122 PROCEEDINGS OF THE AMERICAN ACADEMY. 



dieted by the dynamical equations since, among other things for ex- 

 ample, the latter take no account of restraining forces such as were 

 introduced in this case by the steadying cords. 



Some experiments, on a small scale, were made with rotating tops, 

 driven through a Hooke joint from below. There were indications 

 that this would be a most satisfactory method of driving an unbalanced 

 rotor. The whole field is a very profitable one for research. 



As a practical detail, it should be pointed out that the rotator 

 shaft must be made short enough not to reach its own period of vibra- 

 tion at the speed employed. It was found impracticable to run this 

 rotator with a shaft 22 inches long. 



The Rotator. 



Fig. 4 gives a detail of one of the two arms which screw into the 

 central hub of the rotator. These arms were made from seamless steel 

 tubing bored out to one-half inch inside diameter. The peripheral 

 end of the tube was closed by screwing in a plug of steel, the threads 

 of which were figured to withstand the shear at 8000 revolutions per 

 minute, produced by the combined outward action of the centrifugal 

 force of the plug and that of the contents of the tube, assuming them 

 to be a liquid of specific gravity 1.3. In order to prevent leakage of 

 liquid through the screw threads, the plug was silver soldered in 

 position. 



The thickness of wall at the peripheral end of the tube was enough 

 to prevent bursting as calculated by Clavarino's formula for thick 

 hollow cylinders. This thickness of wall was also great enough to sus- 

 tain the outward tension as far as the point B, 3 inches from the end 

 of the tube. From this point on towards the center the tube had to 

 gradually increase in diameter in order to sustain the constantly in- 

 creasing load. If r is the radius at any point where the section is s, D 

 the density,/ the tensile strength of the material, and n the number 

 of revolutions, evidently fds = ^irhrrDsdr. Integrating this equa- 

 tion and solving, the proper dimensions for the inner end of the arm 

 were found. The screw thread on the inner end of the arm was 

 sufiicient to prevent the arm from shearing out from the hub. 



The Solution Tube. 



The solutions experimented on were iodides with iodine electrodes. 

 The actual tubes which contained the solutions were made of glass. 

 This was the only material found which was an insulator and at the 

 same time was not attacked by the iodine. The latter condition was 



