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[[upper right hand corner]](302
perpendicular to EQ; then per mech. t+1: p over T+1 squared::1:p over T+1 squared multiplied by t+1 equals ET, the pressure upon A, which substraited from E6, leaves PT over T+1 squared multiplied by t+1 equal to Et, the power with which the plane endeavours to move in the direction EB.
  4. Since the plane PEL can only move in a circle round A, EB is an imaginary direction; and therefore this power Et, must be reduced to the direction EQ, perpendicular to EA; whence, per mech. 1: t+1 :: pt over T+1 squared multiplied by t+1 : pt over T+1 squared equals Et+td equals EQ, a general theorem for the power acting against the plane PEL, in the direction QE to sustain the whole in equilibrio. Q.E.F.

Cor. 1. As the distances of A and C from E are not concerned, they may be assumed at pleasure, so that A is perpendicularly over C.
Cor. 2. It appears that the less T is in respect to t, the greater will the effect EQ be upon the rod of the pendulum.

Example
Suppose the [[angle symbol]] CEL=59 1/2 degrees and AEL=51 1/2 degrees, (as I measured them in Ludlam's figure) and the tooth E endued with a power equal to 6 Ounces.
A general Trigonometrical solution.
by supposing p=1. }The red figures are those next above them X6 Ounces for this particular example.
1. In [[triangle symbol]] PEK, PE+PK= 2,6976631 Log. Co Ar. 9[[the 9 has a bar over it]], 5690123
: 1=p :: 1, Rad. : PZ _ _ _ _ _ _ _ =, 3706912= BE [[next number in red,below previous number]]2,2241472 
and PE + PK - PZ = HE ------ = ,6293088 [[next number in red,below previous number]] 3,7758528
2. In [[triangle symbol]]DBE,BE=PZ; & BD+DE=2,6976631, Co Ar. 9[[the 9 has a bar over it]],5690123 :BE=[[strikethrough]]1,6[[overwritten by following number]] 0,3706912 Log. 9,5690123 [[previous number underlined, but line struck through]] 
:: [[strikethrough]]B[[/strikethrough]]DE - = 1,6976631 Log. [[underlined]]-0,2298515[[/underlined]]
:ES= ,2332793 [[long horizontal line]]  9[[the 9 has a bar over it]],3678761 [[next number in red]] 1,3996758
3. In [[triangle symbol]]FbE,EB-ES=Eb=,1374119.& EF+Fb=2,2459742  
Co Ar. 9[[the 9 has a bar over it]].6485952  
:Eb=,1374119 [[long horizontal line]] 9[[the 9 has a bar over it]],1380243  
:: 1=EF:ET=,06118142-8[[the 8 has a bar over it]],7866195  [[next number in red]],36708852.  
4. In [[triangle symbol]]Edt,EB-ET=Et=,0762305, and  [[the next number in red]],457383  
1 Rad :Et=,0762305 Log. 8[[the 8 has a bar over it]],8821287  
::Et+1=2,2769742[[written over another number]] Log. [[underline]]0,3514048[[/underline]][[written over another number]]   
:Et+td=EQ=,1772118[[written over another number]] - 9[[the 9 has a bar over it]],2339330[[written over nother number]]  
[[the following text is red and has strikes through it]],4922496  
[[the following text is red]] 1,0272708