Final answer:
The varying percentages of titanium in different samples of titanium dioxide violate the Law of Definite Proportions of Dalton's atomic theory.
Step-by-step explanation:
The postulate of Dalton's theory that is violated by the observation that one sample of titanium dioxide has 59.95% titanium and a different sample has 60.10% titanium is the Law of Definite Proportions (also known as the Law of Constant Composition).
According to this postulate, a chemical compound should always contain exactly the same proportion of elements by mass. Therefore, the varying percentages of titanium in the samples of titanium dioxide indicate that this law has been violated.