20 REPORT—1840. 
qualities of iron, &c. A similar agreement is found between other 
observations, which we shall describe in the report itself. I think, 
therefore, we may admit the following law, namely, that the amount of 
magnetism received by different iron rods of the same length, and sub- 
mitted to the influence of a current of the same force, is proportional to 
the diameter of the rods. I must remark, that the constant which 
we have added in the formula depends upon the magnetic influence 
which the helix exercises, independently of the nucleus of iron 
which it encloses. The practical consequences which may be de- 
duced from this remarkable law are of considerable importance. 
Among these, however, I will at present mention only the follow- 
ing. Having found that the amount of magnetism is proportional to 
the surface of the malleable iron, and taking into account the quan- 
tity of iron employed in the electro-magnets, it is ascertained that it is 
more advantageous to employ in the construction of electro-magnetic 
machines, rods of small instead of large dimensions ; or rather hollow 
iron, in accordance with my own experiments of 1837, which are found 
in ‘ Taylor's Scientific Memoirs,’ vol. ii. &e. I cannot pass over in si- 
lence the experiments of Prof. Barlow, who, as is well known, proved a 
long time before that the induction of the terrestrial magnetism upon 
malleable iron, depends only upon the surfaces, and is almost inde- 
pendent of the thickness. In order to ascertain the law of electro- 
magnets of different lengths, M. Lenz and I undertook numerous and 
laborious observations, which were extended even to rods of thirteen 
feet in length, and keeping in view at the same time the determination 
of the particular distribution of magnetism in the rods. Among these 
observations I shall only refer to such as seem most applicable to elec- 
tro-magnetic machines, and which have yielded results as simple as 
unexpected. The following table contains the results of some obser- 
vations made with rods of the same diameter, but of different lengths, 
covered with electro-magnetic helices, and influenced by a current of 
the same force. M being the magnetism of the extremities, and 2 the 
number of the coils of the helix, we have — = a, a formula according 
n 
to which we may calculate the numbers contained in the third column. 
The numbers in the fourth column are deduced from a series of other 
observations, made with the same helix of 960 turns, which did not 
cover the whole length of the rods, but were collected at the extre- 
mities only, where they occupied a space of about two inches in length. 
The helices being the same in all the observations, it was only neces- 
sary to divide the magnetism of the extremities by 960, in order to 
find the numbers of this column. 
