442 
Mercury = 4. 
Venus = 4 -f 3 = 7. 
Earth = 4 + 3 X 2 = 10. 
Mars = 4 + 3 X 2 2 = 16. 
= 4 3 X 2 3 = 28. 
Jupiter = 4 -f 3 X 2 4 = 52. 
Saturn =443X2° = 100. 
Uranus = 4 + 3 X 2 6 = 196. 
It will be observed that there is a blank between Mars and 
Jupiter, which has been supplied by the discovery of not one, 
but a series of ninety small planets. In 1^4 
covered Ceres: in 1802, Olbers discovered Pallas, m 1804, 
Harding discovered Juno; and in 1807, Olbers again dis- 
covered a fourth— Yesta. These four small planets lie between 
Mars and Jupiter; their orbits intersect each other, and L their 
mean distance from the sun agrees with Bode s law. Heischel, 
senior, called .them asteroids. Herschel, junior, in wn mg 
his most admirable Popular Astronomy (by far the best m any 
language), in 1838, laughs at what he calls the philosophical 
dream of Bode, which led to them discovery, in these words : 
“This may serve as a specimen of the dreams m which 
astronomers, like other speculators, occasionally and harrn- 
Prora the°fact that the orbits of these four asteroids all inter- 
sect in one point, Olbers, the discoverer of two of them, con- 
jectured that they were fragments of one planet. Lagrange 
determined the force necessary to blow the planet into pieces. 
This theory led to a careful mapping and survey of the heavens 
in the zone of the asteroids' path ; and now the asteroids 
number ninety— and how many more “ fragments may be dis- 
covered no one can conjecture. Sir John Herschel with, 
this passage from the larger astronomy which he published a 
few years since— somewhat prematurely some may thin - ; 
for the discovery of Neptune proved that Bode s law ot 
distances altogether failed as far as that new member of the 
planetary system was concerned. Now, whether deserved y 
or not, the destruction of Olbers' planet is generally con- 
signed to the limbo of hypotheses, as no better than a mere 
philosophical dream. _ 
The history of the discovery of this ring of small planetary 
bodies circulating between Mars and Jupiter is very instruc- 
tive. It shows us that discoveries may be made, even by a law 
deduced from numerous observations and coincidences, capable 
of mathematical expression, which may, after all, turn ou 
to be no law of nature at all, in the philosophical sense. 
Since the small planetary bodies revolving round the sun 
