TRANSACTIONS OF SECTION A. 631 



FRIDAY, AUGUST 29. 



The following Papers and Eeport were read : — 



1. The Seat of the Electromotive Forces in the Voltaic Cell. 

 By Professor Oliver J. Lodge, D.Sc. — See Reports, p. 464. 



2. Report of the Committee for constructing and issuing practical Stan- 

 dards for use in Electrical Measurements. — See Reports, p. 29. 



3. On certain practical applications of a new Mechanical Principle. 

 By Professor H. S. Hele Shaw. 



A paper by the author, dealing with the theory of continuous calculating 

 machines, was communicated to the Koyal Society by Sir William Thomson, and 

 read on June 19 of this year. 1 In that paper a mechanism of a new principle was 

 suggested which would in theory perform the same operation as the disk and roller 

 mechanism, and at the same time was free from the defects of the latter. The 

 present paper is an account of the further development of the principle in the 

 direction of its practical application. 



It was necessary, in order that the mechanism might be understood, to first 

 briefly explain the principle of its action, which consists of two parts : (1) A pro- 

 perty of the motion of a sphere when in contact under certain conditions with 

 suitably placed rollers ; (2) a geometrical principle connecting the relative position 

 of the rollers in contact with the sphere, by which definite numerical results are 

 obtained. The first is as follows : If two surfaces of revolution roll upon one 

 another without slipping, their axes of revolution must lie in the same plane. 

 Suppose any number of disks or rollers to be in contact with a sphere round one of 

 its great circles ; then they will roll upon it if their axes lie in the diametral plane 

 which forms this great circle by its intersection with the sphere. The axis of revo- 

 lution of the sphere must be also in this plane, but may have any position therein. 

 Suppose a second set of disks or rollers in contact with the sphere round another 

 great circle formed by the intersection of a diametral plane perpendicular to the 

 first, and with their axes of revolution in this plane ; then, as before, the axis of 

 rotation of the sphere due to its rolling contact with the second set of rollers must 

 lie somewhere in the second diametral plane. There is, however, only one position 

 for the axis which can satisfy both the above conditions, and that is the intersec- 

 tion of the two diametral planes. Thus, by changing this axis by the mere rolling 

 motion of one set of rollers in a movable frame, any required velocity ratio of two 

 rollers belonging to the other set, which are placed in a fixed frame, can be ob- 

 tained. This is, moreover, done without the application of any force which will 

 produce an error, in the case of exact numerical results being required. 



The practical applications proposed are of two kinds, viz. : (1) for performing 

 mechanically continuous and discontinuous numerical calculations ; and (2) for vary- 

 ing in any required manner appreciable forces transmitted through it. The deter- 

 mination of the proper materials and construction for each case has been to a 

 certain extent guided by theoretical considerations, though it has been chiefly a 

 matter of experiment. 



The paper goes on to describe by means of diagrams, and the actual instru- 

 ment itself, a rolling planimeter, similar in its method of use to those of Sang and 

 -Clerk Maxwell, but differing in its principle of operation and in its ready adaptation 

 for measurement of the moment of area, and moment of inertia. 



An instrument for indicating efficiency is also described and illustrated. In 

 both the above instruments the forces transmitted are inappreciable, and the rolling 

 motion of the sphere is obtained by contact with the disks or rollers in such a way 



1 See Proc. Roy. Soc. vol. xxxvii. p. 189. 



