TRANSACTIONS OF SECTION A. ole 
and the added knowledge of electrical science, in connection particularly with 
the properties of matter, may enable them to review Bessel’s often-discussed 
conjecture as to an explanation of the emission of a sunward tail. But Halley’s 
announcement was made during what may be called the immaturity of the 
gravitation theory; the realisation of the prediction did much to strengthen the 
belief in the theory and to spread its general acceptance ; the crown of conviction 
was attained with the work of Adams and Leverrier in the discovery, propounded 
by theory and verified by observation, of the planet Neptune. I do not know an 
apter illustration of Bacon’s dictum that has already been quoted, ‘All true and 
fruitful natural philosophy hath a double scale, ascending from experiments 
to the invention of causes, and descending from causes to the invention of new 
experiments.’ The double process, when it can be carried out, is one of the most 
effective agents for the increase of trustworthy knowledge. But until the event 
justified Halley’s prediction, the Cartesian yortex-theory of the universe was not 
completely replaced by the Newtonian theory; the Cartesian votaries were not 
at once prepared to obey Halley’s jubilant, if stern, injunction to ‘leave off 
trifling . . . with their vortices and their absolute plenum . . . and give them- 
selves up to the study of truth.’ 
The century that followed the publication of Halley’s prediction shows a 
world that is stgadily engaged in the development of the inductive sciences and 
their applications. Observational astronomy continued its activity quite steadily, 
reinforced towards the end of the century by the first of the Herschels. The 
science of mathematical (or theoretical) astronomy was created in a form that is 
used to this day; but before this creation could ‘be effected, there had to be a 
development of mathematics suitable for the purpose. The beginnings were 
made by the Bernoullis (a family that must be of supreme interest to Dr. 
Francis Galton in his latest statistical compilations, for it contained no fewer 
than seven mathematicians of mark, distributed over three generations), but the 
main achievements are due to Euler, Lagrange, and Laplace. In particular, the 
infinitesimal calculus in its various branches (including, that is to say, what we 
call the differential calculus, the integral calculus, and differential equations) 
received the development that now is familiar to all who have occasion to work 
in the subject. When this calculus was developed, it was applied to a variety of 
subjects; the applications, indeed, not merely influenced, but immediately directed, 
the development of the mathematics. To this period is due the construction of 
analytical mechanics at the hands of Euler, d’Alembert, Lagrange, and Poisson ; 
but the most significant achievement in this range of thought is the mathematical 
development of the Newtonian theory of gravitation applied to the whole 
universe. It was made, in the main, by Lagrange, as regards the wider theory, 
and by Laplace, as regards the amplitude of detailed application. But it was a 
century that also saw the obliteration of the ancient doctrines of caloric and 
phlogiston, through the discoveries of Rumford and Davy of the nature and rela- 
tions of heat. The modern science of vibrations had its beginnings in the 
experiments of Chladni, and, as has already been stated, the undulatory theory of 
light was rehabilitated by the researches of Thomas Young. Strange views as to 
the physical constitution of the universe then were sent to the limbo of for- 
gotten ignorance by the early discoveries of modern chemistry ; and engineer- 
ing assumed a systematic and scientific activity, the limits of which seem 
bounded only by the cumulative ingenuity of successive generations. But in thus 
attempting to summarise the progress of science in that period, I appear to be 
trespassing upon the domains of other Sections; my steps had better be retraced 
so as to let us return to our own upper air. If I mention one more fact (and it 
will be a small one), it is because of its special connection with the work of this 
Section. As you are aware, the elements of Euclid have long been the standard 
treatise of elementary geometry in Great Britain; and the Greek methods, in 
Robert Simson’s edition, have been imposed upon candidates in examination after 
examination. But Euclid is on the verge of being disestablished: my own Uni- 
versity of Cambridge, which has had its full share in maintaining the restriction 
to Euclid’s methods, and which was not uninfluenced by the report of a Committee 
