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SCIENCE 



[N. S. Vol. XL'VTI. No. 1206 



the photogenic organ, by whicli the two 

 layers are formed. About this time the tra- 

 cheal and nerve connections become fully 

 established. At the age of twenty-two days 

 the organ begins to emit light. 



In this connection it may be stated that 

 my observations confirm Dahlgren's recent 

 announcement that the adult organs in the 

 pupa arise from the hypodermis. 



Walter N". Hess 



Cornell Univeksitt 



JOSEPH YOUNG BERGEN 



To THE Editor op Science : In my paper in 

 memory of Joseph Young Bergen, which ap- 

 peared in Science, January 4, 1918, I stated 

 that he was the son of a clergyman. I am now 

 informed by Mrs. Bergen that this statement is 

 incorrect. Edwin H. Hall 



Cambridge, Mass., 

 January 30, 1918 



SCIENTIFIC BOOKS 



The Casting -Counter and the Counting- 

 Board. A Chapter in the History of IvTu- 

 mismatics and Early Arithmetic. By 

 Francis Pierrepont Barnard. Oxford. At 

 the Clarendon Press. 1916. 35Y pp. + 

 LXm. plates. Price £3 3s. 

 When we consider the role played by the 

 abacus in the history of calculation, first as 

 the primitive and probably prehistoric dust 

 board and finally in the form of the elaborate 

 reckoning machines of the present day, we 

 can see that the history of mechanical com- 

 putation is closely tied up with the history of 

 the race. It is true that for long periods we 

 have no reference to such a device as the 

 abacus, but for equally long periods we have 

 no reference to many of the common customs 

 of life and to the everyday implements used 

 in the home. It is probable that one would 

 have to search long in the written records of 

 the early periods to find any reference to such 

 homely words as button or shoestring, or to 

 such common actions as the combing of the 

 hair, the milking of a cow or a goat, the cook- 

 ing of a piece of beef, or the making of a 



sandal or a shoe, and yet all these words and 

 actions have been commonplaces for thou- 

 sands of years. The recording of the use of 

 common devices is generally inversely pro- 

 portional to the frequency of their use, and 

 this is probably one reason why the abacus, 

 in one form or another, is not more frequently 

 mentioned in the chronicles of various peoples. 



There were three standard forms of the 

 abacus in ancient times, the dust board, which 

 was the forerunner of the wax tablet as the 

 latter was of the slate; the board on which 

 counters or small disks were moved about, 

 these counters appearing in Rome as pebbles 

 or marbles (calculi) ; and the bead abacus, 

 the counters running in grooves or on wires, 

 a form still found in schools in our country 

 and familiar as the Chinese suanpan, the 

 Japanese soroian, and the Russian ischotii 

 or the Armenian choreh. 



Of these various forms, the most interesting 

 for the general reader of the Western World 

 is the board on which calculi were moved, 

 since these counters are so often mentioned 

 in our literature. Adelhard of Bath.(c.ll20) 

 speaks of such a table, saying that " quidem 

 mensam pithogoream ob magistri sui reueren- 

 tiam. sed post! tame abacum dixerunt," hav- 

 ing probably in mind a passage from Boeth- 

 ius : " Pythagorici vero . . . mensam Pytha- 

 goream nominabant ... a posteribus apella- 

 batur abacus." We find the name of alacisti 

 given to those who were skilled in computa- 

 tion with the counters, and even the verb " to 

 abacus " is occasionally found, as in a certain 

 manuscript of the eleventh century — " Hoc si 

 abacizando probaveris." In later times the 

 references to counters become very numerous. 

 So we have in English such expressions as 

 " Sitte doun and take countures rounde," " A 

 nest of cowntouris," " The kitchin clarke . . . 

 jangling his coimters," " A counter caster," 

 " Any that can but cast with Counters," and 

 " I shall reken it syxe tymes by aulgorisme or 

 you can caste it ones by counters." From 

 the use of the word as representing a disk we 

 also find it employed to represent the person, 

 as in the expression, " Ther is no countere nor 

 clerke con hem recken alle," and also to repre- 



