728 THE RAMSDEN DIVIDING ENGINE. 



dimeusions given would be according to the metliod of enumeration in 

 general use. 



In noting measurements of length in other portions of the Scrip- 

 tures three-score is used three times : 



1 Kings, 6:2: "And the house which King Solomon built for the 

 Lord, the length thereof was three-score cubits, and the breadth thereof 

 twenty cubits, and the height thereof thirty cubits." 



Ezra, 6:3: " Let the house be builded, the place where they offer sac- 

 rifices, and let the foundations thereof be strongly laid; the height 

 thereof three-score cubits, and the breadth thereof three-score cubits." 



Daniel, 3:1: "Nebuchadnezzar the king made an image of gold, 

 whose height was three-score cubits, and the breadth thereof six cubits." 



The numbers 6 and 12 are used elsewhere as follows : 



Ezelviel," 41:1, revised version: "And he brought me to the temple, 

 and measured the posts, six cubits broad on the one side and six cubits 

 broad on the other side, which was the breadth of the tabernacle." 



Ezekiel, 43,16, revised version : "And the altar hearth shall be 

 twelve cubits long by twelve broad, square in the four sides thereof." 



METHODS OF DIVIDING THE CIRLE BY HAND. 



The most ancient figure with graduated divisions of a circle dis- 

 covered in England, was a quadrant, marked with Roman characters, 

 which was found on a chimney piece at Helmdon, in Northampton- 

 shire, with the date Moi33 (meaning A. d. 1133) marked upon it. 



Different methods of dividing a metallic or wooden circle into degrees 

 and their subdivisons were successfully practiced by the early astrono- 

 mers, notably by Tycho Brahe* (1546-1601), of Sweden; Johann 

 Heveliust (1611-1687), of Dantzic,in Poland; Dr. Robert Hooke (1635- 

 1703), while curator of experiments of the Royal Society; Ole Roemer 

 (1644-1710), the Danish astronomer, of whom it is said that he may be 

 considered "the inventor of nearly all our modern instruments of pre- 

 cision," and many of whose ideas were adopted by astronomers a cen- 

 tury later. 



In attempting to engrave and divide correctly the circles used for 

 mathematical purposes, all of these early laborers in the field of science 

 were compelled to depend entirely upon manual skill. 



The first notable example of the division of circular arcs of which 

 I have found record is the mural arc, of 8 feet radius, which George 

 Graham graduated for the English National Observatory in 1725, The 



* An electro replica of Tj'clio Brahe's quadraut, from the original in the British 

 Museum, is deposited in the Smithsonian Institution. Triangular diagonals are not 

 found in this instrument. Tjclio Brahe's instruments had the advantage of long 

 radii, which rendered any inequalities that might occur in his divisions of less value 

 than instruments of short radii ; the smallest subdivisions into which he professed to 

 mark his spaces were 10' each. 



t The errors of Hevelius' large sextant for 6' radius used about 1G50, amounted to 

 15" or 20". 



