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UNIVERSITY OF COLORADO STUDIES 



o<j=- 



2r 



2+cos' e 



(18) 



On proceeding to the limit (^=0) this gives same result as 

 above (17). 



10. If an ellipsoid, {axes «, h, c, in order of magnittide), 

 receive a displaceinent of pure translation along its a axis, to find 

 the Center of Mass of homogeneous matter -filling the space vacated 

 (or the new space occupied), when the displacement is infinitesimal. 



Fig. 6. 



Let AjBjAj'B/, A2B2A,/B./ (Fig. 6) be sections through the 

 a and h axes of the ellipsoids in the two very near positions, the 

 ellipsoids intersecting in the plane of which NN' is a section. Sup- 

 pose the whole volume AjNA/N' occupied by homogeneous matter, 

 the volume of either ellipsoid is ^irahc, and as the linear displace- 

 ment of all points on the ellipsoid is the same and =A.^K^^O^O^^= 

 A, 'A/, it is easily seen that the volume of NA^N' A, or NA/N' A/ 

 is in the limit the product of the area of the plane of intersection by 

 the linear displacement ='jrhcy^Ofi^. 



Consider the ellipsoid A^A'^. Its Center of Mass is O, and if 

 the portion NAjN'Ag be supposed transferred into the position 

 NA2N'A,, carrying with it its Center of Mass from g' to g the Cen- 

 ter of Mass of the ellipsoid evidently becomes O^ 



