Final answer:
Prior to the instrumental record at Mauna Loa, temperatures were determined through the analysis of proxy data such as Antarctic ice cores, tree rings, and sediment cores, which provide historical climate data.
Step-by-step explanation:
The main method for determining temperatures prior to the instrumental record at Mauna Loa involves analyzing various forms of proxy data. The Antarctic ice cores are particularly significant in this field of study. They provide historical climate data because they trap air bubbles that preserve the atmospheric composition of the past, including temperature and carbon dioxide levels. This allows scientists to estimate Earth's past temperatures. Other examples of proxy data include measuring tree rings and examining sediment cores and fossils. Each of these proxies provides insights into past climates and can be used to infer temperature changes over time.