ON A NEW FORM OF THE PLATOMETEtt. 235 



of adjustment would, in the course of time, produce a considerable deviation 

 from this equality, some contrivance is necessary to secure it. For this purpose 

 a wheel is fixed on the same axis with the ring SOs, and another of the same 

 size is fixed to the frame of the instrument, with its centre coinciding with the 

 vertical axis through C. These wheels are connected by two pieces of watch- 

 spring, which are arranged so as to apply closely to the edges of the wheels. 

 The first is firmly attached to the nearer side of the fixed wheel, and to the 

 farther side of the moveable wheel, and the second to the farther side of the 

 fixed wheel, and the nearer side of the moveable wheel, crossing beneath the 

 first steel band. In this way the spheres are maintained in their proper relative 

 position ; but since no instrument can be perfect, the wheels, by preventing 

 derangement, must cause some slight slipping, depending on the errors of work- 

 manship. This, however, does not ruin the pretensions of the instrument, for it 

 may be shown that the error introduced by slipping depends on the distance 

 through which the lateral slipping takes place ; and since in this case it must 

 be very small compared with its necessarily large amount in the other instru- 

 ments, the error introduced by it must be diminished in the same proportion. 



14. I have shewn how the rotation of the index-sphere is proportional to 

 the area of the figure traced by the tracing point. This rotation must be 

 measured by means of a graduated circle attached to the sphere, and read off 

 by means of a vernier. The result, as measured in degrees, may be interpreted 

 in the following manner: 



Suppose the instrument to be placed with the arm CF coinciding with CD, 

 the equator Bb of the index-sphere touching the pole A of the hemisphere, and 

 the index of the vernier at zero : then let these four operations be performed : 



(1) Let the tracing point be moved to the right till DE = DC, and there- 

 fore DCE, AGP, and P0 = 45. 



(2) Let the instrument be rolled upwards till the wheel K has made a 

 complete revolution, carrying the hemisphere with it ; then, on account of the 

 equality of the angles SOP, PCA, the index-sphere will also make a complete 

 revolution. 



(3) Let the arm CF be brought back again till F coincides with D. 



(4) Let the instrument be rolled back again through a complete revolution 

 of the wheel K. The index-sphere will not rotate, because the point of contact 

 is at the pole of the hemisphere. 



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