August 25, 1905.] 



SCIENCE. 



241 



concludes his argument with a blend of 

 confidence and patriotism : — 



Wherefore if according to what we have al- 

 read}' said it should return again about the year 

 1758, candid posterity will not refuse to acknowl- 

 edge tliat this was first discovered by an English- 

 man. 



Such was Halley's prediction published in 

 the year 1705. The comet pursued its 

 course, and it was next seen on Christmas 

 Day, 1758. Candid posterity, so far from 

 refusing to acknowledge that the discovery 

 was made by an Englishman, has linked 

 Halley's name with the comet, possibly for 

 all time. 



AVe all now could make announcements 

 on the subject of Halley 's comet ; their ful- 

 filment could be awaited serenely. No vi- 

 sion or inspiration is needed; calculations 

 and corrections will suffice. The comet was 

 seen in 1835, and it is expected again in 

 1910. No doubt our astronomers will be 

 ready for it; and the added knowledge of 

 electrical science, in connection particularly 

 with the properties of matter, may enable 

 them to review Bessel's often-discussed con- 

 jecture as to an explanation of the emis- 

 sion of a sunward tail. But Halley's an- 

 nouncement was made during what may be 

 called the immaturity of the gravitation 

 theory; the realization 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 veri- 

 fied by observation, of the planet Neptune. 

 I do not known an apter illustration of 

 Bacon's dictum that has already been 

 cpioted, ' All true and fruitful natural phi- 

 losophy 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 



trustAvorthy knowledge. But until the 

 event justified Halley's prediction, the 

 Cartesian vortex-theory of the universe Avas 

 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 themselves up to 

 the study of truth.' 



The century that followed the publication 

 of Halley's prediction shows a world that 

 is steadily engaged in the development of 

 the inductive sciences and their applica- 

 tions. Observational astronomy continued 

 its activity quite steadily, reinforced to- 

 wards the end of the century by the first 

 of the Herschels. The science of mathe- 

 matical (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 mathe- 

 matics suitable for the purpose. The be- 

 ginnings 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 infinitesi- 

 mal calculus in its various branches (in- 

 eluding, that is to say, what we call the 

 differential calculus, the integral calculus, 

 and differential equations) received the de- 

 velopment 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 immedi- 

 ateh^ 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 achieve- 



