June 29, 1917] 



SCIENCE 



665 



IS reproduced by Smith in his article, above- 

 mentioned, and in the " Rara Arithmetica." 

 Some time ago in discussing before the 

 American Mathematical Society the " Quad- 

 ripartitum " of John of Meurs, written about 

 A.D. 1325, I called attention to the fact that 

 this writer also should be included among 

 those who by use of an analogy with the sexa- 

 gesimal fractions made a near approach to 

 decimal fractions.^" In the passage in ques- 

 tion, which occurs in the twenty-second chap- 

 ter of the second book, dealing with the extrac- 

 tion of square root, zeros in pairs are annexed 

 to the number whose approximate root is de- 

 sired. In extracting the square root of 2, six 

 ciphers are annexed to the 2 and the square root 

 of 2000000 is obtained as 1414. At&st this is 

 changed to sexagesimal fractions and by suc- 

 cessive multiplication of remainders by 60 the 

 root is obtained as 1° (gradus), 24 minutes, 

 50 seconds, and 24 thirds, or 1 24/60 50/3600 

 24/216000. The manuscript proceeds, as fol- 

 lows : " Et si vis posses dicere ab inicio cum 

 habuisti banc radicem 1414 quod unitas que 

 est in quarto loco est sicut integrum et 4 que 

 sunt in tercio loco sunt decima pars integri, 

 et unitas que est in secundo loco est decima 

 decium, et 4 que sunt in primo loco sunt 

 decima decime decime sic 1-4-1-4. Et nota 

 quod istam radicem preinuentam 1414 potes 

 multum bene ponita unitate in loco integrum 

 tres differentias remanentes multiplicare per 

 10, 20, 30, 40, 50, 60, 70, 80, 90 et semper a 

 •producto demptis figuris que excedunt nu- 

 merum medietatis eirculorum, residuas multi- 

 plica per ilium articulum per quern alias ex- 

 tendisti et hoc facto tociens quod non re- 

 maneant nisi tres circuli qui sunt medietas 

 eirculorum. Habebis radicem secundum pro- 

 poTcionem rategri ad articulum per quem 

 fueris operatus." The statement here that in 

 the 1414 (regarded as the square root of 2, 

 evidently) that the first unit (fourth as 



12 I am using photographic copies of pages of the 

 "Vienna MS. 4770; the passage in question is found 

 on folio 224 verso; the manuscript was probably 

 written in the early part of the fifteenth century, 

 containing also Robert of Chester 's translation of 

 the algebra of Al Khowarizmi, recently published 

 in the University of Michigan Humanistic Series. 



counted from the right or ordinary unit's 

 place) is to be regarded as an integer, the fol- 

 lowing 4 as tenth parts of an integer, the 

 following unit as the tenth part of a tenth, 

 and the final (first, counting in the ordinary 

 way from the right) 4 as tenth parts of the 

 tenth part of one tenth borders closely on the 

 idea of decimal fractions. However, John of 

 Meurs, like so many others who made initial 

 steps in this direction, carried the idea no 

 further. Louis 0. Karpinski 



Univeesitt op Michigan 



THE SHORTAGE OF PLATINUM 



According to a bulletin issued by the U. S. 

 Geological Survey most people are apt to think 

 of platinum as preeminently adapted to set- 

 tings for precious stones, but the metal is in 

 fact indispensable to many essential industries. 

 Platinum dishes and utensils are absolutely 

 needed in all chemical laboratories, and upon 

 these laboratories all great industries are de- 

 pendent for guidance. Alloys have been de- 

 vised for use in the ignition systems of inter- 

 nal-combustion engines, but no substitute for 

 platinum has been found for certain delicate 

 parts of these systems. Platinum and allied 

 rare metals are widely employed in instru- 

 ments of precision required for making phys- 

 ical tests of materials of all kinds. Probably 

 platinum is now most valuable for its use in 

 the contact process of making concentrated 

 sulphuric acid, which is essential to a great 

 number of industries that are vitally impor- 

 tant at all times, and particularly in time of 

 war. 



The United States alone annually uses about 

 165,000 ounces of fine platinmn and produces 

 less than 1,000 ounces of crude platinum. 

 Realizing the urgent necessity of increasing 

 the country's production of the metals of the 

 platinum group, the United States Geological 

 Survey, Department of the Interior, has 

 planned an investigation in which L. M. 

 Prindle and J. M. Hill, geologist, will visit 

 places in this country where commercial depos- 

 its of these metals may be found. 



Native platinum, the metal and sperrylite 

 (platinum arsenide) have been found in basic 



