366 
NATURE 
[ FeBruary 18, 1897 
The object of writing 7 for w/g, or of changing to the abso- 
lute unit of force and writing 7 for w, is merely to get rid of ¢ 
in the dynamical equations, which concern the problems which 
alone are capable of direct human measurement. 
But this quantity g, so treacherous as Dr. Lodge can testify, 
should always be kept carefully in sight ; any attempt to get rid 
of it merely causes it to reappear elsewhere in an unexpected 
place (expelles Jurca, &c.). 
The engineer can be left to take care of himself, and does not 
require to be instructed in an art with which he is perfectly 
familiar. Considering that he has been compelled to create for 
himself, without professorial assistance, the whole theory of the 
internal stresses of rapidly reciprocating machinery as causing 
vibration, it cannot be correct to say that acce/eratzon does not 
come under his notice. 
Certainly he often ignores acceleration in his dynamical 
equations, but that is because he prefers to use the principles of 
Energy and Momentum ; and our elementary text-books would 
do well to imitate him. 
As for Dr. Lodge’s hint to the sailor, it is useless and even 
dangerous for navigation, because it gives the distance of the 
offing in military land miles; instead of geographical nautical 
miles, as required, of sixty to the degree. 
Iam reminded of another delicious hint from a theorist to 
practical men, taken from a recent text-book of Theoretical 
Mechanics ; the gunner is instructed not to use his favourite 
whip-on-whip tackle, nor the sailor to set up the backstay in 
the usual manner, because the theoretical writer finds the Third 
System of Pulleys practically useless, the strings of his model 
always becoming twisted. 
An engineer can generally be provided with some quiet 
enjoyment in looking through the pages, and especially the 
diagrams, of our numerous treatises on Elementary Mechanics, 
and he will smile at the mental pabulum chopped up small for 
the benefit of the rising pedagogue. 
In this discussion, Prof. T. W. Wright’s excellent Mechanics 
has been lost sight of; it isa complete contrast to our ordinary 
elementary text-book. 
I thoroughly agree with Prof. Wright that the introduction 
of the fowzdal has done more harm than good, and that it will 
never be employed, even by Electricians always working in 
absolute units, who will confine themselves to the Metric 
System. 
The world will never take kindly to saying that the weight of 
a pound weight is 32°1912 poundals, so long as it is at rest on the 
table; but that the weight changes immediately to 32°2382 
poundals when we toss the weight in the air. 
February 6. A. G. GREENHILL. 
Symbols of Applied Algebra. 
I aM sorry to trouble you with one more letter on this sub- 
ject. Prof. Lodge objected to the energy formula wz?/2g, and 
stated that he could only bestow his approbation on a formula 
which was ‘‘independent of every system of units.” His ex- 
ample of such a formula involved three quantities of the same 
kind—namely, three lengths. Being invited to give a formula 
involving three different quantities—e.g. weight, volume, and 
specific gravity—which should come up to his standard, he 
gives W=sV. Now this formula is certainly independent of 
every system of units, in the sense that it cannot be used with 
any known system of units (not even accurately with the C.G.S. 
units). 
To bring out this point, I inquired how this formula is to 
be used with the poundal. Prof. Lodge observes, in reply, 
that density is not a mere number, and that specific gravity 
may be measured in pounds per cubit foot. The former state- 
ment is irrelevant ; the latter not true if “specific gravity” is 
taken with the meaning with which it is invariably used. 
Dr. O’Reilly overlooks, I venture to think, the difference 
between postponing the consideration of the idea of ‘‘ mass,” 
and confusing it with ‘‘ force.”” Of course, his comment on the 
formula P/Q = /Ja is perfectly correct. C. S. JACKSON. 
Equilibrium of a Cylindrical Shell. 
AMONG some work on the design of arches which Dr. 
Thomson, of the Science College, Poona, and myself are 
preparing for publication in the engineering journals, the 
following elegant case of the equilibrium of a circular rib occurs. 
NO. 1425, VOL. 55] 
As it admits of a simple physical enunciation and a simple 
geometrical proof, I think it may interest your readers. 
A thin hollow cylinder with a uniform circular shell is 
submerged in a fluid, and is lying with its axis horizontal. 
The fluid is excluded from the cylinder by smooth face-plates 
of the same density as the fluid. The weight of the shell 
is such that the cylinder displaces its own weight of the fluid. 
It is evident, then, that the cylinder, as a whole, is in neutral 
equilibrium, at any depth below the surface. But, further, if 
the shell be supposed to be perfectly flexible and incompressible, 
it is still in equilibrium under its own weight and the fluid 
pressure. 
Let the figure represent a ring of the cylinder one foot long, 
normal to the paper, and let the unit of weight be that of a 
cubic foot of the fluid. Consider the equilibrium of the are a c, 
and it will be seen that v, the vertical component thrust at 
C, is given by the area of the shaded trapezium E D O C, made 
up of the superincumbent mass of fluid E p A C, and the weight 
of the arc AC, which is exactly equal to the fluid mass 0 A © 
it displaces. 
La 
Thin Olindricad We 
Shed Usyplacng, 
Cs WUGAC OF 
the Hid. © 
Surface 
D 
= 
Again H, the horizontal component thrust at C is given by 
the area of the shaded trapezium 4 ¢ ed, for H, has to balance the 
whole figure 4 7 when the equilibrium of the quadrant A B is 
considered, and has to balance H together with c 7 when the 
equilibrium of the arc A € is considered. 
Now the two shaded trapeziums have their parallel sides equal 
each to each, so that their areas are proportional to the distances 
between their pairs of parallel sides. Hence 
Hl: Vz: QRORR Eee: ED" :,: cosié!:ismid; 
and it follows that the thrust at C is along the tangent to the 
circle there. In the same way the horizontal and vertical 
component thrusts at N are given by 7 @ and N D, andare again 
proportional to cosine @ and sine 0. TuHos. ALEXANDER. 
Engineering School, Trinity College, Dublin, February 9. 
Oysters and Copper. 
As Prof. Herdman, in his interesting letter on the oyster 
question, appears to doubt the occurrence of copper in oysters, 
it may be of interest to mention that, quite recently, I examined . 
some oysters containing this metal in considerable quantity, a 
single oyster yielding ‘oq grammes (about 3 grain) of copper. 
Some of the oysters were light blue in colour, and others were 
a dark olive-green, and copper was found in both, 
These oysters had been obtained from the Mumbles, near 
Swansea. W. F. Lowe. 
Assay Office, Chester, February 4. 
I aM interested to hear of Mr. Lowe’s case,-where he con- 
siders the oysters from near Swansea owe their colour to a very 
considerable amount of copper. As I stated in the concluding 
paragraph of my last letter (p. 293), ‘‘It is evident that there 
are several distinct kinds of greenness in oysters.” Amongst 
these I cited Dr. Thorpe’s recent demonstration of notable 
amounts of copper in oysters from Falmouth ; so it can scarcely 
be said that I ‘“‘appear to doubt the occurrence of copper.” 
Dr. Charles Kohn has kindly re-investigated the matter for me 
