New Form of Catenary. £5$ 



be imitated in a laboratory. The trailing wire can of course be 

 photographed from another machine flying alongside, but to 

 obtain a sufficient number of such photographs to enable- 

 anything to be directly deduced from them would be an 

 excessively long and costly process. It was therefore 

 thought advisable to investigate the problem mathematically 

 and then obtain a few photographs by which the theoretical 

 results could be tested, it being assumed that if the photo- 

 graphs obtained gave results in fair agreement with the 

 theory, the theory could be accepted in the general case. 

 A few attempts had previously been made to measure the 

 angle of emission of the aerial from the machine by means 

 of a protractor fixed directly on the end of the guide-tube, 

 but such results were not very satisfactory. 



It is in this case difficult to judge when the machine is 

 flying exactly level, and also it is highly probable that in 

 some cases the shape of the first few feet is affected by the 

 slip-stream of the machine. This will have very little effect 

 on the total shape, but may cause such a reading as that 

 mentioned above to be largely in error. 



Like many problems of this type, the full and accurate 

 mathematical analysis of the problem is far too cumbrous 

 for any practical purposes, and it is continually necessary to 

 make assumptions with a view to reducing the algebraical 

 labour and giving a workable result. Such assumptions 

 must of course be made with discretion, but the final test of 

 them is that the result obtained by their means does not 

 differ largely from the true state of affairs. It must always 

 be borne in mind that in practical cases a simple result of 

 moderate accuracy is of far more value than a highly com- 

 plex and cumbrous mathematical expression representing the 

 true state of affairs. 



The primary assumption will be that the wire, which is 

 actually a thin stranded cable, can be treated as a flexible 

 inextensible string. As the forces involved are small and 

 the radii of curvature of the curves are everywhere large. 

 this is not likely to cause much error. Dynamically the 

 wire will be treated as a cylinder whose diameter is small 

 compared with its length, and also the effect of air skin 

 friction will be neglected. The former assumption will be 

 justified later; the latter is necessary for the simplification 

 of the analysis and appears to be justified by the results 

 obtained. 



Proceeding in the usual way, the first process is to form 

 the equations of equilibrium of an element of the string. 



Let S be the distance of the clement Js measured along 



