Step 1: Understanding the Question:
The question requires us to arrange major global milestones in the history of experimental and theoretical psychology in chronological order.
Step 2: Detailed Explanation:
• Let us trace the historical dates for each of the global milestones listed:
• B. Wundt establishes first laboratory of psychology: Wilhelm Wundt established the world's first formal laboratory for psychological research at the University of Leipzig in Germany in $1879$.
• D. William James publishes 'Principles of Psychology': William James published this highly influential, landmark textbook on functional psychology in the year $1890$.
• A. Pavlov studies conditioning: Ivan Pavlov began his famous research on salivary conditioning in dogs in the late $1890$s, presenting his major findings on classical conditioning at the International Medical Congress around $1903$ and winning the Nobel Prize in $1904$.
• E. Mary Caulkins elected first women president of APA: Mary Whiton Calkins was elected as the first female president of the American Psychological Association in the year $1905$.
• C. Carl Rogers helps to start humanistic movement: Carl Rogers published "Client-Centered Therapy" in $1951$, which helped launch the humanistic psychology movement (often called the "third force") during the $1950$s.
• Organizing these dates chronologically: $1879$ (B) $\rightarrow$ $1890$ (D) $\rightarrow$ $1903$ (A) $\rightarrow$ $1905$ (E) $\rightarrow$ $1950$s (C).
• This gives the sequence: B - D - A - E - C.
Step 3: Final Answer:
The correct chronological order of the historical milestones is B - D - A - E - C.