522 Prof. John Perry on a 



this : — If the potential at any point along an axis is expressible 

 as 



A +A 1 z + A 2 z 2 + &c, where A , A 1? A 2 , &c. are constants, 

 then the potential anywhere is 



A P +A 1 P 1 ^ + A 2 P^ 2 +&c. 

 If the potential along an axis is 



T> T> TD 



— 4- -j + -J- + &c, where B , B 1? B 2 , &c. are constants. 



the potential anywhere is 



B P BjPj B 2 P 2 _ 



1 o — I s- + &c. 



I gave to Mr. Holland, as an example, the case of a hollow 

 cylindric coil of wire, 2 centim. long, 1 centim. in radius 

 inside, and 2 centim. radius outside : to find the magnetic 

 potential everywhere when there are n turns of wire in the 

 coil per unit length of the coil and there is unit current in 

 the wire. Mascart gives for such a case the force at any 

 point of the axis, and it is possible to expand Mascaras ex- 

 pression in powers of z and again in powers of - ; so that it 



is easy to get the potential in powers of z and of -, and there- 

 fore, as in the last case, the potential everywhere. Now 

 inside the coil and well outside it only a few terms of the 

 series need calculation ; but just at the ends of the coil the 

 calculation is troublesome because many terms are required. 



Mr. Holland tried to shorten the work in the following- 

 way. He found that the potential at points along the axis 

 could be expressed approximately from z = to z = 2'5, with a 

 maximum error anywhere of only 2 per cent., by 



V=27m 2 (2~'4884£ + -05513/--005182 5 + -00022 s 7 ), 

 z being measured from the middle point of the coil. 



Hence, he said, the magnetic potential at a point r, 6 is 



Y = 27r^{2--4884P 1 r + -05513P 3 r 3 --00518P 5 / + '00022P 7 r 7 }. 



From this he plotted equipotential surfaces and lines of force. 

 He found that, inside the coil, and indeed everywhere near the 

 coil except certain critical positions, these were approximately 

 correct. But at the flat ends close to the wire they were 

 absurdlv wrong. It is easy now to see the physical meaning 

 of Mr. Holland's approximation, and why we cannot use this 



