368 Mr ROHRS, on THE MOTION OF BEAMS 



15 » IS £ 



and y = ttD^ (.847 sinp,a - 1.153 cos p,s + .158 e* » + e~ » «) 



4.69- 



+ t^Di (1.01 sin p^s - .99 COS pi8 - .01 e "+6 ' ") 



5ir « Sir « 



^ f . 5-n-s 1 !51 -?i Sir \ 



+ <3 A ( sm + -g-^ e* a + e a » - cos — si 



/ . 77rs 1 ^1 -^!^« 77r«\ 

 + «4 2)4 I sin — - — i-e*<»+e*<» -cos , 



tit '»> &c. being abbreviations for the circular functions of t they represent, 



+ &c. + Sec + &c. 



If now we determine D,, D^, A> A by the conditions that 



cCy cFy <fy d's 

 d?' d^' d?' d?' 



shall be the same in the statical curve 



3 S 



3 ^ W , A 



and in the dynamical curve when < = 0, and at the origin s = 0, the I*', i***, 5*, 8*, and 9*** 

 differential coefficients will also be equal to each other and to zero in the two curves at the 

 origin, so that the contact there will be of the ninth order. We shall find it unnecessary to 

 determine D3 and Z)^, they are so small as to be fairly omittable from any but an exceedingly 

 close approximation. Hence we shall have 



8.1 A + 44^8 + 123 A + 2421)4 = 3S, 

 10.92 Di + 208 D.^ + 9682)3 + 2662 A = SS, 

 50.22), + 10,630 A + 234,700A + 1,771,000 A = 0, 

 71.03 A + 49,910 2)2 + 1 ,843,000 A + 19,490,000 A = ; 

 whence Di = .42^, 

 A = -.01^, 

 A = .000283, and may be omitted. 



A = 



ya, < =: = 2.307 A - 2 A + 2 A. &c. = .99^ nearly. 



Here where the error is greatest, it is scarcely perceptible. 



J If 



The greatest value of — is 3.5 -j S nearly. 



