V. Whenever several works treating of various subjects are attributed to one and the same author by Hindu writings or traditions, it is often assumed, and apparently without any reason whatever in the majority of cases, that the said works should be considered as the productions of different writers. By this process of reasoning they have discovered two Badarayanas (Vyasas), two Patanjalis, and three Vararuchis. We do not mean to say that in every case identity of name is equivalent to identity of personality. But we cannot but protest against such assumptions when they are made without any evidence to support them, merely for the purpose of supporting a foregone conclusion or establishing a favourite hypothesis. VI. An attempt is often made by these writers to establish the chronological order of the events of ancient Indian history by means of the various stages in the growth or development of the Sanskrit language and Indian literature. The time required for this growth is often estimated in the same manner in which a geologist endeavours to fix the time required for the gradual development of the various strata composing the earth's crust. But we fail to perceive anything like a proper method in making these calculations. It will be wrong to assume that the growth of one language will require the same time as that of another within the same limits. The peculiar characteristics of the nation to whom the language belongs must be carefully taken into consideration in attempting to make any such calculation. The history of the said nation is equally important. Any one who examines Max Muller's estimate of the so-called Sutra, Brahmana, Mantra and Khanda periods, will be able to perceive that no attention has been paid to these considerations. The time allotted to the growth of these four "strata" of Vedic literature is purely arbitrary. We have enumerated these defects in the writings of European Orientalists for the purpose of showing to our readers that it is not always safe to rely upon the conclusions arrived at by these writers regarding the dates of ancient Indian history. In examining the various quotations and traditions selected by European Orientalists for the purpose of fixing Sankaracharya's date, special care must be taken to see whether the person referred to was the very first Sankaracharya who established the Adwaitee doctrine, or one of his followers who became the Adhipathis (heads) of the various Mathams (temples) established by him and his successors. Many of the Adwaitee Mathadhipatis who succeeded him (especially of the Sringeri Matham) were men of considerable renown and were well known throughout India during their time. They are often referred to under the general name of Sankaracharya. Consequently, any reference made to any one of these Mathadhipatis is apt to be mistaken for a reference to the first Sankaracharya himself.