On Printing Presses and their Theory. 325 
Draw BP perpendicular to DE and join AP. Then the 
plane ACDP is perpendicular to the plane BEB’; and BP 
drawn perpendicular to their line of common section is also 
perpendicular to the plane ACDP, and therefore to the line 
PA which it meets in that plane. Hence APB is a right 
angled triangle, and AP? +PB?—AB?. If BD be put= 
r, AC=r, AB=a, CD=z, and BE—s: BP will be- 
come ==sin z, DP. cos 7, and AP? (—DC?+4AC-PD’) 
=«x°+(r'+cos z)*. Hence sin? z4+22 +(7" 70s 2)*__a?. 
Expanding (r’ » cos z)?, and substituting r* for sin ?z-+ cos? 
z, we have z*+7r?—2r' cos ae =a?, Taking the flux- 
ions, 2 vdr= 21 E d (cos z= "2. sin z dz; and by resolu- 
tion, dz: —dz::> ~ sin 2 2e, But dv and —dz express the 
velocities of te points to which the weight and wee power are 
respectively applied; so that power : weight: : 7 ~ Sinz tert | 
sin BDE to rad. AC : CD. 
Cor. 1. When BDE=0 or 180°, sin BDE vanishes, and 
the gain of power becomes infinite. But DE is ee 
the position which BB assumes when AB and A’B’ com 
into the same vertical plane. Hence the weight init 
exc nece ee: eet Fi’ when she 0 
rae asus Ge tee cee vertical plane. When the e 
EDB is so small, or the line DC so large, that the ‘Scie 
of DC may be neglected, the r necessary to 
a given weight will vary as the sine Ae EDB, the angle 
eens | from the position at which it becomes evanescent 
2. Every thing else being the same, the gain of pow- 
er bes this combination will increase in the same se 
tion as the distan ee.ef iis lowes est points of the ee 
is diminished. 
Cor. 3. If, as will sepibtally be the case, the two extrem 
ities of each rod ar ¢ equidistant from the central line CF, 
or AC ae the power will be to the ween sth as 
BP: 
