54-] DETERMINATION OF CENTROIDS. 33 



(50) Prove that the volume of a truncated right cylinder (i.e. a right 

 cylinder cut by a plane inclined at any angle to its base) is equal to the 

 product of the area of its base into the height of the truncated cylinder 

 at the centroid of its base. 



(51) Prove that the volume of a doubly truncated cylinder is equal 

 to the product of the area of the section at right angles to the axis into 

 the distance of the centroids of the bases. 



54. For the theory of moments and centres of mass the student is 

 referred to W. SCHELL, Theorie der Bewegung und der Kr'dfte, Leipzig, 

 Teubner, Vol. I., 1879, PP- 81 100; E. J. ROUTH, Analytical statics, 

 Cambridge, University Press, Vol. I., 1891, pp. 270-314; J. SOMOFF, 

 Theoretische Mechanik, iibersetzt von A. Ziwet, Leipzig, Teubner, Vol. II., 

 1879, pp. 1-72. For problems see in particular W. WALTON, Problems 

 in illustration of the principles of theoretical mechanics, Cambridge, 

 Deighton, 1876, pp. 1-45 ; M. JULLIEN, Problemes de mecanique ration- 

 nelle, Paris, Gauthier-Villars, Vol. I., 1866, pp. 1-46; F. KRAFT, Prob- 

 ieme der analytischen Mechanik, Stuttgart, Metzler, Vol. I., 1884, pp. 

 527-617. Compare, also, B. PRICE, Infinitesimal calculus, Oxford, 

 Clarendon Press, Vol. III., 1868, pp. 163-206; MOIGNO, Lemons de 

 mecanique analytique, Statique, Paris, Gauthier-Villars, 1868, pp. 106 

 206 ; G. MINCHIN, Treatise on statics, Oxford, Clarendon Press, Vol. 

 I., 1884, pp. 261-305 ; I. TODHUNTER, Analytical static ~s, edited by J. D. 

 Everett, London, Macmillan, 1887, pp. 115-189 ; W.WALTON, Problems 

 in elementary mechanics, London, Bell, 1880, pp. 56-78; and for geo- 

 metrical methods, the works on graphical statics. 



PART ii 3 



