VALUE OP THE BRITISH ASSOCIATION UNIT OP RESISTANCE. 
231 
Thus when the coils are separated by the long rods 
7^=3365*64 7-y=7l2-36 
y=62° 36' 32". 
log M 0 /4tt v/Ao = U5718069 
and this gives, taking A as 25750, a as 25760 
M 0 = 761225 XI0 8 . 
whence 
From the table 
When, however, the dimensions It, k of the section are too large in comparison with 
b to allow us to mass all the windings together, we may use a formula of approximation 
due to Mr. H. J, Purkiss (Appendix ii., ch. xiv., Maxwell, second edition). 
Let the suffix ^-h denote that for a is substituted a i h in the corresponding 
functions, ±k that b d: k replaces b, and similarly for accented letters. Then 
M=e {M /t +M_ 7t +M /( /+ M_ /t /+ M/.+ M._/,-fM/.+ M_^—2M 0 }. 
I * 
To calculate these eight quantities in a methodical manner we notice that 
r X k —rpd- 2(A+a)/i+^ 3 
r 2^ 2 ■— — 2 (A-|- a) h -j- h" > 
&c. j 
and that consequently we have to add in each case a correcting square, and add or 
subtract a correcting product. The corresponding y is found, and the rest of the 
calculation effected just as for the mean windings. 
When the coils are separated by the long rods the greatest and least values of y are 
y_A=6 3° 26' 54", and y / = 61° 46' 56", the final value result being 
M=761921 X 10 8 . 
It thus differs by nearly 1 in 1000 from the uncorrected value. 
The values of b differ slightly according to the four positions of the coils, and 
a slight correction has to be made in the values of A, a assumed above. 
It therefore becomes of importance to determine the correction in M to be made 
for the addition of ‘001 centim. to A, a, or b. 
Siuce cos y—rji\, it follows that 
S„y=S A y=-001(A + o)/r 1 3 tan y in circular measure. 
This gives for the long rods 
S„y= P64". 
