher speeds on all but the steepest hills. In addition, the large wheel gave a smoother ride, important before the invention of pneumatic tires.

Although the high riding position seems daunting to some, mounting can be learned on a lower velocipede. Once the technique is mastered, a high wheeler can be mounted and dismounted easily on flat ground and some hills.

An attribute of the penny-farthing is that the rider sits high and nearly over the front axle. When the wheel strikes rocks and ruts, or under hard braking, the rider can be pitched forward off the bicycle head-first. Headers were relatively common and a significant, sometimes fatal, hazard. Riders coasting down hills often took their feet off the pedals and put them over the tops of the handlebars, so they would be pitched off feet-first instead of head-first.

Penny-farthing bicycles often used similar materials and construction as earlier velocipedes: cast iron frames, solid rubber tires, and plain bearings for pedals, steering, and wheels. They were often quite durable and required little service. For example, when cyclist Thomas Stevens rode around the world in the 1880s, he reported only one significant mechanical problem in over 20,000 km, caused when the local military confiscated his bicycle and damaged the front wheel.

Whether they were ever used in Waikanae is unknown, but it seems unlikely.