To determine the correctness of the given statements regarding historical scientific observations:
Statement (I): "According to the Law of Octaves, the elements were arranged in the increasing order of their atomic number."
Analysis: The Law of Octaves, proposed by John Newlands in 1864, is one of the early attempts to categorize elements. He arranged them by increasing atomic mass (not atomic number) and noted that every eighth element shared similar properties, much like the octaves in music. Hence, this statement is incorrect.
Statement (II): "Meyer observed a periodically repeated pattern upon plotting physical properties of certain elements against their respective atomic numbers."
Analysis: Julius Lothar Meyer was one of the scientists who contributed to the development of the periodic table. He plotted physical properties of elements (such as atomic volume) against atomic masses (not atomic numbers) and discovered a periodic pattern. Although he used atomic masses for his analysis, the concept of periodicity aligns with later developments using atomic numbers. Thus, the periodic pattern observed is consistent with modern understanding, even if atomic numbers were not used at that time. Therefore, this statement is considered true in the context of periodic law's development.
Conclusion: The correct answer is: "Statement I is false but Statement II is true."