278 Mr. A. Schuster on the Influence of the 



If the calculation is conducted in the same way for straight 

 bars of uniform cross section a, the result is 



h=- 9 -&- (4) 



* 5Ya 2 W 



Hence for pointed needles of cross section a the displacement 

 of the centre of gravity is smaller in the ratio of 18 to 5 as 

 compared with needles having an uniform cross section a 

 throughout. 



To apply the results obtained to our problem, we must 

 multiply the value of h by cos c/>, because if the needle is not 

 horizontal the gravitational force has to be resolved at right 

 angles to the needle in order to obtain that component which 

 serves to bend it. 



We substitute the value h from equation (3) into (1) and 

 may thus calculate the correction of the dip due to bending 

 by the formula 



where V is the volume occupied by the needle. 



If the dimensions of the needle are known all quantities 

 except Young's modulus and the magnetic moment may be 

 introduced into the equation. As regards Young's modulus, 

 the values given for it lie between 21 x 10 12 and 2*5 x 10 12 . 

 I take the latter number, as it is my object to show that 

 bending is sufficient to account for the diminished dip of the 

 longer needles, and I wish therefore to underrate the effect of 

 bending. It is more difficult to form an estimate of the 

 magnetic moment per unit volume or M/V. Kohlrausch, in 

 his l Physical Measurements,' states that with thin long 

 needles values as high as 785 may be obtained, but that such 

 magnets as are used in Physical Laboratories seldom show a 

 greater magnetic moment than 312 C.Gr.S. per unit volume. 

 The shape of dipping-needles and the method of magnetiza- 

 tion does not render it probable that these needles reach the 

 lower number given by Kohlrausch, for the central parts of 

 the needle will add more to the weight than to the magnetic 

 moment. If, therefore, we make M/V = 320, this will pro- 

 bably be above the correct value. 



With these numbers I have calculated the value of 8, taking 

 the width and length of the needles used at Greenwich. I 

 have to acknowledge the kindness of the Astronomer Royal 

 in giving me detailed information on the dimensions and 

 shape of the needles used at the Royal Observatory. The 



