584 Messrs. Cowley and Levy: 2lethod of Analysis suitable 



(2) Relative number of high- velocity') 



oxygen atoms produced by collision > 1 in 10 5 approx. 

 of a-particles with oxygen in mica. J 



(3) Relative number of particles of^ 



range exceeding 11*3 cm. (probably > 1 in 10 6 approx* 

 hydrogen atoms). J 



Items (2) and (3) are only rough estimates based on rather 

 slender evidence. 



In conclusion, I should like to express my warmest thanks 

 to Sir Ernest Rutherford for many helpful suggestions 

 during the progress of this research. Also to Prof. L. R. 

 Wilberforce for his kindness in lending me the source of 

 radio-thorium and the microscope used in the experiments. 



LIIL On a Method of Analysis suitable for the Differential 

 Equations of Mathematical Physics. By W. L. Cowley, 

 A.R.C.Sc, D.I.C., and H. Levy, M.A., D f Sc* 



Part I. 



A TTEMPTS to obtain solutions of the differential 

 jt\. equations of mathematical physics applicable to 

 problems of practical importance are usually handicapped 

 by the fact that the differential equations arising cannot 

 be solved in terms of the simpler functions without the 

 introduction of restrictions tending to invalidate or limit 

 seriously the application. To the practical calculator, 

 however, the derivation of a complete solution expressible 

 in this form is of merely secondary importance, and does 

 not in fact frequently weigh with him at all. Since the 

 instruments at his disposal can at best only attain a certain 

 degree of accuracy, an equally approximate solution, other- 

 wise unrestricted, of the equations is sufficient. But when 

 the investigation does not merely deal with the evaluation 

 of some quantity for a definite problem, but with the 

 selection of a particular member of a class satisfying 

 certain requirements, particular forms of solution, especially 

 particular forms of expansion, are most convenient for the 

 analysis. 



On general considerations the practical requirements that 

 must be satisfied by such solutions are easily outlined. The 

 ■evaluation of the separate terms in the solution should be 

 suitable for application in a drawing office ; that is to say, 

 they should depend purely on graphical or arithmetical 

 * Communicated "bv the Authors. 



