of Action bétween Magnets. 129 
There are, as will appear in § 24, other possible contri- 
butions to the value of the couple L, but as these arise from 
instrumental or observational defects it is desirable to post- 
pone their consideration. 
§ 16. There has been considerable difference of opinion as 
to the ratio between the pole-distance 2 and the length / of 
an ordinary magnet. Kohlrausch found to a close degree 
of approximation 
2r/l=5/6=0'83. 
Bérgen concludes that the average value of the ratio is 
°805, deducing this as a mean from numerous experiments 
based on a theoretical investigation, which appears more 
complete than Kohlrausch’s, though not absolutely free from 
assumptions. Bérgen finds that as the magnetic moment of 
a magnet is reduced, the pole distance tends normally to 
increase, until in avery weak magnet 2A// may rise to *815. 
Whether he regards this as an absolutely limiting value is 
nut quite clear, but he strongly combats the idea that it can 
ever approach unity, a result which he attributes to Mr. 
Blakesley * in a paper read before this Society in 1890. 
§ 17. As the two magnets of an English magnetometer are 
fairly similar in type, there are grounds even apart from 
Bérgen’s experiments for regarding the assumption 
Ab Paro oh wwii (25) wil BD) 
as likely to be at least approximately true. Adopting this 
hypothesis, provisionally, for the average magnetometer of 
any particular make, and for shortness writing z for \’/A, 
we have 
PA, 0) =p'(1/4)(2—322) =pP7a(z), say, . . . (36) 
Oe N= p'*(3/128)(8— 402? 4 1Lb24)=pttf(z), - . .- CD 
RA, X’) = p*l® (1/256) (16 — 1682? + 21024 — 352°) = pl*f,(z). (38) 
Table XI. gives the values of the above functions of z for 
values of 2 increasing by ‘1 from 0 to 1, including the range 
encountered in practice. 
TABLE XJ, 
ee UE Es ee ey a eR 
107,(2)= +5000 +4925 +4700 +4325 +3800 +3125 +2300 +-1825 + 200 —1075 —2500 
10*f,(2)= +1875 +1782 +1506 +1060 + 465 — 249 —1044 —1875 —2685 —3412 —3984 
10*f,(z)= +6250 +5602 +3755 + 998 —2206 —5243 —7382 —7819 —5734 — 351 +8984 
* Phil. Mag. March 1891, p. 281. 
Phil. Mag. 8. 6. Vol. 8. No. 44. dug. 1904. K 
