for turning Ovals. 383 
s and l, an oval will yet be defcribed, whole center will 
be the fame with that of the oval firft defcribed when 
the tool was at m; but its principal axis will crofs the 
principal axis of that oval (fig. 2. and 3.). Draw right 
lines both from m the old place of the tool, and from m 
the new place of the tool, to the point e marked on the 
reft. Half the angle which thefe two lines make with 
each other will be the angle which the principal axis of 
the new oval makes with the principal axis of the old 
one. 
It is well known, that when the oval engine is fet in 
order for working, there is a part which Hides back, and 
is then fixed, which feparates the two centers of motion 
and gives the eccentricity ; for the difference between the 
firft and fecond femi-axes will be juft as much as the cen- 
ters are thus feparated : call the diftance between the two 
centers e; let now the tool be fixed in any place, upon, 
above, or below the rejl\ call rn E the diftance of the tool 
from the middle point between the centers (marked e on 
the reft) d ; and the greater femi-axis of the oval fo de- 
fcribed will be d +|-E, and the lelfer femi-axis d- \ e; and 
thus both the form and pofition of the oval will be 
known. All workmen know the tool mult never be 
raifed above the place where it was at firft held, and we 
fee 
7 
