252 Proceedings of Royal Society of Edinhurgh. [sess. 
have measured the linear dilatations of the tubes when subjected to 
the same magnetising forces. There are, however, certain very 
interesting conclusions which may at once he drawn. 
1. Positive dilatations in higher fields are shown only in the 
tube of widest bore (Tube I.) ; and positive dilatations in 
low fields occur only in the tube of narrowest bore 
(Tube V.). 
2. A maximum negative dilatation is found only in the first 
three tubes, and the field in which the maximum occurs 
is higher for the narrower bore or thicker wall. The 
graphs for Tubes IV. and V., however, show an undula- 
tion suggestive of a maximum. 
3. By running the eye along the successive rows, or better, by 
study of the graphs, we have evidence of the gradual 
penetration of the magnetisation in through the walls, 
which become thicker in the order I., II., III., IV., V. 
4. The large values of the dilatations in the tubes of narrowest 
bore are particularly worthy of note. In Tubes IV. and 
V. there is no evidence of a limit being approached ; the 
inner surfaces seem far from a condition of saturation. 
5. A comparison of the results for Tubes I. and II. suggests 
the existence of a tube of intermediate bore, which would 
show no change of internal volume in moderate and high 
fields; and this again suggests the existence, within the 
substance of a magnetised bar, of a surface enclosing a 
volume of zero dilatation. This surface, beginning at or 
near the external surface, advances inwards towards a 
limiting position as the field is increased. 
