1884.] Theory of Continuous Calculating Machines, fyc. 189 



which may be neglected ; and we have 



which shows that at a distance of 4 centims. from either end, the 

 temperature is less than in the middle by e" 1 , that is l/2'7 of the 

 middle temperature; at 8 centims. it is less by l/7'4 ; and at 

 12 centims. it is less by 1/20. Thus we see that the cooling by 

 the ends is very sensible through a quarter of the length from either 

 end ; and must be carefully allowed for by aid of (7), unless lengths 

 of considerably more than half a metre are taken. But we also see 

 that the results stated in this preliminary paper are not sensibly 

 affected, or hardly sensibly affected, by cooling from the ends. 



XVII. " The Theory of Continuous Calculating Machines, and 

 of a Mechanism on a New Principle for this and other 

 purposes." By H. S. HELE SHAW. Communicated by Sir 

 WILLIAM THOMSON. Received June 19, 1884. 



(Abstract.) 



The paper commences with a statement of the conditions which 

 must be fulfilled by the mechanism of a continuous calculating 

 machine of the most general kind. It is shown that both the opera- 

 - tions of differentiation and integration must be performed by snch an 

 instrument. 



The only hitherto known mechanisms with which it appears possi- 

 ble to accomplish this are the " disk and roller," and its modification 

 the disk-globe and cylinder-integrator, or with some device which 

 relies on the same principle of action. A brief account is given of 

 the applications of the disk and roller itself, which mechanism was 

 first suggested by Poncelet, for integrating the pi-oducts of the two 

 . variables in a traction ergometer, and has since been applied by 

 various inventors the disk being sometimes replaced by a cone, as 

 a planimeter or platometer and integrator. 



The applications for the converse process of differentiation are less 

 known, and do not appear to have been brought into successful 

 operation. 



A speed indicator, in which a screw replaced the usual axis of the 

 roller, the roller forming the nut, was made three years ago by the 

 author. In this case the screw was driven at a speed which varied 

 with the space passed over by the moving body, and the disk at a 

 constant speed by a clock. The position of the roller on the disk was 



