a 
foa2 
502 
NA TORE 
[April 7, 1870 
daher, wie schon friiher die Vorlesungen iiber die Warme, so 
auch jetzt die vorliegenden Vortrage tiber den Schall unter ihrer 
besonderen Aufsicht tibersetzen lassen, und die Druckbogen einer 
genauen Durchsicht unterzogen, damit auch die deutsche Bear- 
beitung den englischen Werken ihres Freundes Tyndall nach 
Form und Inhalt moglichst entsprache.—H. HELMHOLTZ, G. 
WIEDEMANN.” 
Prof. Tyndali’s work, his account of Helmholtz’s Theory of 
Dissonance included, having passed through the hands of Helm- 
holtz himself, not only without protest or correction, but with 
the foregoing expression of opinion, it does not seem likely that 
any serious damage has been done. ] 
Apparent Size of Celestial Objects 
Aout fifteen years ago I was looking at Venus through a 
40-inch telescope, Venus then being very near the Moon and 
of a crescent form, the line across the middle or widest part 
of the crescent being about one-tenth of the planet’s diameter. 
It occurred to me to be a good opportunity to examine how 
far there was any reality in the estimate we form of the 
apparent size of celestial objects. Venus through the telescope, 
with a magnifying power (speaking from memory) of 135, 
looked about the size of an old guinea, #2, of a crescent cut 
off from that coin. The Moon, to my naked eye, appeared 
the size of a dessert plate. Having fixed their apparent 
dimensions in my mind, I adjusted the telescope so that with 
one eye I could see Venus through the telescope, and with 
the other the Moon without the telescope, and cause the 
images to overlap. I was greatly surprised to find that Venus 
instead of being about one-sixth of the diameter of the Moon 
was rather more than double its diameter, so that when the 
adjustment was made to bring the upper edge of the Moon 
coincident with the upper point of the crescent of Venus, the 
opposite edge of the Moon fell short of the middle of the 
crescent, a very palpable demonstration of the fallacy of 
guesses at size, when there are no means of comparison. 
On another occasion a lady was looking at Jupiter through 
my telescope, and having first put on a power of 60 I changed 
it for one of 140. ‘Lo my question, what difference she 
observed in the size of the planet, she answered, I see no 
difference in size, but a good deal in brightness. | Here the area 
of the one image was more than five times that of the other. 
The fallacy of guesses at size without objects of comparison is 
most strikingly shown in the ordinary expression ofan ignorant ob- 
server looking at objects by day through aspy-glass. If you ask, as 
I have often done, a person unacquainted with optics whether he 
recognises any difference in size between an object, say a horse 
or a cow, seen with or withouta telescope, he will always answer 
No, but it (the telescope) brings it much nearer. ‘This, of course, 
is really an admission of increased magnitude, but the observer 
is unconscious of it; a horse to him is as big as a horse, no larger 
or smaller, whatever be the distance. 
The assistance which may be derived from the degree of 
convergence of the optic axes alluded to by your correspondent 
“«<“T. RK.” may be something when we know what the object is, 
or when it is moved to and fro, but if the object be unfamiliar, 
and there be no standard of comparison, I doubt whether any 
fair guess could be made. 
Suppose all objects had never been seen but at one and the 
same distance, then an observer looking at a given object without 
any external standard of comparison, would probably make a 
fair guess at its size, for the picture on his retina would have 
a definite size, and his mind would estimate it by relation to 
other pictures of known objects which he had seen at other 
times ; but as we see all the objects with which we are familiar 
at all degrees of distance, we have no standard of comparison 
for an image on the retina. 
The common phantasmagoria effect where a figure appears to 
advance or recede from us though it really does not change its 
position, but its size is one of the many illusions produced by 
representing things as they are seen under certain circumstances 
which have become habitual, and habit interprets the vision. 
So if one lie on his back in a field, and throwing the head 
back, look at distant trees or houses, they will appear to be in 
the zenith, because when we ordinarily look at the zenith the 
head is thrown back. 
