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UNIVERSITY OF COLORADO STUDIES 



in this plane, and 0G=: — by (7). If now the hemisphere be rotated 



round the diameter perpendicular to the plane of the paper, through 



a very small Za, so that the section becomes A'CB' and the Center 



of Mass G', the result is the same as if a lune /a were transferred 



over and attached to the opposite edge of the hemispherical shell, 



carrying its Center of Mass from g to g' . 



^ ^ 1 GG' lune ,. , ^ 



We have then, = which becomes, when a is 



gg ' hemisphere 

 r 



Xa 



indefinitely diminished, 



20^ 



^ .-.0(7= as above. (8) 



TT 4 



The case of the spherical cap, deduced otherwise above (6), 

 would afford a favorable example for the application of the method 

 of this article, by transferring an infinitely thin lune from one semi- 

 edge to the other. 



The Center of Mass of a solid hemisphere is immediately re- 

 ducible to that of a homogeneous hemispherical shell. Its distance 



3r 

 from the center of the sphere is as is well known (10) 



8 



6. Knowing this: — 



To find the Center of Mass of a semicircular wedge of infinitely 

 small angle. 



Let the section ACB (Fig. 3) now represent a section of a solid 

 hemisphere. OG now =|r by (10) and AOA' is a section of a 



