SOME ‘‘ CURIOUS MATHEMATICKS ”’ 191 
Consequently, if the thickness of 19602000000 
ar pe 300 
a sand-grain is 1, the vessels in cae A eee 
the little animalcules are 5880600000000 
And because this number is so exceeding great, I have 
thought good to express the proportion in terms of a 
hair’s breadth in relation to the circumference of the 
earth. 
5400 miles’ for the length of the circumference 
2000 rods for every mile 
gives 10800000 rods for the circumference 
12 feet for one rod 
g1ves 129600000 feet for the circumference 
12 inches in one foot 
gives 1555200000 inches in the circumference 
600 hairbreadths in one inch 
gives 933120000000 hairbreadths for the length of the 
circumference. 
This number of hairbreadths, which is equal to the 
length of the circumference of the earth, even when again 
multiplied by 6 will not equal that number aforesaid 
which represents the proportion of the vessels in the little 
animals to the thickness of a sand-grain (as we have 
estimated it above). To sum up, then: 
As a sixth of a hair-breadth is: 
To a length of 5400 miles: 
So is one of the smallest vessels in the smallest 
animalcules : 
To the thickness of a sand-grain (of such size that 
80 thereof, lying one against another, equal a 
length of one inch). 
Sir, you have here the wonderful proportions that I 
‘ Leeuwenhoek’s ‘‘ mile’’, consisting of 2000 “rods” of 12 feet, is, as a 
simple calculation shows, equal to some 4% English miles. (The English 
mile = 320 rods, and the English rod = 162 feet.) 
