8 
MR. J. E. H. GORDON ON THE DETERMINATION OF 
Hence 
Now 
r»6h 
N=i u x dx=Yo 4‘39 centims.{16-707+48-620 + 34-596}P 
Jo 
=131*732[LP]P d *. 
P D =81-1620, 
.-. 131-732 P D =10751-96. 
Now in order that this may be a number it is necessary that [P] should equal [Lr 1 ] ; 
and if we consider the equation of moments we shall see that this is so. For consider 
a small magnet (length 2 1) at the centre of the dynamometer, we have, when a current 
passes, 
H sin U [H . L]=PC cos i l [PC . L], 
[H]=[P.C], 
or 
[L-^PT- 1 ] 
[IiMiT- 1 ]' 
=[L-]. 
(4) 
Now the value of N for any helix with unit current taken with respect to the whole 
length of its axis produced to an infinite length in both directions is, by Art. 676 of 
Professor Clerk Maxwell’s ‘ Electricity,’ 47 m, where n is the number of windings. 
When the length l is finite compared with the radius a, the value of N for that part 
of the axis which is included between the ends is 
N=4 n (5) 
(see Clerk Maxwell’s ‘Electricity,’ Art. 676). 
N l 
Now if we calculate n=- 77 -—^ , taking a the mean radius, this will give the 
4 7r y/ 2 -t-a 2 — a 0 b 
number of windings in the helix. 
Now as a—4i'S4: centims., and N=10752, we have 
10752 26-34 . 
H ~ 4tt '{26 t 34 2 + 4 t 84 2 }*-4-84 ’ 
.-. log 74 = log 10752+log 26-34— log 4 tt— lo g(F-\-a 2 )*—a 
{last term = log 21-92} 
= 4-0314893+1-4206158 — 1-0991971 — 1-3408405 
= 3-0120680, 
.-. 74=1028-15, 
.*. there are 1028 windings on the helix. 
* Professor Clerk Mas-well’s method of representing the units by quantities in [ ] has been used throughout 
the paper. Thus a length L is represented by L[L], where L is a number and [L] the unit of length. 
