194 Dr. J. Prescott on tl 



te 



examine the method in further detail ; but since I do not 

 wish to found ray plea for Z.S. rather than L.S. on theoretical 

 considerations, the examination will be left for a subsequent 

 occasion. All that I am concerned to prove here is that 

 Z.S. is much more convenient than L.S. in the problems 

 which arise in physics, and that since L.S. is certainly not 

 theoretically unobjectionable, there is nothing to outweigh 

 its practical inconvenience. 



Summary. 



It is urged that, for the adjustment of observations in those 

 problems which are of importance in physics, there is a method 

 much simpler and more convenient practical^ than the con- 

 ventional Method of Least Squares. This method, which is 

 called that of Zero Sum, depends on the principle that the 

 sum of a large random collection of errors is zero. 



It is not maintained that the method of Z.S. is completely 

 valid theoretically, but it is maintained that it is no less 

 valid than the Method of Least Squares. Accordingly the 

 burden of proof rests on those who continue to use a method 

 which is neither practically convenient nor theoretically 

 unobjectionable. 



However, in a subsequent paper it will be maintained that 

 the method of Z.S. has the advantage in theoretical validity 

 as much as in practical convenience. 



Research Laboratories of the 



General Electric Co. Ltd. 



Nov. 1919. 



XIX. The Buckling of Deep Beams. (Second Paper.) By 

 J. Prescott, M.A., D.Sc, Lecturer in Mathematics in 

 the Faculty of Technology of Manchester University • with 

 an Appendix by H. Carrington, B.Sc, M.Sc.Tech. y 

 A.M.LM.E* 



IX the first paper on this subject f it was shown that a 

 deep beam may fail by a sort of torsional instability, 

 and the particular load at which this instability occurs was 

 calculated for beams under uniform loads or under concen- 

 trated loads with various methods of support. In this paper 

 more general forms of the differential equations will be 

 deduced than in the earlier paper, and some of the results 

 will be extended. Moreover, the appendix contains a veri- 

 fication of one of the formulae by means of experiments, 



* Communicated by the Author. 

 t Phil. Mas-. October 1918. 



