472 PROFESSOR MOSELEY, ON THE THEORY OF 



„ „ . . g tan a, - tan a-^ tan a^ ^ 



"* (tan a, + tan a^)-' ■' (tan a, + tan a.,)- •' 



,, .tanai + atanc, „ , 1 tanoi + Stana^ ., , d; , /l^^ 

 '* (tanoi + tan aa)' ' -^ 12 (tana,+tana.,)- - ' 



5. The Pier. 



If a, = oa, (see Fig. 6), the mass may be taken to represent a pier or 

 a wall of uniform thickness, and the equation (7) to its line of resistance 

 will become 



_ |rts'{tana, — tan Q] +»|sec0SPsin<I)+^ffl'} +sec02± Pic cos<^ 

 ■^ ^ rts + seceSPcos* ■■■ '■ 



Which is the equation to an hyperbola whose axis is inclined to the 

 axis of :s at an angle represented by the formula 



itan ' j^^ ^—r-i\ (19), 



^ Itan a, - tan ej ' 



and the co-ordinates of whose center are 



2Psincl)-(tana, -tane)2Pcos<t> + Afr , 2Pcos* 



^ ~ and -— (20). 



a cos G a cos O ' 



In the case in which 9 = 0, or the intersections are horizontal, 

 (Fig. 7), equation (17) gives for the equation to the line of pressure, 



s2Psin>t> =-acotcr./-|-«'cota-SPcos't'>y+— rt'cota-2± P^cos*...(21), 



which is the equation to a parabola whose axis is vertical, whose para- 



. 1 a cot a J , ,. ^ , 



meter is - ; ^ „ . — r, and the co-ordinates of whose vertex are 

 2 2P sm '^ 



- "p ■ ° {(i«-- tana2PcosfI)y-|«= + -tana2+P/i-cos<l>' 

 2 SPsin <b ^^* a ^ a 



) ' 



and \a tan aSP cos *. 



* a 



