437 



cast-iron bars, under the direction of Professor Hodgkinsou. The 

 bars consisted of seventeen different kinds of iron, each set of bars 

 being of the like quality and manufacture ; and in several of these 

 sets, which might have been expected to yield the same results, the 

 difference is fully as great as in the cases here exhibited. From this 

 fact an inference may be drawn in favour of the general applicability 

 of the principles developed in the foregoing pages to cast-iron btams 

 and girders of every variety of section. 



II. " On the Theory of the Gyroscope." By the Rev. WILLIAM 

 COOK, M.A. Communicated by Professor A. WILLIAMSON, 

 F.R.S. Received February 13, 1857. 



(Abstract.) 



The explanation of the movements of the Gyroscope (as well as 

 its mathematical theory) is founded on the principle enunciated in 

 the two following verbal formulae. 



I. When a particle is made to move s r ? a plane by any 



applied force, but in consequence of its connexion with some rigid 

 body on the same side of the plane, loses some of its momentum in 

 a direction perpendicular to the plane ; all the momentum so lost is 

 imparted to the rigid body, which is consequently impelled 



f towards 1 , , , 

 (from ) ^e plane. 



II. When a particle is made to move < ,. 0wa S > a plane by any 



applied force, but in consequence of its connexion with some rigid 

 body on the same side of the plane, receives an extra momentum in 

 a direction perpendicular to the plane ; all the momentum so gained 

 is taken from the rigid body, which is consequently impelled 



The mass of the disc of the gyroscope is supposed to be com- 

 pressed uniformly into the circumference of a circle of given radius 

 (?), and to revolve round an axis with a given uniform angular ve- 

 locity (w). To facilitate the arithmetical computation of the for- 



