NA TURE 



[November 22, 1S94 



amused herself, as is common on such occasions, with 

 various idle trains of thought. Then it occurred to her 

 to tr\" mental sums, and finding, much to her surprise, 

 that she had great facility in doing them, she became 

 interested and exerted herself to the utmost. Before her 

 train had reached Lyons, she had successfully multiplied 

 one series of eleven figures into another series also of 

 eleven figures. She subsequently trained herself to 

 multiply fifteen figures into another fifteen. I am 

 informed that her first attempt at the latter had one 

 error, and, on being told that it was not correct, she went 

 over it again mentally and gave the correct result. 

 Another case comes to my memory. It appears 

 that there was a craze for mental arithmetic in the 

 period 1S20-30, or thereabouts. My father was in- j 

 terested in the subject and made experiments on many 

 friends and on all his servants, with the result, as I used 

 to hear, that the best performer of all, and a really re- 

 markable one, was a somewhat obtuse and uninteresting 

 servant girl. She took no especial pleasure in calculation, 

 and on that account would never have made a study of 

 its processes by herself ; nevertheless, she had the 

 capacity for using them. An innate passion for arith- 

 metic, such as all the great calculators possessed, is 

 certainly uncommon. If only a moderate passion for it 

 should exist, it is likely to become repressed by circum- 

 stances, because it is nearly useless to the possessor. 

 It is difTicult to imagine that anyone who was not 

 fascinated by figures would devote the best part of 

 his time and energy to them. Professional calculators 

 are said to be usually (by no means always) narrow- 

 minded, and to have their heads filled with mnemonic 

 contrivances. 



I may be permitted to allude to an inquiry analo- 

 •gous to that which has here been made into the visual 

 and auditive imaginations, which 1 made on myself, 

 on a small scale, in respect to the olfactile imagin- 

 ation. I tried to perform mental arithmetic, not by 

 imaginary visual symbols, or by imaginary sounds, but 

 by imaginary smells. As sums are set in the two former 

 cases, either in really visible symbols or in really audible 

 sounds, while the results are reached through imaginary 

 ones, so in my experiment the sums were set in real odours, 

 and were worked out through imaginary odours. I de- 

 scribed the result briefly, not many months ago, in the 

 American Psychological Review, and think the imiuiry 

 worth repetition, especially by experimenters, who may 

 possess the power of re-presenting odours to themselves 

 more vividly than I have. It would enable them to per- 

 ceive the processes gone through in mental arithmetic 

 from a new point of view. My apparatus consisted of 

 glass lubes, each drawn to a nozzle at one end like a short 

 syringe. One end of a piece of india-rubber tube, six or 

 eight inches long, was pushed tightly over the other end 

 of the glass. A different odorous substance, camphor, 

 carbolic acid, gasolin, &c., was inserted and packed 

 lightly with cotton wool in the several lubes, whose ends 

 were afterwards tied up. On grasping one of these tubes 

 tightly, at the moment when its nozzle was brought to 

 the nostril, a whiff of its peculiar odour was ejected and 

 simultaneously sniffed up. This could be rapidly repeated 

 three or four times without much diminution of the 

 odour of the whiff. (An arrangement with valves would 

 NO. 1308, VOL. 51] 



have much improved its action, by ensuring that no air 

 should be ejected that had not passed through the scent.) 

 I thus possessed a set of tubes that could be used 

 sincllingly, in the same way as the symbols i, 2, 3, &c., 

 are used visually, or the words one, two, three, &c., are 

 used audibly. This is not the place to enter into further 

 details. I only desire to emphasise one fact which the 

 e.xperiment taught me, namely, the existence of a large 

 substratum of mental work that my power of introspec- 

 tion failed to penetrate. I progressed far enough to be 

 able to add or subtract small sums, so that a i followed 

 by a 2, both in smell language, associated themselves at 

 once with the imaginary sniff of a 3, whenever I was en- 

 gaged in addition, or with that of a i when I was engaged 

 in subtraction. But the two associations of 3 and i 

 never clashed ; they were mutually exclusive. I could not 

 ascertain through introspection what was the nature of 

 the atlitude of tnind which determined whether the 

 association was to be the one needed for addition or for 

 subtraction, for division or for multiplication. Another 

 point that strongly impressed me was the enormous | 

 amount of labour that must have been gone through [ 

 by all of us in thoroughly learning the multiplication | 

 table. I made a very few similar experiments with the | 

 gustatile or taste-imagination, but they were trouble- 

 some, and I did not follow them up. 



There is little room now left to speak of the latter half 

 of Binet's volume, which refers to the great chess-players, 

 who play eight or more games blindfold and simul- 

 taneously. The evidence is overwhelming that the faculty 

 of visualising is not exercised by them in the same sharp 

 and distinct way that it is commonly supposed to be 

 They do not see the chessmen and the complete board all 

 at once and with clear definition, but they commonly see 

 all besides the portion they are considering, more or less 

 vaguely, and they appreciate the positions of the men 

 as hidden centres of forces. Two letters, which close 

 the volume, by the distinguished chess-players Goetz and 

 Tarrasch, seem to me models of exact introspection and 

 of clear description. Francis Galion. 



THE COLLECTED IVORKS OF OLBER^. 



Wilhelm Others, sein Leben und seine Werke. Im Auf- 

 trage der Nachkommen herausgegeben von Ur. C. 

 Schilling. Erster Band, Gesammelte Werke. xix. + 

 707 pp. Svo., with portrait. (Berlin, 1894.} 



GERMANY has not produced as many amateur 

 astronomers as England has, but among them the 

 man whose complete writings have now been published 

 occupies a most remarkable place. Olbers was an 

 amateur, but his work was that of a professional as- 

 tronomer. Though occupied all day in the extensive 

 practice of a physician, he devoted his nights to search- 

 ing for comets, making micrometric observations of 

 these bodies, whether found by himself or others, with 

 the annular micrometer, an instrument the immense value 

 of which he was the first to perceive, and computing 

 their orbits by the simple method devised by him, which 

 he is said first to have applied practically while watching 

 at the bedside of a patient. At the top of his house in 

 the Sandstrasse in Bremen he had his exceedingly 



