14 
NATURE 
[Vov. 2, 1882 
elements of the problem that the advantages of the hoop 
system can be properly developed. 
In illustration of this we refer to three diagrams of Sir 
Joseph Whitworth’s 12-inch steel gun. The first, c,, shows 
the strains, if the hoops are put in with no initial strain, 
that is to say, if each hoopisan exact fit to the one below 
it, which is Sir Joseph’s present practice. The gun in 
this state is in the same condition under internal pressure 
as a homogeneous or solid gun of steel. The tensions 
with an initial pressure of 24 tons per square inch would 
be 28°18 tons and 2°3 tons per square inch at the inner 
and outer circumference respectively. The second dia- 
gram, C,, would be the state of the strains, if the Woolwich 
rule of a uniform shrinkage of 1 in 1000 were adopted. 
The inner tube and the first hoop would never be out of 
compression, the second hoop would be strained to 8-44 
tons and 3°85 tons, the third ring to 17"40 tons and 12°84 
tons, and the fourth ring to 27°64 tons and 22°82 tons at 
the inner and outer circumferences respectively. 
The third diagram, C,, shows the gun as it would be 
strained if the initial shrinkages had been properly calcu- 
lated and applied. For every hoop the tension of the 
inner circumference would be 10 tons per square inch, 
whilst that of the outer circumferences would be 1 ton 
compression for the tube, 4°11 tons, 6°51 tons, 7°72 tons, 
and 8°82 tons for the hoops respectively. 
Thus it is seen that by a multiplication of hoops with 
initial strains properly applied the maximum strain is 
reduced from 28 tons to 10 tons per square inch. But on 
the other hand, by the Woolwich rule of a uniform 
shrinkage of 1 in 1000, some of the hoops would be always 
under compression, whilst others would be more or less 
strained, and the maximum would attain nearly the same 
as in the homogeneous gun—28 tons per square inch. 
Another remark must here be made. Referring to dia- 
gram C; it is seen that in the case of each hoop the strain 
decreases rapidly from the inner to the outer circum- 
ference. Thus in the first hoop the strain decreases from 
Io tons to 4 tons, in the next from Io tons to 6$ tons, and 
so on. Now by greatly increasing the number of hoops and 
consequently decreasing the thickness of each, the strains 
on the outer circumference may be brought very nearly up 
to the same strain as the inner circumference, and this is 
what is attained by the use of wire. A coil of wire is but 
a very thin hoop, and if, instead of a hoop of 4% inches of 
steel, 36 coils of wire of }th inch had been used, the dif- 
ference of strain between the inner and outer circum- 
ference of each coil would be inappreciable, and the whole 
thickness of the gun would have been uniformly strained, 
and the maximum strain would not have exceeded 6 tons 
per square inch, or if the wire were strained to 10 tons 
per square inch the thickness of the gun might be reduced 
from 22? to 133 inches. 
But this is not all the advantage of the use of wire. 
Wire of small section is greatly stronger than the same 
material in mass. It is within the truth to say that steel 
which in mass might be safely strained to 15 tons per 
Square inch, might in the form of wire be strained to 30 
fons per square inch. Consequently the wire gun would 
be as safe under a strain of 20 tons as the hoops under 
fo tons, and therefore the thickness of a wire gun of 
equivalent strength to that represented in diagram C, 
might be reduced to 6] inches instead of 223 inches. 
From the preceding remarks and the diagram of Whit- 
worth’s 12-inch gun, it will be seen how very important 
is the question of the degree of shrinkage in built up guns. 
It is worth while to dwell a little longer upon this ques- 
tion, and to illustrate it we now give diagrams showing 
how the strength of a gun may be reduced by a small 
difference in the shrinking such as would be caused bya 
slight error in the dimensions of one of the hoops, due 
either to miscalculation, imperfect workmanship, or irre- 
gular contraction in cooling. The diagrams D, and D, 
represent the strains on the hoops of an 8-inch gun, built 
up of an inner tube and three concentric hoops of iron 
having an elastic limit of 12 tons per square inch. D, 
shows the strains when the gun is completed and free 
from internal pressure, on the hypothesis that the shrink- 
ages are correctly calculated and accurately worked too. 
The tube and first hoop are in compression, the two outer 
rings in tension. D, represents the strain when subjected 
to internal pressure, so as to make the maximum strain 
12 tons per square inch, and it is seen that all the hoops 
are equally strained up to the elastic limit. D, shows the 
strain in the same gun on the hypothesis that either from 
miscalculation or inaccurate workmanship the outer hoop 
has been made 1/5o0o0th of an inch too small, and when 
by internal pressure the maximum strain reaches 12 tons 
per square inch. . : 
It is apparent at a glance what a great difference this 
error has made in the distribution of the strains. Without 
going into detail, it may be stated that the strength of the 
gun has been reduced 4o per cent. by the small error of 
1/50oth of an inch in one of the hoops. Accurate work- 
manship is, however, only one of the difficulties to be 
encountered in shrinking on hoops. Different qualities 
of iron shrink differently in cooling from the same tem- 
perature ; moreover they do not shrink back in all cases 
to the size from which they were expanded, but to a some- 
what smaller size. This depends on the temperature to 
which they have been heated. Moreover the shrinkage 
varies according to the number of times they have been 
heated. For instance, a wheel tier 7 feet diameter was 
heated red-hot, and cooled thirteen times in succession 
with the following results :— 
Ist time it contracted % in. in length. 
2nd ” ” it ” ” 
3rd ” ” 1s ” ” 
4th ” ” 3 ” ” 
Sth ” ” 3 ” ” 
6th ” ” z ” ” 
7th ” ” t ” ” 
8th ” ” 3 ” ” 
oth ” ” + ” ” 
Toth ” ” $ ” ” 
11th ” ” 2 ” ” 
ES 12th ” ” re ” ”) 
13th ” ” 3 ” ”? 
Thus altogether it contracted 53 inches from its original 
length of 22 inches. 
It is clear therefore that however accurate the calcula- 
tion and workmanship, there must be great difficulty in 
ensuring the exact amount of tension in this system of 
gun construction, and if guns are made without regard to 
calculation, without regard to the peculiar idiosyncracy of 
the iron, and without regard to the temperature from 
which the shrinking is made (and such is pretty much 
the case at Woolwich), it is no wonder that they split their 
tubes or shift their hoops in action. Many Woolwich 
guns have done this even under trial, and it is not im- 
probable that in the late operations at Alexandria two of 
the guns of the A/exandra were injured in this way. 
Another objection to this method of gunmaking is the 
possibility of latent defects in the hoops. It is impossible 
always to detect a flaw, even of considerable magnitude, 
ina hoop of iron or steel 10 to 18 inches thick such as 
are used in the large Woolwich guns, and such latent 
flaws may prove fatal to the gun even if in other respects 
it were properly constructed. 
JAMEs A. LONGRIDGE 
( To be continued.) 
Mk. FORBES’ ZOOLOGICAL EXPEDITION UP 
THE NIGER 
R. W. A. FORBES writes from Lokoja, on the 
Niger, at the confluence with the Binué (Sep- 
tember 9) as follows:—I have been here on and off 
