264 Mr. Nicholson on Legend-re's Functions and the 



Copper wire 5 No. 27 S.W.G. I = 26*50 cms., mean diameter 

 '0412 cm. .". area a of cross-section = -00133 sq. cm., 



and '^ = l-37xl0 10 . 

 a 



Initial 



stretching 



force in 



dynes. 



M. 

 gr. 



y 



mean, 

 cms. 



M 



— ■ j v-. 



v i y 



U i 



M 1 M 



tfi y' 



1 



M, M 



Mi y . 



Vx-y- 



€. 



dynes/sq.cm. 



650 # 



15 



25 



35 



•2749 

 •4024 

 •5034 



54-56 

 6203 

 6953 



•0756 7-47 

 •1619 750 

 •2534 14-97 



•0863 

 •0915 



•1778 



86-6 

 82-0 



84-2 



1-19X10 12 



112 



115 



380 # 



15 



25 

 35 



•3630 j 41-32 

 •4925 50-76 

 •5876 59-55 



•1318 9-44 

 •2426 8-80 

 •3453 18-24 



•1108 

 •1027 

 •2135 



85-2 

 85-7 

 85-4 



117 



117 



117 



630 g 



15 



25 

 35 



•2774 . 54-07 

 •4044 61-82 

 •5025 ; 69-65 



•0769 7-75 

 •1635 783 

 ■2525 15-58 



•0866 89-5 

 •0890 i 88-0 

 •1756 88-7 



1-23 

 1-21 

 1-22 



Mean e = M8xl0 12 . 



Table of Results. 





Young .> Modulus 

 at 16° C. 



Iron wire. No. 34 a 



„ ' No. 34b 



No. 29 



dynes per sq. cm. 

 1-95 x 10 la 

 2-01 

 2-00 

 2-70 

 2-78 

 2-04 

 1-18 



Steel pianoforte-wire, No. 29 a. 



„ # „ ^ No. 29u. 

 Nickel wire, No. 30 . . . , 



Copper wire, No. 27 



XXVI. On the Application of Legendre's Functions to the Theory 

 of the Jacobian Elliptic Integrals. By J. W. Nicholson, 

 B.Sc.(Lond. §* Vict.) , Trinity College, Cambridge*. 



TT^HE object of this paper is to indicate a method of some 

 -L generality, of expanding (1) functions expressible in 

 terms of the complete elliptic integrals of Jacob! ; and (2) 

 definite integrals containing incomplete elliptic integrals in 

 their integrand, in series of Legendre coefficients of increasing 



* Communicated bv the Author. 



