the Velocities of Machinery . 45 



tity of mercury sufficient, than what must have been em- 

 ployed either with a cyhndrical or hemispherical vessel. 

 In every case two precautions are necessary to be observed: 

 — First, That when the cup is revo'ving with its greatest ve- 

 locity, the mercury in the midc'le shall not sink so low as 

 to allow any of the spirits in the tube to escape from the 

 lower orifice, and that the mercury, when most distant from 

 the axis, shall not be thrown out of the cup. Secondly, 

 That when the cup is at rest, the mercury shall rise so high, 

 above the lower end of the lube, that it may support a co- 

 lumn of spirits of the proper length. 



Now in order that the quantity of mercury, consistent 

 with these conditions, may be reduced to its minimum, it 

 is necessary — first, that if MM, fig. i, is the level of the 

 mercury at the axis when the cup is revolving with the 

 greatest velocity, the upper part MMXY of the cup should 

 he of such a form as to have the sides covered only with a 

 thin film of the fluid ; and secondly, that for the purpose of 

 raising the small quantity of mercury to the level LL, which 

 may support a proper height of spirits when the cup is at 

 rest; the cavity of the cup should he in a great measure 

 occupied by the block KK, having a cylindrical perforation 

 in the middle of it for the immersion of the tube, and leav- 

 ing sufficient room within and arouud it for the mercury to 

 move freely both along the sides of the tube and of the 

 vessel. 



The block KK is preserved in its proper position in the cup 

 or vessel XYZ, by means of three narrow projecting slips 

 or ribs placed at equal distances round it, and is kept from 

 rising or floating upon the mercury by two or three small 

 iron or steel pins inserted into the underside of the cover, 

 near the aperture through which the tube passes. 



It would be extremely difficult, however, nor is it by any 

 means important, to give to the cup the exact form which 

 would reduce the quatitity of mercury to its minimum ; but 

 we shall have a sufficient appro.ximation, which may be 

 executed with great precision, if the part of the cup above 

 MM is made a parabolic conoid, the vertex of the generat- 

 ing parabola being at that point of the axis to which the 

 mercury sinks at its lowest depression, and the dimensions 

 of the parabola being determined in the following- manner: 

 Let VG, fig. .3, represent the axis of the cup, and V the 

 point, to which the mercury sinks at its lowest depression ; 

 at any point G above V, draw GH perpendicular to VG ; 

 let n be the number of revolutions which the cup is to per- 

 form 



