40 



The best method of showing the tar in gas is to pass it through 

 or over well-purified coal-oil, and subsequently through a good con- 

 densing arrangement. 1 have known colourless coal-oil become of 

 a dark mahogany colour, and have separated sulphuretted hydrogen, 

 ammonia, and solid pitch by distillation. 



IT. " On the Gyroscope." By ARTHUR HILL CURTIS, Esq. 

 Communicated by Professor BOOLE. Received Sept. 

 20, 1860. 



(Abstract.) 



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 



