262 Prof. J. Thomson on [Feb. 3, 



III. " On an Integrating Machine having a New Kinematic Prin- 

 ciple." By Professor James Thomson, LL.D., F.H.S.E. 

 Communicated by Prof. Sir William Thomson, F.R.S. 

 Received January 31, 1876. 



The kinematic principle for integrating ydce, which is used in the 

 instruments well known as Morin's Dynamometer* and Sang's Plani- 

 meter f , admirable as it is in many respects, involves one element of 

 imperfection which cannot but prevent our contemplating it with full 

 satisfaction. This imperfection consists in the sliding action which the 

 edge wheel or roller is required to take in conjunction with its rolling 

 action, which alone is desirable for exact communication of motion from 

 the disk or cone to the edge roller. 



The very ingenious, simple, and practically useful instrument well 

 known as Amsler's Polar Planimeter, although different in its main 

 features of principle and mode of action from the instruments just 

 referred to, ranks along with them in involving the like imperfection of 

 requiring to have a sidewise sliding action of its edge rolling wheel, 

 besides the desirable rolling action on the surface which imparts to it 

 its revolving motion — a surface which in this case is not a disk or cone, 

 but is the surface of the paper, or any other plane face, on which the 

 map or other plane diagram to be evaluated in area is drawn. 



Professor J. Clerk Maxwell, having seen Sang's Planimeter in the 

 Great Exhibition of 1851, and having become convinced that the com- 

 bination of slipping and rolling was a drawback on the perfection of the 

 instrument, began to search for some arrangement by which the motion 

 should be that of perfect rolling in every action of the instrument, cor- 

 responding to that of combined slipping and rolling in previous instru- 

 ments. He succeeded in devising a new form of planimeter or inte- 

 grating machine with a quite new and very beautiful principle of kine- 

 matic action depending on the mutual rolling of two equal spheres, each 

 on the other. He described this in a paper submitted to the Eoyal 

 Scottish Society of Arts in January 1855, which is published in vol. iv. 

 of the Transactions of that Society. In that paper he also offered a 



* Instruments of this kind, and any others for measuring mechanical work, may- 

 better in future be called Ergometers than Dynamometers. The name " dynamometer " 

 has been and continues to be in common use for signifying a spring instrument for mea- 

 suring force ; but an instrument for measuring work, being distinct in its nature and 

 object, ought to have a different and more suitable designation. The name " dyna- 

 mometer," besides, appears to be badly formed from the Greek, and for designating an 

 instrument for measurement of force. I would suggest that the name may with advan- 

 tage be changed to dynamimeter. In respect to the mode of forming words in such 

 cases, reference may be made to Curtius's Grammar, Dr. Smith's English edition, § 354, 

 p. 220.— J. T., 26th February, 1876. 



t Sang's Planimeter is very clearly described and figured in a paper by its inventor, 

 in the Transactions of the Eoyal Scottish Society of Arts, vol. iv. January 12, 1852. 



