TENDENCIES IN MATHEMATICAL SCIENCE 345 



enough to show precisely the displacement discovered. In 1837 

 Bessel attacked this ancient problem successfully by making 

 extremely accurate observation of the relative positions of a certain 

 double star (71 Cygni) and its celestial neighbors. He obtained 

 for the distance of the double star 657,000 times the mean dis- 

 tance from the earth to the sun. Such inconceivably vast dis- 

 tances have been since conveniently expressed in a unit called the 

 light-year, i.e. the distance a ray of light travels in an entire year 

 at 186,000 miles per second. 



MATHEMATICAL PHYSICS. The further progress of applied 

 mathematics in the nineteenth century has been interestingly 

 summarized by Woodward in a presidential address to the Ameri- 

 can Mathematical Society, from which the following extracts are 

 quoted. 



Next came the splendid contributions of George Green under 

 the modest title of 'An essay on the application of mathematical 

 analysis to the theories of electricity and magnetism/ It is in this 

 essay that the term ' potential function' first occurs. Herein also 

 his remarkable theorem in pure mathematics, since universally known 

 as Green's theorem, and probably the most important instrument 

 of investigation in the whole range of mathematical physics, made its 

 appearance. We are all now able to understand, in a general way at 

 least, the importance of Green's work, and the progress made since 

 the publication of his essay in 1828. But to fully appreciate his 

 work and subsequent progress one needs to know the outlook for the 

 mathematico-physical sciences as it appeared to Green at this time 

 and to realize his refined sensitiveness in promulgating his discoveries. 

 'It must certainly be regarded as a pleasing prospect to analysts/ 

 he says in his preface, ' that at a time when astronomy, from the state 

 of perfection to which it has attained, leaves little room for further 

 applications of their art, the rest of the physical sciences should show 

 themselves daily more and more willing to submit to it.' . . . ' Should 

 the present essay tend in any way to facilitate the application of 

 analysis to one of the most interesting of the physical sciences, the 

 author will deem himself amply repaid for any labor he may have 

 bestowed upon it ; and it is hoped the difficulty of the subject will 

 incline mathematicians to read this work with indulgence, more partic- 



