332 Mr Pochlington, Electrical Oscillations in Wires. [Oct. 25, 



(iii) If one of the factors, e.g. the last, of the term under the 

 second log sign be small we have, since a and ft cannot then both 

 be small, 



2 (cc 2 a 2 sec 2 &) — ft 2 ) sin <o log e = ^a 2 a 2 log (1 — ft — aa tan a>). 



In this case we must have ft<aa sec to, so that the velocity of 

 propagation measured along the Avire must be greater than V. 

 There is however no superior limit to the value that it may have. 

 There is an inferior limit to a. Hence for periods which are not 

 greater than a certain value, there are two velocities of propaga- 

 tion along the wire, one = V given by (i), the other, > V, given 

 by (iii). 



No other cases arise by making a and ft great, since we must 

 then recur to (7), as (8) does not then hold ; and here if a and ft 

 are great, we simply have a 2 a 2 sec 2 &> — ft 2 — 0, the case considered 

 in (i). 



(2) On Circles, Spheres and Linear Complexes. By Mr J. H. 

 Grace. 



This paper is printed in the Transactions, Yol. xvi. Part ill. 



(3) Reduction of a certain Multiple Integral. By Arthur 

 Black. Communicated by Professor M. J. M. Hill, M.A., Sc.D., 

 F.R.S. 



This paper is printed in the Transactions, Vol. xvi. Part in. 



(4) On the Gamma Function. By Mr H. F. Baker. 



The Gamma Function could be defined for real values of x 

 by the conditions (i) that Y (1) = 1, (ii) that^ Y(x + 1) = xY (x), 

 (iii) that, for a fixed finite h, as x tends to + oo , the difference 



Y'(x+h) Y'{x) 



Y(x + h) Y {x) 



The condition 

 suit 



r'(*) 1 fr^ /i.a-^ 



tends always to zero. The condition (iii) was well known, being 

 deducible from the result 



-\ogx=f [e- xt -(l+t)- x ] 

 Jo 



Y(x) & Jo L ' J t 



and was of suitable character for a definition; it was desirable 

 however to deduce it immediately from the equation 



/•GO 



T (x) = e-H*-Ht ; 



Jo 



this note dealt with such a deduction. 



