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rilANgsACTIONS OF SECTION A. 



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FlilDAY, AUai'ST 29, 

 'J'he followiii£^ Pajx^rs and Report were read :— 



1. The Sent of the Elcdromnti'i-e Forces in the Voltaio Cell. 

 Jjij Professor Oliver J. Lodhk, D.Hc. — See Reports, p. 404. 



2. Report of the Committee for constructing avd issx^ing 'practical Stan- 

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



o. Oil certain practical appAtcatiuns of a new Mechanical Trinciple. 

 llg Professor H. S. Hi;le Shaw. 



A jiapor by tlie autlaor, dealing witli the theory of continuous calculating 

 jiiacliiues, was communicated to the lloyal Soeii'ty by Sir AN'illiam Thomson, and 

 rriid on June 11> of this year.^ In that paper a mechanism of a new princi])le was 

 iugpested wliicli would in theory perform the same operation as the disk and roller 

 mechanism, and at tlr^ same time was free from llie defects of tlie 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 mitrht bo understood, to first 

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

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

 suitably ]daced rollers ; (2) a geometrical principh?. connecting the relative position 

 of tlie rollers in contact with tlie sphere, by which deiiuite numerical results are 

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

 anotlier witliout slipping, their axes of revolulion must lie in the same plane. 

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

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

 which i'orms this great circle h\ its intersection with the spliere. The axis of revo- 

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

 Suppose a second set of disks or rollers in contact with tlie sphere round anotlier 

 irreat circle formed by the intersection of a diametral plane perpendicular to llie 

 lirst, 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 tlu; 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 

 niechanically 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 eiliciency is also described and illustrated. In 

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

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



' Sec Proc. Roy. Soc. vol. xxxvii. p. 18!>. 



