452 Capt. J. Hollingworth on a 



The motion resembles that observed by 0. Reynolds 

 in his experiments on flow through pipes (Scientific Papers,, 

 vol. ii.). 



Conclusion. 



The view put forward in this note is that solutions of the 

 type considered may be used to indicate where existing 

 motions may be expected to break down ; to suggest where 

 viscosity will cause vortices to form ; and to enable an 

 estimate to be made of the effect of alteration in shape 

 on the resistance of a body moving at a given speed. 



My thanks are due to" Prof. A. R. Forsyth, Mr. C. H. 

 Kebby, and Prof. A. N. Whitehead, of the Imperial College 

 of Science and Technology, S.W., for their assistance. 



XLII. On a New Form of Catenary. 

 By J. Hollingworth, M.A., B.Sc, Capt. R.A.F* 



HPHE advent of aircraft during the war has naturally given 

 JL rise to a large number of new dynamical problems of 

 great variety. 



The particular one under consideration here has been sug- 

 gested by the application of wireless telegraphy as a means 

 of communication between aircraft and the ground. For 

 this purpose the aerial structure, which, as is well-known T 

 on the ground consists of an arrangement of wires on high 

 poles, is replaced on aircraft by a Jong flexible wire lowered 

 by the operator from the machine as soon as it has gained 

 sufficient height and having generally a weight on the end 

 to assist the lowering. 



Owing to the high airspeed of aircraft this wire trails 

 behind the machine as the result of wind-pressure on its 

 surface. The actual curve formed by the wire, which has a 

 considerable effect on its electrical properties, is. determined 

 by the wind-pressure and various physical constants of the 

 wire, and it is this curve which is investigated in the following- 

 paper. 



It must be understood that the calculations which follow 

 are based on the assumption that the machine is flying in a 

 straight line at a constant speed. Sudden variations in the 

 movement of the aeroplane, even if they could be expressed 

 mathematically, would produce transient effects of extreme 

 complexity. 



A problem dike this is almost incapable of direct experi- 

 mental investigation, as the state of affairs cannot possibly 



* Communicated by the Author. 



