228 report — 1859. 



line together also. Occasionally the presence of iron for a short time may 

 cause an abrupt rise and fall of small size in the curve, the one motion 

 being due to the approach of the iron, and the other to its removal. These 

 must be taken into account in tabulating from the curves. An instance of 

 this occurs in the curves appended to this Report. 



Section V. Improvements in the Construction of a Set of Self- 

 recording Magnetographs since made. 



Magnetographs very similar to those here described have been lately set 

 up in a house constructed to receive them about 70 yards from the Kew 

 Observatory. 



The following improvements were made in their construction : — 



1. Instead of one large glass shade standing upon the marble slab, each 

 magnetograph has a gun-metal cylinder, which stands upon the slab, and is 

 surmounted by a glass shade of comparatively small size. An opening is cut 

 in the side of the cylinder, in which there is inserted a piece of perfectly 

 plane glass ; this glass covers that space which in the old arrangement would 

 have been occupied by the two round holes already described. The lens 

 is apart from the cylinder, and has an adjustment to admit of its distance 

 from the mirror being altered if necessary. 



This arrangement permits the shades to be removed without disturbing the 

 lenses. It also renders the working of the instrument less liable to inter- 

 ruption in case of any accident happening to the shade. 



There is also a tube inserted through the marble, which may be connected 

 with an air-pump and the interior of the cylinder and shade exhausted, if 

 this be thought necessary. 



2. The second improvement consists in having reading telescopes with ivory 

 or other scales mounted on pillars, and so placed that the light from the 

 divisions of the scale falling upon the moveable mirror attached to the 

 magnet is reflected into the telescope. In consequence of this, the motion 

 of the mirror will cause an apparent motion of the scale in the field of view 

 of the telescope. The position of the magnet will therefore be known by 

 observing what division of the scale is in contact with the vertical wire of 

 the telescope. 



We may thus combine the photographic record with eye observations. 

 The advantage of the latter is that we see what is taking place at the very 

 moment of its occurrence, whereas we only obtain the photographic record 

 a couple of days after the changes to which it relates have happened. 



Should a disturbance take place, we are thus not only made aware of it at 

 the time of its occurrence, but we may, by having a telescope scale of greater 

 range than the recording cylinder, obtain eye observations, when owing to 

 excessive disturbance the dot of light has altogether left the sensitive paper. 



Report on the Theory of Numbers. — Part I. 

 By H. J. Stephen Smith, M.A., Fellow of Balliol College, Oxford. 



1. The ' Disquisitiones Arithmetics? ' of Karl Friedrich Gauss (Lipsias, 

 1801) and the ' Theorie des Nombres' of Adrien Marie Legendre (Paris, 

 1830, ed. 3) are still the classical works on the Theory of Numbers. 

 Nevertheless, the actual state of this part of mathematical analysis is but 



