232 ON A NEW FORM OF THE PLATOMETER. 



the horizontal disc ; so that in working the instrument, the motion of the index- 

 disc is compounded of a rolling motion due to the rotation of the first disc, 

 and a slipping motion due to the variation of the generating line. 



5. In the instrument presented by Mr Sang to the Society, the first disc is 

 replaced by a cone, and the action of the instrument corresponds to a mathe- 

 matical valuation of the area by the use of oblique co-ordinates. As he has 

 himself explained it very completely, it will be enough here to say, that the 

 index-wheel has still a motion of slipping as well as of rolling. 



6. Now, suppose a wheel rolling on a surface, and pressing on it with a 

 weight of a pound; then suppose the coefficient of friction to be |, it will 

 require a force of 2 oz. at least to produce slipping at all, so that even if the 

 resistance of the axis, &c., amounted to 1 oz., the rolling would be perfect. But 

 if the wheel were forcibly pulled sideways, so as to slide along in the direction 

 of the axis, then, if the friction of the axis, &c., opposed no resistance to the 

 turning of the wheel, the rotation would still be that due to the forward motion ; 

 but if there were any resistance, however small, it would produce its effect in 

 diminishing the amount of rotation. 



The case is that of a mass resting on a rough surface, which requires a 

 great force to produce the slightest motion ; but when some other force acts 

 on it and keeps it in motion, the very smallest force is sufficient to alter that 

 motion in direction. 



7. This effect of the combination of slipping and rolling has not escaped 

 the observation of Mr Sang, who has both measured its amount, and shown how 

 to eliminate its effect. In the improved instrument as constructed by him, I 

 believe that the greatest error introduced in this way does not equal the ordi- 

 nary errors of measurement by the old process of triangulation. This accuracy, 

 however, is a proof of the excellence of the workmanship, and the smoothness 

 of the action of the instrument ; for if any considerable resistance had to be 

 overcome, it would display itself in the results. 



8. Having seen and admired these instruments at the Great Exhibition in 

 1851, and being convinced that the combination of slipping and rolling was a 

 drawback on the perfection of the instrument, I began to search for some 

 arrangement by which the motion should be that of perfect rolling in every 



