Tninsactions Society Naval Archilecis and Marine Engineers, Vol. i8, igio. 



To illustrate paper on " The Gyroscope for Marine Purposes," 

 by Elmer A. Sperry, Esq., Member. 



Plate 57 



771 J*"^ T T I II 



+Ssin 7// cos TpMrii^-a^sin jf/cosil;cos(f>-\- ycos^-il/cos <p . 



low as before put m = 

 Then 



W 



-^v^ 



-,dl/j 





sin^cos 



^z~e7T 



'S 



/3^sm ^sin i//cos -il/dil/^-sajScos^sin if/c{y/-Osm<f>diff-^cos © 

 ~ 2' (^siml/cosTp'd'il/ 



Evidently the EOiaents for a ooHplete ring of radius r and weight 

 w will be obtained ty integrating the above exprssfior.s v.-ith re- 

 spect to 1^ "from to 25r» 



Sow 



"-Ztt 



sin\lfcosilr<li(/^0 / sin^if^dxl/ ^7r==\ cos'^dY 



Jo Jo 



let lly_ ?Jiy M2 denote the raornents for the complete ring» Ta&n 

 evidently 



27TCC/ 



',/3cos(l*-v2rr'/^in(lt =^r^ia/]co^^-^ysin(pK 



