And if yoa ftppofe the Heads of fuch a Cask to be two Plaint 
txGSt to the Axis , and alike remote from the Center , cutting 
off both ends of the figure produced 3 thenj if the middle /r«- 
(lum, fo intercepted, be computed as ^^^^^^^ ^.^^ 
Gallons is about 
rSoUdZonc] ] rSphseroid — — ^\i26^ 
I I a ^ Parabolical—— — l i JSJ 
Th ' lof ' ^Spindle. 5 
I I I two? Parabolical ? bafe and 112^,- 
[Trunci J J Conoids y height J 
the Method of Calculation being very eify by either fort of 
Tables 5 and ofgreataffinity in all thefe figures. And whereas 
the Learned have commonly fuppofed , Cask to be the midl^ 
frufta of Spheroids ^ and given Rules accordingly for Guaging 
them 5 thofeluppoffcions , as Vintners and others upon expe- 
rience alFert , are found too much cb enlarge the Capacity 5 fo 
that a Ca^fary Pipeythac is reputed to hold about 1 24J.gallons5up"- 
on Experiment hath been foand to contain but i i^.gallons: Aad 
to determine^what figure is moft proper to be admitted , cughc 
to be built upon fuch an Experiment as this 5 
Conceive a Caske to lye upon an HorizontalPhin with its 
paralel thereto 5 snd Perpendiculars on the outfide of the 
fmooth boards of the Cask to fall^ from the Head, Bourjg-> 
and fome intermediate point bctweenjUpon the Plain or Floore^ 
and in like manner the ajiis to be dcfigncd : Then find out fuch 
a curved line of fomc property 3 that may pafs thorough the 
faid Points , which conceive to have a rotation about the Axis^ 
line.'the round folid fo made m^ay be taken to reprefent the Cask^ 
and in the Writings o{ {geometers divers Curves are to be found;, 
that are capable ofpaffing through fuch Points and their round 
Solids meafured. But if the Reader think this too nice and trou- 
blefome, and that the Sfhxreidwxy is too great , and the Fa-^ 
. fdolick fpindle too little , then the Author gives fcope enough 
between 5 ftiowinghowto contrive fuch Rules ^ as (hall bcfi^- 
gree with Experience, . 
