"Ahh, ... er ... yes," he stammered, turning his thoughts back to the topic at hand and thinking fast. "Exchange of materials, er, yes ... and surface area, ... of course."
Makyatta took pity on him, he had seen the internal struggle, said; "And wouldn't you say that all living things need to exchange materials across surfaces; like air in our lungs, gasses into tree leaves, even juices into and out of those little cells you were telling us about?"
"Cells, and surfaces, why yes," agreed Mendel, taking the life line he had just been thrown. "Even those smallest globules of life will need to pass juices into and out of their tiny bodies. If we accept for the moment that cells contain 'protoplasm', this internal fluid must constantly be refreshed by contact with the bodily fluids"
"And all this exchange must take place, like the leaf, across the surface."
"Of course."
More himself once more, Mendel became conscious of the effect his confusion was having on the youths before him. A puzzled look was replacing the fearful looks that had been on each young face a moment ago. For the second time today they were seeing a side to Mendel's personality they had not suspected. Now he was looking fallible, and unable to dominate the subject under discussion; he was confused and uncertain. What was going on?
It was at that moment automatic mechanisms buried deep in Mendel's brain came to his rescue. Without realizing it, and while he had been talking to the class using one part of his brain, another part of his brain had taken two unrelated ideas and brought them together in a new relationship. Many good scientists who are also good teachers report a similar phenomena. It is as if, under the stress of performing in front of a body of students, all of whom look up to you as an authority, your brain comes to your rescue and stops you from looking the fool, by making connections that would never be made under a less powerful motivating force. Deep in Brother Gregory's thought process, a relationship formed, vague at first, but deepening as he tried to explain what he was thinking.
"But," he went on, groping for the right terms, "this would explain why you cannot see cells."
Everyone in the room returned a puzzled look to their faces, Brother Gregory's performance was becoming more and more erratic. What was happening?
"You mean, why cells are so small that we need these microscopes to see them?" Makyatta asked for conformation. "You think you know why?"
Mendel's whole body became more animated and his voice increased in volume as he replied; his tone more forceful and the hesitation vanished. "Think about it for a moment," he said, "assume all cells are spheres - although Professor Purkinje would not agree with that!" He laughed, "The amount of surface area across which the protoplasm can exchange juices is given by the formula so excellently supplied by Master Kolreuter." He smiled at the boy, who gladly accepted the sudden change in his teacher's attitude, and sat down.
"As the cell increases in size, the radius of the cell increases, and the surface area increases. But ..." He paused and looked around the class for dramatic effect. "The volume of the cell, or sphere, also increases, but by a different formula!" At the last phrase, his voice reached its loudest volume and he clapped his hands. His mind had made the final connection. But nobody else in the room had even made the first connection. Although Mendel was clearly back to his old self, he still needed to slow down, and expand on his new idea more methodically.