August 2, 1886.] 



KNOWLEDGE ♦ 



311 



locomotion are twofold ; with its four glossy and beautifully 

 fringed wings it can fl}' toleraljly well ; but with its six 

 long-jointed legs, it can also run rapidly, carrying its wings 

 close alongside its body, and vibrating its antenna^ with an 

 incessant tremor indicative of the excitement which now^ 

 thrills through its little frame. It needs no food, and 

 indeed there is probably nothing within reach that could 

 serve it as such ; for the gross aliment which delighted it 

 when a grovelling grub, possesses no charms for it in its 

 higher state of existence, and indeed, were its tastes to tend 

 in that direction, it could not gratify them, for, like the rest 

 of its order, it has no jaws wherewith to reduce the tough 

 fibres of cloth, and even the usual flexible maxillie, the two 

 long coils which form the sucking apparatus of moths for 

 imbibing honey, are present only in a rudimentary condition, 

 as is the case throughout the genus Tinea. Its sole business, 

 therefore, is to get mated, lay its eggs and die. 



As might be expected, the eggs are extremely minute, and 

 they are carefully deposited by the mother on the cloth, or 

 in crevices and corners close to a supply of food. The young 

 gi-ubs hatched from these soon manifest theii- tailoring pro- 

 pensities, but they seem, at this early stage, to prefer second- 

 hand garments, or I'ather shoddy, to an entirely new " rig 

 out." In other words, they attack the old cases of their 

 progenitors, which are sure to be lying about in plenty, and 

 by cutting up these larger garments, manage to make some 

 respectable coverings for their own tiny forms; the filaments 

 of wool and fur which have been submitted to the action of 

 the more powerful jaws of their adult ancestors, are in a 

 more managealile condition for the weaker weapons of the 

 juveniles than would be those of cloth that had never under- 

 gone such a preparatory process. 



Tinea pellionella is one of the commonest and most 

 destructive of our clothes-moths, and is especially partial to 

 furs and feathers ; its attachment to the former is indicated 

 in its name, which is derived fi-om the Latin " pellio," a 

 " furrier." It is sometimes therefore called the fiu'-moth. 

 Its larva has also been known to feed on cobwebs. 



Our other clothes-moths must be left till the next paper. 



{To be continued.) 



COUNTING UNCONSCIOUSLY.* 



By Professor W. Preyer, of the University of Jena. 



> ^ ^T first sight the superscription, "counting 



unconsciously," seems to contain a contra- 

 diction. For whoever counts from one to one 

 hundred realises at each number that he is 

 counting ; yet, in truth, there ai-e so many 

 instances where an educated person counts 

 without realising it that he would feel 

 utterly lost in this world should the faculty 

 be suddenly taken from him. 



Three coins being placed on a table, any one will, on 

 being asked, " How many are there ? " answer, after but a 

 glance, " three." Even when four or five coins are seen but 

 for a moment the answer as to their number will be cor- 

 rectly given. So quickly is the answer returned that no 

 time can possibly have been taken for counting. Hence it 

 follows that counting unconsciously is really an everyday 

 occurrence. The objection that this is no longer to be termed 

 counting is not valid, for if anyone can positivel}^ state 



* The experiments suggested here would afford capital amuse- 

 ment as parlour games— having also the advantage of being useful 

 and instructive. 



that there are lying before him three, or four, or five objects 

 he must be able to distinguish numbers ; and it is certainly 

 a foct that one who cannot count can also not answer such 

 cjuestions. Children, in order to distinguish three marbles 

 from four, must first add each marble to the other ; in this 

 way many learn to count before knowing the numerals. 

 From this it follows that in order to count a knowledge of 

 the numerals is not a necessity ; even untrained deaf mutes, 

 who can neither read nor write, are capable of counting, 

 without figures, merely by the aid of their fingers. 



From the action of a child who has learned the meaning 

 of the numerals it furthermore follows that it is only by 

 practice, that Ls, by oft-repeated counting of actual objects, 

 that surety is gained in the art of counting small numbers 

 unconsciously. An idiot, or whoever does not practise, 

 cannot count three without adding one by one, and will 

 never rise above the lowest plane of mental development. 



Now, however, as is well known, no one can tell in a 

 moment how many objects are lying before him, provided 

 the number of these objects is somewhat large — approxi- 

 mates, say, fifty. Some persons can count more rapidly 

 than others : a broker's apprentice will make groups of 

 three, of five, of ten coins, and then add the groups to- 

 gether ; the experienced money-broker is able to determine 

 in a few seconds what the amount is, and this, perhaps, 

 without even touching the coins. But he too, as well as 

 everyone else, must count attentively as soon as the number 

 of pieces exceeds a certain limit. But what is this limit ? 



Dase, the well-known calculator, who died in 1861, stated 

 that he could distinguish some thirty objects of a similar 

 nature in a single moment as easily as other people can 

 recognise three or four, and his claim was often verified by 

 tests. The rapidity with which he would name the number 

 of sheep in a herd, of books in a book-case, of window-panes 

 in a large house, was even more remarkable than the 

 accuracy with which he solved mentally the most diflicult 

 problems. Not before or after his time has such perfection 

 been attained ; but as evei-yone possesses this faculty to a 

 small extent, and, as it can be improved by practice, it is 

 not impossible that in future other experts in this line may 

 appear. The only trouble is that so few know how easy it 

 is to practise. 



In the first place one can by a few trials readily gain the 

 conviction that, without practice, not everyone can dis- 

 tinguish six and seven objects as easily as three and four. 



In order to learn that it is a comparatively easy matter 

 to e.stimate up to six and seven, and then up to nine, as 

 correctly as from three to five, one need only make a few 

 trials in guessing at an unknown number of matches or pins 

 that are concealed beneath a sheet of paper, and are then 

 exposed to view but for a second. 



Great care must be exercised, however, that one does not 

 consciously count in these attempts, nor \vi\\ it answer to 

 attempt analysis from memory after the objects are again 

 hidden from view ; all this would consume too much time. 

 It is, in fact, neces.sary to do nothing more than to estimate, 

 but this must be done with the utmost attention. 



Whoever has for any length of time tried seriously to 

 guess correctly will be surprised to find that his guesses will 

 soon grow to be generally correct, whereas at the start they 

 were often erroneous. Only when the number of objects 

 seen exceeds nine will mistakes again occur more frequently. 

 However, further practice in estimating greater numbers of 

 small objects will soon cause considerable improvement even 

 here. Many, however, do not succeed in estimating 

 con-ectly beyond ten, probably because the attention 

 is not sufiiciently concentrated at the time, and as it 

 is necessary, at the start at least, that one's whole 

 attention be closely given ; only after having attained some 



