TO » REPORT—1874. 
to see but a few steps in advance. And when at times a thicker darkness has 
seemed to gather before them, men have recoiled as from an impassable barrier, 
and for a while that path has been closed. -But only for a while. Some happy 
accident, some more daring adventurer, it may be time itself, has shown that the* 
darkness was but a cloud. The light of Science has pierced it; the march of 
Science has left it behind ; and the impossibility of one generation is for the next 
but.the record of a new triumph. 
If seeming plausibility could give to man the right to draw across any path of 
scientific discovery an impassable line, surely Comte might be justified in the line 
which he drew across the path of chemistry. Fifty years ago it might seem no’ 
unjust restriction to say to the chemist, Your field of discovery lies within the 
bounds of our own earth. You must not hope to place in your laboratory the 
distant planet or the scarce-visible nebula. You must not hope to determine the: 
constituents of their atmospheres as you would analyze the air which is around your 
own door; and you never will do it. Fifty years ago no chemist would have 
complained that chemical discovery was unjustly limited by such a sentence; per- 
haps no chemist would have refused to join in the prediction. Yet even those who 
heard it uttered have lived to see the prediction falsified. They have seen the 
barrier of distance vanish before the chemist, as it has long since vanished before 
the astronomer. They have seen the chemist, like the astronomer, penetrate the 
vast abyss of space and bring back tidings from the worlds beyond. Comte might 
well think it impossible. We Imow it to be true. ; 
We have learned from this episode of scientific history that the attempt to draw 
an impassable line between the domain of the chemist and the domain of the astro- 
nomer was not justified by the result. Another generation may learn to obliterate 
as completely the line between the domain of the chemist and the domain of the 
mathematician. When that shall be, when Science shall have subjected all natural 
phenomena to the laws of Theoretical Mechanics, when she shall be able to predict 
the result of every combination as unerringly as Hamilton predicted conical refrac- 
tion or Adams revealed to us the existence of Neptune—that we cannot say. That 
day may never come, and it is certainly far in the dim future. We may not 
anticipate it—we may not even call it possible. But not the less are we bound to 
look to that day, and to labour for it as the crowning triumph of Science, when 
Theoretical Mechanics shall be recognized as the key to every physical enigma— 
the chart for every traveller through the dark Infinite of Nature. 
Maruematics, 
On the General Equations of Chemical Decomposition. 
By Prof. W. K. Currrorn, RS, 
On a Message from Professor Sylvester. By Prof. W. K. Crirrorn, F.R.S.. 
On certain Applications of Newton's Construction for the Disturbing Force 
exerted by a distant Body. By Professor Curtis. 
The author remarked that the similarity hetween the expressions for the com- 
ponents, round the principal axes through the centre of gravity of a rigid mass A, 
of the moment due to the attraction of a distant hody B and those for the eompo- 
nents of the moment due to the centrifugal force arising from a rotation of A round 
an axis would naturally suggest a physical resemblance between the two; and he 
showed, from Newton’s construction, that the couple exerted on A by the attraction 
of a distant body B, of mass L and at a distance a, is the same in magnitude as, 
and. opposite in sign to, that which would result from the rotation of A, with an 
angular velocity , round a line in'the direction of the distant hody, and passing 
