396 Royal Society .— 



theless made, and even now the triammonium- and tetrammonium- 

 compounds begin to unfold themselves in unexpected variety. One 

 of the most remarkable compounds belonging to the triammonium- 

 group is diethyl ene triamine, 



c,h„n s = (C =^ ) "=}n, 



This base, the first triacid triammonia, forms splendid salts of the 



formula ^ ftyt^ ^ N jw» C \, 



which will be the subject of a special communication. 



December 6. — Major-General Sabine, Treasurer and Vice-President, 

 in the Chair. 



The following communication was read : — 



"On the Gyroscope." By Arthur Hill Curtis, Esq. 



The object of this paper is to deduce on strict mechanical prin- 

 ciples all the known properties of the gyroscope. The only assump- 

 tion made is that the velocity of rotation impressed on the instru- 

 ment is very great compared with that which the attached weight 

 would produce on it if acting alone for an instant in a direction per- 

 pendicular to the axis. The theorems which the author establishes 

 are the following : — 



Theorem I. — The curves described by the extremity of the axis 

 of the gyroscope are a system of spherical cycloids generated by the 

 motion of a point on the spherical radius of a circle, which, con- 

 stantly remaining on the same sphere, rolls without sliding on the 

 circumference of another fixed circle situated on the same sphere. 

 These cycloids may be either ordinary, curtate, or prolate — including 

 the case when the system degenerates into a circle, in which case the 

 generating point becomes the centre of the rolling circle. Their 

 species depends on the direction of the initial velocity communicated 

 to the axis, the direction in which the instrument is set rotating, and 

 the position of the attached weight ; when, for instance, no initial 

 velocity is communicated to the axis, the cycloids will be ordinary 

 at first, and would continue so if the gyroscope were a perfect in- 

 strument for illustrating the motion of a body round a fixed point ; 

 but the inertia of the rings on which it is mounted, and of the at- 

 tached weight, as well as the resistance of the air, after a short period 

 has elapsed, has the effect of imparting to the axis a certain velo- 

 city which modifies the curves described by it, and at last causes the 

 motion of the axis to become for a time sensibly one of uniform pro- 

 gression ; it then becomes oscillatory again, the amplitudes of the 

 oscillations being smaller than before. 



Theorem II. — If the outer ring be fixed in any position so as to 

 restrict the axis of the gyroscope to a fixed plane, the motion of the 

 axis, when a weight is attached as above, is the same whether the 

 instrument be set rotating or not. It is proved that the angular 

 motion of the axis is determined by an equation of the same form as 

 that of a circular pendulum, which does not involve the angular 

 velocity of rotation impressed on the gyroscope. 



