360 Prof. Challis on the Hydrodynamical Theory of the 



No. of the 







Value of 



Value of Excess of 



Excess by 



P> 



?• 



w by ob- 



(i) by the 



observed 



Ampere's 



series. 







servation. 



theory. 



value. 



theory. 





in. 



in. 



o 







o 







1. 



0-00 



2-26 



00 



00 



00 



00 



2. 



1-34 



2-26 



90 



10-5 



— 1*5 



-11 



3. 



2-68 



2-26 



209 



21-8 



-0-9 



-07 



4. 



4-02 



2-26 



35-8 



35-8 



00 



+11 



5. 



5-36 



2-26 



57-0 



56-9 



+ 0-1 



+2-2 



6. 



670 



2-26 



86-9 



88-4 



-1-5 



-0-6 



7. 



778 



1-70 



121-8 



121-6 



+0-2 



(-3-4) 



8. 



8-20 



074 



154-8 



1535 



+ 13 



-0-6 



9. 



000 



373 



o-o 



00 



00 



00 



10. 



1-34 



373 



122 



14-6 



-2-4 



-1-8 



11. 



2-68 



373 



275 



29-6 



-21 



-15 



12. 



4-02 



3-73 



44-3 



45-8 



-1-5 



-03 



13. 



5-36 



373 



722 



64-6 



( + 7-6) 



( + 6-4) 



14. 



6-70 



373 



82-4 



86-0 



-3-6 



-3-8 



15. 



7-83 



3-44 



1029 



105-2 



-23 



-17 



10. 



8-82 



2 80 



122-8 



1251 



-23 



+0-3 



' 17. 



949 



1 82 



144-6 



145-8 



-12 



-04 



18. 



9-70 



0-73 



164-4 



165-9 



-1-5 



-08 



Respecting these results, it is first to be noticed that the ob- 

 served and calculated values of co differ so little from each other 

 (except in the instances of Nos. 7 and 13, which seem to be 

 affected by some incidental errors), that the differences scarcely 

 exceed what might be attributed to unavoidable errors of obser- 

 vation. It is evident, therefore, that the effect of not taking the 

 direct action into account must be very small ; and I have conse- 

 quently not thought it worth while to employ the calculations 

 indicated in art. 53 for ascertaining its amount. The reason 

 that the direct action has comparatively so little effect I take to 

 be, its being due only to the transverse circular motions about 

 parts of the coil contiguous to the plane passing through the 

 axis of the coil and the centre of the small magnet in a very thin 

 slice; whereas the indirect effect results from the transverse mo- 

 tions about all parts of the coil, and increases both with its length 

 and with the area of its transverse section. 



It may, however, be remarked that there is a preponderance 



of 



minus si 



gns in the excesses of the observed values, and that 



this is the case in somewhat greater degree relatively to the hy- 

 drodynamical theory than to that of Ampere. The argument in 

 art. 52 shows that, by taking account of the direct action, the 

 angle co would be diminished, so that the minus errors might 

 thus be made less, and the calculated and observed values be 

 brought into closer agreement. In the calculation of the direct 

 action the transverse dimensions of the coil are explicitly taken 



