324 
in the equator at such a rate that the difference be- 
tween its right ascension at any time, and that of the 
true sun, consists entirely of periodicterms. This dif- 
ference is called the equation of time, which, there- 
fore, by its very nature, cannot contain any term 
increasing indefinitely with the time. Mean noon at 
any place is determined by the transit of this imagi- 
nary body over the meridian of the place, just as 
apparent noon is determined by the transit of the 
true sun. 
Thus mean time is defined with reference to a 
natural phenomenon; viz., the transit of the real sun 
over a given meridian: and we cannot have one 
length of a mean solar day according to Bessel, and 
another length according to LeVerrier, any more 
than we can have different lengths of the apparent 
solar day. 
A mean solar day, according to Mr. Stone’s theory, 
is something totally different from that above defined. 
It has no reference to the average length of the ap- 
parent solar day, but is purely artificial or conven- 
tional in character. Practically, Mr. Stone’s mean 
solar day is the time during which the mean longi- 
tude of the sun increases by some definite amount. 
Bessel gives one determination of this amount, and 
LeVerrier a different one: hence Mr. Stone is obliged 
to employ two mean solar days, which are of different 
lengths, according as Bessel’s or LeVerrier’s mean 
motion of the sun is used. On this principle, every 
fresh investigator of the sun’s motion would require a 
mean solar day peculiar to himself. We are tempted 
to ask, What was the meaning of the mean solar day 
before Bessel’s time ? 
The origin of Mr. Stone’s misapprehension on this 
point seems to be the following. In the ordinary 
practice of an observatory it is usual and convenient 
to deduce the mean solar time from the sidereal time 
supposed to be known, instead of finding it by direct 
observation of the sun. In order that this conversion 
of sidereal into mean solar time, however, may be 
correctly performed, it is necessary to employ the 
correct mean longitude of the sun at the given in- 
stant. Any error in the assumed mean longitude 
will produce an equivalent error in the mean time 
deduced; and, if the sun’s mean motion be incorrectly 
assumed, the error of time thus produced will gradu- 
ally accumulate. 
Thus the error of mean solar time as deduced from 
sidereal time by means of Bessel’s formula, which 
amounted in the year 1864 to a little more than half 
a second, has increased to a little more than six- 
tenths of a second at the present time. The increase 
of the error of mean solar time in nineteen years is 
in reality rather less than eight-hundredths of a 
second, whereas Mr. Stone’s theory makes it amount 
to twenty-seven seconds! In fact, the error, accord- 
ing to Mr. Stone’s theory, is about three hundred and 
sixty-five times as great as it should be. The reason 
is, that mean time is measured, not by the sun’s mean 
motion in longitude, as Mr. Stone’s theory supposes, 
but by its mean motion in hour-angle, which is about 
three hundred and sixty-five times as great; so that 
the error in time produced by a small error in the 
AY re 
SCIENCE. 
eee 
[Vou. III., No. 58. i 
mean motion in longitude is only about $5 of that 
which would be produced if the error in time bore 
the same proportion to the time that the error in the 
mean motion in longitude bears to this mean motion 
itself. 
If n denote the sun’s mean motion in longitude in 
a mean solar day, then the ratio of the length of a . 
mean solar to that of a sidereal day is 
560° = 1 = 3602. 
And if n + dn denote a slightly different deter- 
mination of the mean motion in longitude, this ratio 
will be altered to 
360° +- n + dan: 3602; 
Hence the measure of the sidereal interval corre-- 
sponding to any given number of mean solar days 
will be altered in the ratio of 
360° +. n + dn’: 360° Fae 
dn 
or iL se 360° + n 5 1; 
that is, since 360° is nearly equal to 3865 n, the sidereal 
measure of the interval will be altered nearly in the 
ratio of 
instead of in the ratio of 
Lat aa He 
n 
as it should be by Mr. Stone’s theory. 
In conclusion, we will test Mr. Stone’s theory of 
mean solar time by supposing an extreme case. Let 
us imagine that the sun had no motion in longitude, 
but, like a fixed star, retained a constant position in 
the heavens. On this supposition, mean solar time 
would be just as intelligible as it is at present, and it 
is evident that the mean solar day and the sidereal 
day would become identical with each other; but 
what would become of mean solar time according to 
Mr. Stone’s idea of it ? 
MORPHOLOGY OF THE PELVIS AND 
LEG. 
Miss ALICE JOHNSON, at the suggestion of the late 
F. M. Balfour, has investigated the development of 
the pelvic girdle and hind-limb of the chick (Quart. 
journ. micr. sc., xxiii. 899). On the fourth day of 
incubation the limb is merely a local exaggeration 
of the Wolffian ridge, consisting, like it, of a mass of 
rounded mesoblastic cells crowded together. The 
first trace of the skeletal parts appears on the fifth 
day; the mesoblastic tissue of the axis of the limb 
becoming more condensed, and, by the seventh day, 
converted into recognizable cartilage. Ossification 
begins very late. The entire skeletal anlage of the 
girdle and limb is at first continuous, making a T, of 
which the stem represents the limb, and the cross 
the girdle running dorsoventrally. The pelvic anlage 
soon expands, above the centrally placed acetabular 
region, into a broad plate, the ileum; below, and in 
front, into the narrow pubis. A little later the pec- 
¢ tineal process grows out in front from the upper part 
