Bending of Magnetic Needles on the Magnetic Dip, 279 



following Table embodies the results of the calculation. 

 Columns I. and II. give the length and width of the needles 

 in inches. Column III. gives the diminution of dip due to 

 bending of needles, having a greatest width equal to that of 

 the Greenwich needles, but tapering uniformly towards the 

 end, as shown in fig. 1. Column IV. shows what the diminu- 

 tion in dip would be if the needles had everywhere the same 

 width a. It is reasonable to suppose that needles of the shape 

 actually used would give values for 8 intermediate between 

 those of columns III. and IV. Column V. gives the difference 

 in dip between the two longer needles and the one having a 

 length of only three inches, the bending of which may be neg- 

 lected. To obtain this difference I have taken the mean dip 

 of the three sets of needles for the six years 1882 to 1887, 

 as published in the Annual Eeports of the Greenwich Obser- 

 vatory ; its value is entered into column VI. 



I. 



II. 



III. 



IV. 



V. 



VI. 



21. 



a. 



8. 



(needles.) 



8. 



(bars.) 



8. 

 (Greenwich.) 



Mean Dip. 



3 



•33 



5 



6 2 



:...':. 



67 29 57 



6 



•39 



7 



24 



26 



67 29 23 



9 



•47 



23 



1 19 



1 00 



67 28 57 



Considering that we have throughout underrated the effect of 

 bending, especially by assuming a value for the magnetic 

 moments which is in all probability too high, the figures leave 

 no doubt that the difference in the dip shown by needles of 

 different lengths can be accounted for by their bending. The 

 calculated value for pointed needles is about three times too 

 small ; that for needles of uniform cross section gives results 

 closely agreeing with the observed differences in the dip ; 

 while the actual shape of the needles agrees more closely with 

 that of uniform bars than with that of pointed needles. 



The results of calculation quite justify Joule's remark as to 

 the importance of using short needles to avoid the introduction 

 of appreciable errors ; and the question arises whether long 

 needles are entirely to be rejected, as is done in most Observa- 

 tories, or whether a correction should be made for the 

 diminution of the dip. The difficulty in measuring angles to 

 a sufficient accuracy is increased if the needles are as short 

 as the shortest Greenwich needles, and hence there is some 



X2 



