﻿96 Mr. A. E. Young on the Form of a Suspended 



reason for this lack of generality is the condition that the 

 laws of conservation should be fulfilled. This limits the free 

 choice of coordinates and specializes the admissible systems. 

 It is, however, to be expected that to these differential equa- 

 tions there will correspond other general equations, which 

 preserve their forms for more general transformations. 

 Einstein and Grossmann have found these equations in 

 March 1914, in the form of a variation principle analogous 

 to Hamilton's principle. Indeed, Hamilton's principle is 

 more general than the principle of conservation of energy. 

 Their results have been published in the Zeitschrift fur 

 Mathematik wid Fhysik, lxiii. p. 215 (May 1914). 



The general covariancy of the equations is the great 

 achievement of Einstein and Grossmann's theory. 



Leeds, July 1914. 



XT. On the Form of a Suspended Wire or Tape including 

 the Effect of Stiffness. By Alfred Ernest Young, 

 Assoc. Mem. Inst. C.F., Felloiv of City Guilds Institute, 

 late Deputy Surveyor-General in the Federated Malay 

 States *. 



IN the Philosophical Magazine for July 1903 there 

 appeared a paper by Professor Richard C. Maclaurin 

 on " The Influence of Stiffness on the Form of a Suspended 

 Wire or Tape," the opening paragraph of which states : — 



" Some of the greatest improvements in modern surveying 

 are due to the substitution of a steel tape or wire for the old 

 surveyor's chain. The newer instrument can, with proper 

 precautions, be made an exceedingly accurate measurer of 

 distances. So minute have been the corrections applied in 

 some recent surveys, that it it has been questioned whether 

 we may, with propriety, any longer regard the form in which 

 the 'chain 5 hangs as a catenary. It is true that the sur- 

 veyor's tape is so thin as to be very flexible, but for some 

 purposes there are advantages in using a circular wire, 

 which is, of course, more rigid than the tape for the same 

 weight. It may be thought that, at any rate for the circular 

 wire, the hypothesis of perfect flexibility (on which the 

 investigation of the form of the catenary rests) may intro- 

 duce an error comparable with those for which corrections 

 are applied in the best modern surveys. The object of this 

 paper is to settle the matter by investigating the correction 

 that must be applied when the rigidity of the tape or wire is 

 taken into account/' 



* Communicated bv the Author. 



