Towards the end of May I thought I would teach her fractions, and she apparently understood what I meant, but for a beginning I could only put questions, such as: "How many _wholes_ are there in 20/4, 12/4, or 11/2" etc. Indeed, I was at first at a loss as to what form of expression I should use here--so as not to come into collision with those already resorted to, thus giving rise to confusion. At first I thought it might be more convenient to let her rap out the denominator with her right paw and the numerator with her left--but I soon came to see that even with 3/16, this method could no longer be maintained. At length I let her simply rap out the numerator--then I would ask for the denominator, and let her rap this, so that in the case of 3/16 she rapped the 3 first with her right paw; then gave the denominator, i.e. 1 rap with her left paw and 6 again with her right. This mode or procedure came quite naturally to her, and so it was retained. The questions were practised in the following manner:--"How do you rap 3/8, 12/6?" etc., and I followed this up with easy exercises such as: "How much is 2/8 + 1/4?" the simplified answer being "1/2." I had, as may be imagined, already given her repeated and detailed explanations on the subject before she was capable of giving such answers as "1/2," to the above question. Simplifying was also practised separately thus: "Simplify 20/16!" Answer: "1-1/4." this being given with "1 r" (pause) "1 r" (another pause); "and the denominator?" "4 r." To anyone following her actions, the meaning would appear quite distinct. I now determined that she should add together numbers having different denominators--as, for example: 1/4 + 1/3, and here I had myself to cogitate as to how this ought to be done, for at school, my enthusiasm for arithmetic had never been great and much of what I had then learnt has been forgotten. So I talked the question over with a friend--in Lola's presence and out loud--and finally arrived at the solution. As she had been listening most of the time while we sought, found, and discussed the solution, I soon ventured to put a few tests to her, and the answers proved that she had actually been listening while our conversation was going on, and that what we had talked about had lingered in her memory. By the way, it is reported of Jean Paul Richter, that when on some occasion a friend came to him desirous of talking over some matter, the nature of which none other was to know, Jean Paul said to his poodle, who was under the table: "Go outside, we want to be alone!" The dog vacated, and the poet remarked: "Now, sir, you can talk, for no one will hear us!" Lola solved the following problems: "1/5 + 1/3 = ?" A. "8/15." "1/7 + 5/8 = ?" A. "43/56." "1/2 + 1/3 = ?" A. "5/6." "1/4 + 2/5 = ?" A. "13/20."