.Notices respecting New Boohs. 331 



the constant is determined exactly as i£ the term represented 

 a true Bessel function through the relation 



J_ C a 



r 2 . r dr — J A a 4 = 1 rf(f) r dr. 

 o Jo 



For instance, using my original notation, in the case of a 

 torsional force Tr* over z = l, the term additional to ordinary 

 Bessel terms is 



w =4(« + 3)-V ( sT6i l "- 1 /n. 



With this addition and mode of interpretation, the solution 

 of 1887 includes the ordinary text-book case for which i = l, 

 and so possesses a greater generality than I originally 

 supposed. The additional term, as explained above, is 

 always of the ordinary text-book type, but it is important 

 unless i is large, I am thus much indebted to Mr. Bridgman 

 for raising the point, and to Mr. Berry and Dr. Hobson for 

 their assistance. Considering the date of the solution it seems 

 curious that the point has not been raised before. 



C. Chree. 



XXTX. Notices respecting New Books. 



A Study of Splashes. By Professor A. M. Worthington, F.E.S. 

 "With 197 Illustrations from Instantaneous Photographs. 

 Longmans, Green & Co. 1908. Price 6s. 6d. net. 



'TMIIS enticing volume is the outcome of an experimental study 

 lasting over fourteen years. Yet even so, its publication was 

 at the last delayed in order to be able to include additional and 

 unexpected information relating to cases in which the height of 

 fall is increased above a certain critical value. It is impossible in 

 a short note to do more than call attention to the extreme beauty 

 of many of the photographs reproduced here ; and to express 

 delight at the very lucid aud ingenious explanations which ac- 

 company the reproductions. What is to be desired greatly (and 

 what we believe Professor Worthington himself desires greatly) 

 is that some hydrodynamician may see his way to tackle the 

 problems presented and express them in mathematical language. 

 The present publication will do much to spread a knowledge of the 

 phenomena themselves. 



