Mr. Lubbock on Cask-Cktffins. 



327 



subject in question. I shall limit myself, in the following brief 

 remarks, to the gaging of casks lying, not entering upon the 

 question of the gaging of ships, or stills, or any other irre- 

 gular figures, merely premising that this can only be done by 

 quadratures, or, as it is termed in works on gaging, by the 

 method of equidistant coordinates. A very material differ- 

 ence, however, exists between these problems and the one 

 which I propose here to notice, and which consists in this 

 circumstance, that in the one case extreme dispatch is a ne- 

 cessary requisite in the method employed; in the other, that 

 is to say, in ascertaining the tonnage of ships, or the content 

 of any fixed reservoirs, such as distillers' vats, &c, time not is 

 so great an object; so that the peculiar difficulty of cask- 

 gaging arises from the necessity of combining accuracy with 

 celerity in the operation. 



It has long been customary to divide casks into four varieties, 

 which are thus defined : 



1. The middle frustum of a spheroid. 



2. The middle frustum of a parabolic spindle. 



3. The frustums of two equal parabolic conoids. 



4. The frustums of two equal cones. 



X M 



O JC 



I find these distinctions in a work, entitled " Cosmographia" 

 by Dr. John Newton, published in 1679, and they appear to 

 have continued ever since. 



I place the origin of rectangular coordinates at the centre 

 of the cask, and I suppose the cask to be a figure of revolu- 

 tion about the horizontal axis Ox, as in the diagram annexed. 

 According to the preceding definitions, in the first variety 

 the arc ABC is considered to be a portion of an ellipse of 



