who was the latter?
He was a German-born lecturer at Oxford specialising in comparative philology, the science of language.
1860 Boden Professor of Sanskrit election
 The other, Max Müller, was a German-born lecturer at Oxford specialising in comparative philology, the science of language. 
what does the term "1860 boden professor of sanskrit election" refer to? A competition between two candidates offering different approaches to Sanskrit scholarship. who were the candidates? Monier Williams, Max Müller
wiki:7799791
1860 Boden Professor of Sanskrit election [SEP] Introduction
The election in 1860 for the position of Boden Professor of Sanskrit at the University of Oxford was a competition between two candidates offering different approaches to Sanskrit scholarship. One was Monier Williams, an Oxford-educated Englishman who had spent 14 years teaching Sanskrit to those preparing to work in British India for the East India Company. The other, Max Müller, was a German-born lecturer at Oxford specialising in comparative philology, the science of language. He had spent many years working on an edition of the "Rig Veda" (an ancient collection of Vedic Sanskrit hymns), and had gained an international reputation for his scholarship.