BY R. M. JOHNSTON, F.L.S. 131 



measuremeuts or proportionals relatingto the earth's diameter, 

 ■circumference, distance from the sun, annual period of 

 revolution, etc.; for it is easy by slight variations of any root, 

 arbitrarily made, and ai'bitrarily selected multiples, to make 

 any number approximate to some important terrestrial 

 measurement, provided that the computer is himself pre- 

 viously aware of the proportional, size, or measurement, with 

 ■which a show of correspondence is de^fired. Much of the so- 

 called remarkable coincidences of mystical writers are of this 

 class ; for it not unfrequently happens that the same root 

 measurement, by slight alteration, is worked up to bring about 

 coincidences with very different things. Thus Mr. Piazzi 

 Smith, by taking the height of the niche of the Queen's 

 Chamber of the G-reat Pyramid as 182'62, and multiplying it 

 by 2, he obtains 365 242, equivalent to the days in the year; 

 and again by arbitrarily taking the same dimensions as 185, 

 and multiplying it successively by 3*1416 and 10, he obtains 

 5,812, which he arbitrarily concluded to be the height 

 of the Great Pyramid in inches. But curiously enough 

 the same dimensions, 182-62, multiplied by 10 and divided 

 by 2 (why not at once multiply by 5'^) is made to show an 

 approximate to length of one of the sides in inches. These 

 are common examples of the facility with which many fancy 

 the discovery of purposeful design in numbers or dimensions, 

 when dealt with in a fanciful and arbitrary way. 



It seems to have been forgotten by such persons that any 

 root figure, by the arbitrary selection of a multiplier or divisor, 

 may be made to coincide exactly with any other number 

 provided the manipulator knows hefcrehand the numher or 

 proportional with which correspondence is sought to be 

 established. 



But making all allowance for the vagaries of the mystics, 

 there are many legitimate subjects of enquiry, upon 

 which some light might be thrown by the careful investigation 

 of ancient structures At the present day it is remarkable 

 how largely the numbers 7, 12, and 10, or simple multiples of 

 these enter into standards of space, time, weight, and value. 

 It is easy to imagine how 10 was seized upon so frequently as 

 a standard of measurement; for counting by means of the 

 digits of the two hands so universal and so natural at once 

 suggests a probable reason ; but the reasons for the original 

 selection of 7 and 12 for a similar purpose are not so easily 

 conceived. 



What, for example, were the determining causes for the 

 selection of the many sub-divisions of weights, values, time, 

 lineal and square measure ? 



Why have we a sequence of 4, 12, 20, in English money 

 in sub-divisions of the penny, shilling and pound ; of 14, 28, 

 56, 112, 2,240, in sub-divisions of a ton weight ; of 44, 440, 



