The detail that shows Clara’s purpose for writing A Story of the Red Cross is:
"I have dedicated this little volume to the people with whom, and for whom, have gone the willing labors of twenty-five years—initial labors, untried methods, and object lessons."
This statement indicates that her purpose is to honor the people involved in her work with the Red Cross and to document her experiences and efforts over the years. It emphasizes her dedication to those she served and the importance of sharing her insights and experiences.