!8o ANSWERS. 



(49) Taking the axis of the cup as axis of x, let (a, b) be the cen- 

 troid of cup and handle, m their mass ; (x lf o) the centroid of the 

 water whose mass can be expressed by (m/c)x^ where c is a constant. 

 Then the co-ordinates x, y of the centroid of cup, handle, and water 

 together fulfil the equation (a -f- c)y 2 bxy 2 bey + b~c = o, which 

 represents a hyperbola. 



(50) Taking the axis of z parallel to the axis of the cylinder, and the 

 origin in the line of intersection of the bases, we have F== ( \ zdxdy, or 

 if <f> be the angle of inclination of the bases : 



F= tan< f \ydxdy = tan <f> -y \ \ dxdy. 



(51) Apply (50) twice. 



Page 35. 



(1) 300 ooo F.P.S. units. (3) 71600. 



(2) 34^ miles per hour. 



Page 40. 



(1) 6.4 x io 5 poundals= 8.9 x io 9 dynes. (3) 0.14. 



(2) 4.5 pounds. (5) 60. 



Pages 51-53. 



(4) 100 V7 ; tan- 1 1 Vs. 

 (7) ioV^(V 

 (9) <2 = i(- 



(io) R = 569 ; angle with horizon = 99 27'. 



(12) Twice the focal distance. 



(13) 124 i2 f .5. 



(14) 90. 



(15) (a) V~2.W; (S) 2Wcosi(ir/2-0). 



(18) 2 Wcos %(ir/2 + a), etc. 



(19) (a) a = 30, =120, 7=30; () impossible. 

 (21) T=fsW, nearly; ^=C=o.86W^ ^=0.675^. 



