( vii ) 



if hollow, like a round pipe, and, if folid, like a round (lick, wire, 

 or rope, and he conveys to iiis readers an idea of tiieir niinutenefs, by 

 comparing them with the known fize of a finglc hair. The method 

 u'ed by him in afcertaining this proportion he defcribes as follows : 

 ' In examining the inteltines of flies and other infc6ls by the mi- 



* crofcope, I have difcovered vefTels conveying the blood and juices, 

 ' the fmalleft ramifications or branches whereof appeared to me more 

 ' than two hundred thoufand times lei's than an hair of my beard. 

 ' And I will liere explain how I compute this proportion, which to 



* many may appear wonderful. 



' I have a plate of copper, with many lines engraven on it, and 

 ' divided into a number of fmall equal parts. I then carefully ob- 



* ferve how many of thefe parts one hair taken from my beard, and 

 ' feen through the microfcope, appears to cover. Suppofmg that the 



* diameter of this hair, when magnified, appears equal to fifty of 



* thofe parts, then with the point of a needle I trace on tlie copper 

 ' a line, of the fame fize by the naked eye as is equal to one of thole 

 ' fmall veins or vefiels in a fly, feen through the microfcope ; and I 

 ' find that nine of thofe fmall lines fo traced witli a needle, when 

 ' placed clofe together, are a fiftieth part of the diameter of the hair. 

 ' If then 450 diameters of thofe fmall veins which I moft plainly fee in 

 ' a fly are no more than equal to the diameter of one hair taken from 

 ' my beard, it follows,* by the rules of arithmetic, that one of fuch 



* Mr. Lceuvvcnhoek here confiders the hair to be round, as well as the fmall veflels he 

 alludes to, and, fuppofing^each of thefe to be cut through or acrofs the middle, the fe£lion 

 would exhibit a circle. Now the areas of circles being in proportion to the fquares of their 

 diaiiKtcrs, the Author's propofition is mathematically dsmonftrated thus: 



450 

 450 



2 2i;oo 

 1800 



202,500 



