59 



VI. CAPACITY. 



New measures. 



Substitute for. 



Near values. 



Litre 



Quart 



61 cubic inches. I 





metre cubed. 



I litre 



Pint 





} litre 







Decilitre 



Gill 



6 cubic inches. 



Decalitre 



2 gallons 



610 cubic inches. 



J decalitre 



Gallon 



305 cubic inches. 



2 decalitres 



Bushel 



1220 cubic inches. 



Catolitre 



Barrel 



26 gallons. 



2 catolitres 



Hogshead 



52 gallons. 



Chilolitre 



Tun 



260 gallons. 



I have spoken only of the measures used in the common 

 business of daily life : they, as well as the more rarely used 

 instruments employed in the measurement of the results of 

 the action of the various physical forces of gravity, light, 

 heat, electricity, etc., are all direct functions of one simple 

 element of linear dimension only (for surface and volume 

 are respectively mere products of two and of three linear 

 dimensions), and destined exclusively to the measurement 

 of certain contents of space without reference to time. 

 But space is really constituted of two different elements, 

 namely, linear magnitude and angular magnitude : these 

 elements, though not heterogeneous, are mutually incom- 

 mensurable, insomuch that angular magnitude is only 

 approximately measured by the straight line through the 

 intervention of its corresponding circular arc ; but so close 

 may this approximation be carried, that for every practical 

 purpose the measure of angular magnitude becomes also a 

 definite function of linear dimension. But while the unit 

 of linear magnitude is naturally indeterminate, and only to 

 be fixed by arbitrary decision, we have in angular magni- 

 tude an absolutely determinate unit in the sum of all the 

 plane angles that can have place (without interference or 



