232 SECTION MECHANICS. 



this, with the exception that the sliding motion is entirely got rid of,, 

 being replaced by the motion of a sphere which rolls both on a sphere 

 and on a cylinder. The motion that it records depends upon the dis- 

 tance of the point of contact with the sphere from the centre of the 

 disc on which it rolls. In principle it is exactly the same as this, and 

 the principle of both is the same as in ordinary integration, namely, 

 the ordinary rule that the area equals the integral of y d x. 



With regard to the measurement of solids, the general principle 

 of solid measurement in ordinary use is simply that of displacement 

 or replacement, namely, that a standard measure is made, and all other 

 measures are compared with that by actually pouring some kind of 

 material, either corn, or some dry material of that kind, or water, from 

 one to the other. The most obvious measurement of solids by displace- 

 ment, is by filling a vessel up to a certain edge with a liquid, and dipping 

 the solid into it either entirely, or up to some measured point, and 

 ascertaining the quantity that overflows. We have, I am afraid, no 

 exemplification of either of those modes of displacement here in their 

 simplest form. With regard to some instruments I have seen, I may 

 mention that it is necessary to observe great caution in the form of the 

 lip by which the overflow takes place if you wish to secure any accurate 

 measurement, for a difference in the form will make it measure differ- 

 ently, and there is also great difference in the viscosity or molecular 

 character of different liquids, and scarcely any two liquids measure 

 alike. It would not be fair, however, to say that is the only mode of 

 measuring solids. Of course, practically, the first thing you have to do 

 in order to compare solid-measure with linear, is to construct very 

 carefully a solid, either hollow or not, upon geometrical principles, so 

 as to connect it with linear-measure, and the most [ordinary mode of 

 doing that is by making cylinders of which you can measure the height 

 with very great accuracy, and in which you can secure a very con- 

 siderable degree of accuracy in form, and also are able with accuracy 

 to measure the diameter. Taking the three things together, I do not 

 think it can be said, that these measures at all approach in accuracy 

 the linear-measures. There are various reasons why they should not. 

 In the first place, they depend not only on three different sets of linear- 

 measure, each one of which requires to be got with accuracy, but also- 

 depend on accuracy of form, and upon the possibility of measuring 