Is the apparent size of the Sun or Moon, as expressed in com- 
mon parlance, anything more than a reference to some standard 
which we have early adopted, and which, not having any means 
of rectifying, we assume. To me the Moon at an altitude of 
45° is about 6 inches in diameter ; when near the horizon, she is 
about a foot. If I look through a telescope of small magnifying 
power (say 10 or 12 diameters), so as to leave a fair margin in 
the field, the Moon is still 6 inches in diameter, though her 
visible area has really increased a hundred-fold. 
Can we go further than to say, as has often been said, that all 
magnitude is relative, and that nothing is great or small except 
by comparison ? W. R. GROVE. 
115, Harley Street, April 4 
An After Dinner Experiment 
Suppose inthe experiment of an ellipsoid or spheroid, referred 
to in my last letter, rolling between two parallel horizontal 
planes, we were to scratch on the rolling body the two equal 
similar and opposite closed curves (the fo//ods so-called), traced 
upon it by the successive axes of instantaneous solution ; and 
suppose, further, that we were to cut away the two extreme seg- 
ments marked off by those tracings, retaining only the barrel or 
middle portion, and were then to make this barrel roll under the 
action of friction upon its bounding curved edges between the 
two fixed planes as before, or, more generally, imagine a body 
of any form whatever bounded by and rolling under the action 
of friction upon these two edges between two parallel fixed 
planes ; it is easy to see that, provided the centre of gravity 
and direction of the principal axes be not displaced, the law of 
the motion will depend only on the relative values of the principal 
moments of inertia of the body so rolling, in comparison with the 
relative values of the axes of the ellipsoid or spheroid to which 
the fo/hods or rolling edges appertain; and consequently, that, 
when a certain condition is satisfied between these two sets of 
ratios, the motion will be similar in all respects to that of a 
free body about its centre of gravity. 
That condition (as shown in my memoir in the Philosophical 
Transactions) is, that the nine-membered determinant formed by 
the principal moments of inertia of the rolling body, the inverse 
squares and the inverse fourth powers of the axes of the ellipsoid 
or spheroid shall be equal to zero—a condition manifestly 
satisfied in the case of the spheroid, provided that two out of 
the three principal moments of inertia of the rolling solid are 
equal to one another. 
My friend Mr. Froude, the well-known hydraulic engineer, 
with his wonted sagacity, lately drew my attention to the familiar 
experiment of making a wine-glass spin round and round on 
a table or table-cloth upon its base ina circle without slipping, 
believing that this phenomenon must have some connection with 
the motion referred to in my preceding letter to NATURE: an intui- 
tive anticipation perfectly well founded on fact ; for we need only 
to prevent the initial tendency of the centre of gravity to rise by 
pressing with a second fixed plane (say a rough plate or book- 
cover) on the top of the wine-glass, and we shall have an excellent 
representation of the free motion about their centre of gravity of 
that class of solids which haye, so to say, a natural momental 
axis, z.e. (in the language of the schools) two of their principal 
moments of inertia equal. For greater brevity let me call solids 
of this class uniaxal solids. I suppose that the centre of 
gravity of the glass is midway between the top and bottom, and 
that the periphery of the base and of the rims are circles of equal 
radius. These circles will then correspond to folheds of a 
spheroid, conditioned by the angular magnitude and dip 
of the spinning glass ; to determine from which two elements 
the ratio of the axes of the originally supposed but now super- 
seded representative spheroid is a simple problem in conic 
sections ; this being ascertained, the proportional values of the 
moments of inertia of the represented solid may be immediately 
inferred. The wine-glass itself belonging to the class of uniaxal 
bodies, the condition that ought to connect its moments of inertia 
with the axis of the representative spheroid (in order that the 
motion may proceed fari passu with that of a free body) is 
necessarily satisfied. 
The conclusion which I draw from what precedes is briefly 
this—that a wine-glass equally wide at top and bottom, and 
with its centre of gravity midway down, spinning round upon 
its base and rim in an inclined position between two rough but 
level fixed horizontal surfaces, yields, so long as its vzs-viva 
remains sensibly unaffected by disturbing causes, a_ perfect 
representation, both in space and time, of the motion of a free 
uniaxal solid, as e.g. a probate or oblate spheroid, or a square or 
equilateral prism or pyramid about its centre of gravity, and 
