According to Ebbinghaus's (1913) savings curve, savings is a function of .

Hermann Ebbinghaus was a pioneer in the study of memory. He is famous for his experiments on forgetting and his development of the forgetting curve. He used nonsense syllables to study memory in a controlled way, minimizing the influence of prior knowledge.

Ebbinghaus measured memory retention by the concept of "savings." Savings refers to the reduction in the amount of time or effort required to relearn previously learned material compared to the original learning time. If it takes less time to relearn something, it means some memory of it was "saved."

Ebbinghaus's forgetting curve demonstrates that memory retention decreases over time. Consequently, the amount of "savings" when relearning material is directly dependent on how much time has elapsed since the initial learning. The longer the elapsed time, the less is remembered, and thus the less "savings" will be observed during relearning.

• a. word familiarity: Ebbinghaus specifically used nonsense syllables to avoid the influence of familiarity.
• b. reaction time: While a measure in psychology, it's not the primary variable Ebbinghaus linked to savings.
• c. sensory modality: This refers to the sense used for input (e.g., sight, sound) and was not the central variable for his savings curve.
• d. elapsed time: This is the core variable in Ebbinghaus's forgetting curve, directly determining the amount of savings.

Therefore, savings is a function of elapsed time.

The final answer is $\boxed{\text{d. elapsed time}}$.