370 Prof. Charlotte A. Scott. On Plane Culrics. [Nov. 23, 



the centres of the side spans. In doing so, however, the experiments 

 show that there is a danger of the calculated speed exceeding the 

 actual, whilst by taking all the pulleys on the two side spans into 

 account the calculated speed will be slightly less than the actual 

 speed. 



If the spans of a continuous shaft, supported on bearings placed at 

 equal distances apart, are all loaded in the same manner, each whirls 

 independently of the rest, and the problem reduces to that of a loaded 

 shaft supported on bearings at the ends. 



The experimental apparatus by which the calculated results have been, 

 for the most part, verified is shown in a figure. The experimental 

 shaft was 2 ft. 8 in. long and 0'2488 in. diameter. The motion was 

 transmitted from the headstock spindle to the experimental shaft by 

 a fine piece of steel wire (about 1J in. long and 21 B.W.Gr. diam.), 

 so that the shaft was subjected to very little constraint at the end. 

 The experimental pulleys were models of actual pulleys being de- 

 signed for both weight and inertia. The headstock spindle was 

 driven from a turbine, the constancy of the speed being shown by the 

 steadiness of a column of liquid forced by a centrifugal fan indicator 

 up a glass tube. In taking the number of revolutions corresponding 

 to any period of whirl an ordinary counter pushed into the end of the 

 headstock spindle was used. In making any experiment three trials 

 were made (each of three minutes' duration) and the mean of the 

 results taken. Over 150 experiments have been made with this ap- 

 paratus, and the observed results invariably approximate very closely 

 to the calculated results. Experiments have also been made with 

 actual cases of shafting, and it would appear that, following the 

 method of solution sketched above, the calculated speed is about 

 3 or 4 per cent, less than the actual speed. 



The experiments were carried out in the Whitworth Engineering 

 Laboratory, the Owens College, Manchester. 



V. " On Plane Cubics." By CHARLOTTE ANGAS SCOTT, D.Sc. 

 (Lond.), Professor of Mathematics at Bryn Mawr College, 

 Pennsylvania. Communicated by A. R. FORSYTE, Sc.D., 

 F.R.S. Received September l, 1893. 



(Abstract.) 



In this paper the first few sections are devoted to certain 

 constructions for the cubic, its Hessian, and its Cayleyan. As- 

 suming three collinear inflexions for the cubic, and the tangents 

 at these points, i.e., eight conditions, one more point determines the 

 cubic, and, consequently, also the Hessian and Cayleyan. Taking 



