THE LOCATION OF THE CUBIC PARABOLA. 



129 



To determine the value of </> from the above equation let 

 us put 



11 



then 



Cos 3a = - 4 P/n 3 

 Cos <t> = n Cos a. 



Example. 



R '= 68 R 2 = 165 a = 3*14 

 Log /? = 9*8107212 Log w = 0*1669830 



4 = -0-6020600 



cos a = 9*8235023 



0*4127812 

 0*5009490 



Log n 3 = 

 „cos3«= -9*9118322 

 3 « = 144° 42' 46"*2 

 « = 48 14 15*4 



l/c = f i? 2 sin 2 <f> cos 



„ cos <f> = 9*9904853 



<£ = 11° 56' 58"*8 



R x versin <f> + a 



from which we And y c , equals 4*61358, and from the equation 



h \ 



1 + -£- = cos (1 + I sin 2 <£) 7 



we may find "fe." To simplify the numerical calculation 

 of this equation we may put 



1 +" AV== 2 cos <f> cos 2 i f. 

 -0,2/ 



Cos "A = | sin 2 •<£. 



I— June 6. 1917. 



