134 H. Nagaoka on Hysteresis attending Change of 



The optical method for observing the change of angle 

 requires little explanation. When the Grauss-PoggendorfF 

 method is used at a great distance, it requires very strong 

 illumination of the scale and a good observing-telescope ; or 

 when the reflected spot of light is read on the scale, electric- 

 or lime-light must be used. This inconvenience can be 

 removed in the following manner (see fig. 4). 



A fine glass thread t is placed vertically in the focus of a 

 small achromatic lens c, and illuminated by a lamp. The 

 ray, after passing the lens, is reflected by a right-angled 

 prism p, and thrown on the mirror m. After reflexion in the 

 plane mirror, the ray traverses an achromatic lens L (whose 

 focal length was about 70 centim. in my experiment). The 

 image of the glass thread is then observed by means of a 

 microscope, M, provided with a micrometer. I used a micro- 

 scope detached from a geodetic comparator ; the magnifying- 

 power was about 40, but if great exactness be desired it can 

 be increased about five times, provided sufficient illumina- 

 tion be given. In place of the glass thread at t I tried a 

 fine slit, spider or silk thread, and diamond traces on glass ; 

 but it was found best to use a glass thread of such thickness 

 that its image was a little greater than the movable double 

 threads of the micrometer. In the present experiment, 

 1776 divisions of the micrometer were equal to 524"*1, so 

 that a single division was equal to 0"*295. The displacement 

 of one micrometer division, therefore, gave a change of 

 length 



0-1125 x 0*295 x 4-848 x 10~ 6 ... 

 = : centim. 



2 



= 0-805 x 10- 7 centim. = 0*00137 X D , 



where X D represents the wave-length of the sodium-line D. 



In experiments with the nickel wire through wide ranges 

 of magnetizing force, the contraction was so great that the 

 image of the thread passed out of the field of the microscope. 

 The lens and microscope were then replaced by a telescope, 

 in the focus of which was placed a scale divided to tenths of 

 a millimetre ; a single division corresponded to 20*2 x 10~ 6 

 centim. It is easy to see that the collimating-lens c can be 

 replaced by the lens L. For this, it is necessary to place 

 the prism between M and L, and the thread t at such a 

 distance that the optical path through the prism to the lens 

 is equal to its focal length. This method of measuring small 



