Magnetic Susceptibility and Retentiveness of Iron and Steel. 381 
In the second spectrum the difference will be doubled, and 
so on. The corresponding departure from theoretical perfec- 
tion in ruling is, according to Prof. Rowland, 
^ co 3 tan -\jr. 
Thus in the two gratings discussed in my former paper, the 
extreme difference of phase in the first spectrum will be about 
01 x A. tan o/r instead of *7\, and '04 x X tan •v/r instead of 4*8 x A,. 
Quantities like this are quite inappreciable; and Professor 
Rowland may indeed claim that his gratings are perfect so far 
as this qualification is concerned. It will be interesting to 
calculate the difference in the position of the extreme line in 
the grating, supposing that the lines were ruled with equal 
spaces along the arc instead of along the chord. The differ- 
ence clearly is that between aa> and a sin &>. For if <o r be the 
angle to the extreme line in this case we have 
aco' = n<T=as'm &) = a(<w — tj<» 3 ) ', 
and difference required is a{oo — &/), or 
laco 3 . 
Taking the grating mentioned by Prof. Rowland in his paper, 
the value of this is about jq o o o °^ a centimetre, or little more 
than the distance between two consecutive lines on the grating. 
The extreme minuteness of the change required to produce so 
great an alteration in the theoretical definition is very remark- 
able, and may help to give us some idea of the difficulties 
Professor Rowland has had to surmount to produce his 
gratings. 
LIII. On the Magnetic Susceptibility and Retentiveness of Iron 
and Steel. By J. A. Ewing, B.Sc, F.R.S.E., Professor of 
Engineering in University College, Dundee, formerly Pro- 
fessor of Mechanical Engineering and Physics in the Univer- 
sity of Tokio*. 
DURING three years the writer has been engaged, while 
in Japan, in prosecuting researches on the magnetiza- 
tion of iron and steel, and on the effects of stress on magnetic 
susceptibility and thermoelectric quality. Preliminary notices 
of some of his earlier results have appeared in the l Pro- 
ceedings of the Royal Society ' (Nos. 214 and 216, 1881, and 
No. 220, 1882); but a detailed account of the work has still 
to be given. Meanwhile, the following points, not previously 
noticed, are perhaps of sufficient interest to justify their sepa- 
rate publication. 
* Communicated by the Author, having been read before Section A of 
the British Association at Southport. 
