THOMSON AND TAIT's NATURAL PHILOSOPHY. 785 



evils, and raised to the rank of one of the most powerful aids to science. 

 Rolling and sliding have been more than once combined in the hope of obtaining 

 accurate measurements, but the combination is fatal to accuracy, and these 

 new machines, one at least of which has been actually constructed and used, 

 are the first in which pure rolling friction has had fair play given it as a 

 method of mechanically accurate integration. 



A method is also given of combining a number of disk, globe, and cylinder 

 integrators, so as to form a machine the motions of two pieces of which are 

 related to each other by a differential equation of any given form. These 

 machines all work in a purely statical manner, that is, in such a way that 

 the kinetic energy of the system is not an essential element in the practical 

 theory of the machine (as in the case of pendulums, &c.), but has to be taken 

 into account only in order to estimate the magnitude of the tangential forces 

 at the points of contact which might, if great enough, produce slipping between 

 the surfaces. Thus, by means of a machine, which will go as slowly as may 

 be necessary to keep pace with our powers of thought, motions may be 

 calculated, the phases of which in nature pass before us too rapidly to be 

 followed by us. 



In the original preface some indications were given of what we were to 

 expect in the remaining three volumes of the work. We hope that the reason 

 why this part of the preface is omitted in the new edition is that the work 

 will now go on so steadily that it will be unnecessary to preface performance 

 by promise. 



VOL. II. 



