314 Hon. Ralph Abercromby. On Meldrum s Rales [June 14, 



If we put x( x ) = + % in this integral, we shall obtain a per- 

 fectly correct result. 



I discovered the following integral some years ago. It may have 

 been discovered before, although I have been unable to meet with it. 



[ T d9 (2 cos sin (m + 2r + 1) d 

 Jo 



1 . 2 . 3 . . . . r 



4 m (m + 1) (m f 2) . . .. (ra + r) 



From this may be deduced an enormous number of results, as will 

 be at once apparent. I will write down two of them. 



Pg- , cos 50 sin + (1 — x) sin 50 cos 

 J Q + 2a; + 2 + O 3 + 2») cos 20 



Now let G r = cos n ~ r sin (r + 2) 0. 



ThGn J ((« 2 - 2«T2) + («* - 2.) cos 20Y dd 



7T 1 



24 ' 8 - 4a ' 

 The first integral was derived from the series 



x° x* 

 1.2.3 ~ 2.3.4 



1.2.3 2.3.4 

 1 . 2 . 3 + 2 . 3 . 4 



+ . . . , the second from ., ' n ' + -—-w—i * + 



VI. " On Meldrum's Rules for handling Ships in the Southern 

 Indian Ocean." By Hon. Ralph Abercromby, F.R. Met. 

 Soc. Communicated by R. H. Scott, F.R.S. Received 

 June 7, 1888. 



(Abstract.) 



The results of this paper may be summarised as follows : — 

 The author examines critically certain rules given by Mr. C. 

 Meldrum for handling ships during hurricanes in the South Indian 

 Ocean, by means both of published observations and from personal 

 inspection of many unpublished records in the Observatory at 

 Mauritius. The result confirms the value of Mr. Meldrum's rules ; 

 and the author then develops certain explanations, which have been 

 partially given by Meldrum, adds slightly to the rules for handling 



