492 Squares of Ellipsoidal Surface Harmonic Functions. [Dec. 2, 



bling ones found in the lobus pyriformis, and it seems likely that 

 these are the end-stations for fibres proceeding from the inner olfactory 

 root. 



A total absence of large fibres and large cells and a simple plan 

 of arrangement is the general character of this area and does not 

 lend colour to the doctrine that it, and not the Rolandic region, is a 

 centre for common sensation. 



" On the Integrals of the Squares of Ellipsoidal Surface Harmonic 

 Functions." By G. H. DARWIN, F.R.S., Plumian Professor 

 and Fellow of Trinity College, Cambridge. Received Decem- 

 ber 2, Read December 10, 1903. 



(Abstract.) 



This paper is a sequel to three others on ellipsoidal harmonic- 

 analysis and its applications, published in Series A of the 'Philo- 

 sophical Transactions/ vol. 197, pp. 461557 ; vol. 198, pp. 301331 ; 

 and vol. 200, pp. 251314. 



The integrals referred to in the title are absolutely essential for 

 practical applications of this method of analysis. A table of all such 

 integrals is given in the first of the above-named papers, but the results 

 are only approximate. In the present paper the rigorous forms of the 

 integrals, numbering 1 + 3 + 5 + 7, are given for the surface harmonics 

 of orders 0, 1, 2, 3. 



A mistake is detected on p. 556 of the first of the previous papers, 

 where the coefficient of /? in the cosine-function of the third zonal 

 harmonic is erroneously given as 3 ; it should have been 4. 



