Some of the lectures were almost easy for me—­for instance, those on mathematics.  I have always been able to perceive with ease and pleasure relations of geometrical figures and of planes; so that it seemed inexplicable to me that every farmer should not be equally capable of understanding them.  This I had said before to my brother, who tried to give me an explanation; but I did not yet grasp it.  I had expected I don’t know exactly what, but certainly something higher, something grandiose; very likely I had expected something with more life in it.  The mathematical course, therefore, at first seemed to me unimportant; but later on I found that I, also, could not follow every detail.  However, I did not think much of this, because I readily understood the general meaning, and I said to myself that particular cases would not cause me any mental fatigue if I found it necessary to learn them.

The lectures of my excellent teacher were not so useful to me as they might have been, if I could have seen in the course of instruction and in its progress somewhat more of necessary connection and less of arbitrary arrangement.  This want of necessary connection was the reason of the immediate dislike I always took to every course of instruction.  I felt it even in pure mathematics, still more was it the case in applied mathematics, and most of all in experimental physics.  Here it seemed to me as if everything were arranged in arbitrary series, so that from the very first I found this study a fatigue.  The experiments failed to arrest my attention.  I desired and sought after some inner connection between the phenomena, deduced from and explained by some simple root principles.  But that was the very point withheld from me.  Mathematical demonstrations came like halting messengers; they only became clear to the mind’s eye when the truth to be demonstrated lay before me already in all its living strength.  On the other hand, my attention was riveted by the study of gravitation, of force, of weight, which were living things to me, because of their evident relation to actual facts.

In mechanics (natural philosophy) I could not understand why so many of the so-called “mechanical powers” were assumed, and why several of them were not reduced to cases of the inclined plane.

In mineralogy my previous education had left many gaps unfilled, especially as regards the powers of observation.  I was fond of mineral specimens, and gave myself much trouble to comprehend their several properties; but in consequence of my defective preparation I found insuperable difficulties in my way, and perceived thereby that neglect is neither quickly nor lightly to be repaired.  The most assiduous practice in observation failed to make my sight so quick and so accurate as it ought to have been for my purpose.  At that time I failed to apprehend the fact of my deficient quickness of sight; it ought to have taught me much, but I was not prepared to learn the lesson.