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[ 460 ] F Brentano , Psychologie , i , 9 , 88 ff . — Merkel thinks that his results with the method of equal - appearing intervals show that we compare considerable intervals with each other by a different law from that by which we notice barely perceptible intervals . The stimuli form an arithmetical series ( a pretty wild one according to his figures ) in the former case , a geometrical one in the latter — at least so I understand this valiant experimenter but somewhat obscure if acute writer . [ 461 ] This is the formula which Merkel thinks he has verified ( if I understand him aright ) by his experiments by method 4 . [ 462 ] Elsas : Ueber die Psychophysik ( 1856 ) , p . 41 . When the pans of a balance are already loaded , but in equilibrium , it takes a proportionally larger weight added to one of them to incline the beam . [ Pg 550 ] CHAPTER XIV . [ 463 ] ASSOCIATION . After discrimination , association ! Already in the last chapter I have had to invoke , in order to explain the improvement of certain discriminations by practice , the ' association ' of the objects to be distinguished , with other more widely differing ones . It is obvious that the advance of our knowledge must consist of both operations ; for objects at first appearing as wholes are analyzed into parts , and objects appearing separately are brought together and appear as new compound wholes to the mind . Analysis and synthesis are thus the incessantly alternating mental activities , a stroke of the one preparing the way for a stroke of the other , much as , in walking , a man's two legs are alternately brought into use , both being indispensable for any orderly advance . The manner in which trains of imagery and consideration follow each other through our thinking , the restless flight of one idea before the next , the transitions our minds make between things wide as the poles asunder , transitions which at first sight startle us by their abruptness , but which , when scrutinized closely , often reveal intermediating links of perfect naturalness and propriety — all this magical , imponderable streaming has from time immemorial excited the admiration of all whose attention happened to be caught by its omnipresent mystery . And it has furthermore challenged the race of philosophers to banish something of the mystery by formulating the process in simpler terms . The problem which the philosophers have set themselves is that of ascertaining principles of connection between the thoughts which thus appear to sprout one out [ Pg 551 ] of the other , whereby their peculiar succession or coexistence may be explained .
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