736 On the Form of the Trailing Aerial. 



Napierian — it is possible to plot immediately any required 

 curve when p is given. When p is not absolutely negligible 

 this seems to offer a most satisfactory mode of solving the 

 problem for all except heavy cables requiring higher powers 

 of p to be taken into consideration. In any case the 

 constant C affects the scale and not the form of the curve. 

 In conjunction with these expressions for the rectangular 

 coordinates the equation (4) can be conveniently used when 

 a fourth small table giving the function multiplying p is 

 also provided, in addition to tan 0. The equations might 

 look a little simpler if written in the form : 



x/C = cosecvjr+^fjjcot 3 -^— cot^+ cosec-v/rlog cot-J^] 



y/C = log COt ^yjr + ip [cot 2 i/r + (log cot i^) 2 ] 



s/C= cot^+jt?[l — sini|r) 2 (l + 2 sin^r)/ 3 sin 3 ^ + cot -v/r log cot %\]r~\ 



where yjr is the inclination of the wire to the horizonlal and 

 changes in the direction 90° to 0° in passing up the wire 

 from its lower end. 



8. In reading Captain Hollingworth's paper the difficulty 

 of remembering certain elementary integrals in the forms 

 commonly given was acutely felt. Perhaps the forms 



J' 



f 



dx . „ 7 9X _ i __! b + a cos x 



(a £ — b") 2 cos 



a + b cos x a + b cos x 



_!& + a cos x 



(fr 2 — a 2 ) -cosh; 



a + b cos x 



dx , n 7 ox -i _i&4- asm x 



=— i = — [a- — u z ) 'cos j—. 



a i- 6 sin x ' a + bsmx 



n o os -i i _ifr + asin x 

 = — (b 2 — a 2 ) 2 cosh ,-^ 



recommend themselves best for the purpose. They can be 

 retained by a single act of memory, being immediately 

 deducible from one another, and once remembered they can 

 be readily changed to any other desired form. The limiting 

 cases, when b= ±a, hardly require special mention. But 

 when a=l they all follow the single rule 



1 dy t s i n 



y dx ' J - cos ' 



the most general function ol this type being 

 y=i sin 2 c(x-\-a)/2c 2 . 



Cdx = 



J y " 



