appeared in the "Spectator," of December 28th last, two very interesting letters concerning a peculiar form of visualizing possessed by the late Mr. Bidder, the engineer, known in early life as the "calculating boy," and this gift is possessed in a high though less degree by several of his descendants. Thus the eldest son, Mr. George Bidder, Q. C, can mentally multiply fifteen figures by fifteen, though not with the same precision and rapidity as his father. One of the two letters is from Mr. Bidder's friend, Professor Elliot, who writes thus:
If he saw or heard a number, it seemed permanently photographed in his brain. In like manner he could study a complicated diagram without seeing it, when walking and apparently listening to a friend talking to him on some other subject. The diagram stood before him in all its lines and letters.
The second letter is from Mr. George Bidder, who writes:
His memory was of a peculiar cast, in which figures seemed to stereotype themselves without an effort. . . . (accompanied) by an almost inconceivable rapidity of operation. I speak with some confidence on the former of these faculties, as I possess it to a considerable extent myself (though not to compare with my father). Professor Elliot says he always saw mental pictures of figures and geometrical diagrams. I always do. If I perform a sum mentally, it always proceeds in a visible form in my mind; indeed, I can conceive no other way possible of doing mental arithmetic.
Mr. Bidder continues, in a letter addressed to myself:
If my mind is engaged solving a geometrical problem including the relations of lines, plans, etc., I deliberately build up in my mind a figure, plane or solid, as the case requires; but there is a limit to my power in this respect, e. g., if the problem includes the relative positions and intersections of many surfaces, it becomes a painful effort to grasp them all simultaneously.
All this shows that mental impressions of extreme vividness may at the same time have great mobility and be subject to "an almost inconceivable rapidity of operation," and that they need not be fixed in the way that hallucinations often are.
Next as regards actual blending. Mr. G. Bidder, in very kindly replying to some questions that I put, writes:
Nothing is easier than to imagine, and to watch mentally, the rotation of anything to which such motion is natural, e. g., a wheel, a crank, etc. In many such cases I incline to think the process consists in calling up a sort of typical image formed out of innumerable bygone experiences.
This was Mr. Bidder's own view, quite independent of any suggestions from myself, and is therefore all the more valuable.
The strongest proof that those who have vivid memories of special objects are also capable of blending them is found in the works of such men as Macaulay. I am assured on excellent authority that his visual memory of book, page, and line was of the clearest possible char-
