ADVANCED ARITHMETIC 91 



imagined, already given her repeated and detailed 

 explanations on the subject before she was capable of 

 giving such answers as " |," to the above question. 

 Simplifying was also practised separately thus : 

 " Simplify f- ! " Answer : " i." this being given 

 Eith " i r " (pause) " I 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 : 

 + , and her 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 1 " The dog 

 vacated, and the poet remarked : " Now, sir, you can 

 talk, for no one will hear us ! " 

 Lola solved the following problems : 



-?" A. "&." "* + f?" A."H." 

 = ? " A. " |." i + = ? " A. " ." 



