1869.] Mathematical and Physical Science. 589 



of her young and buoyant sister could not fail to impart ; short 

 roads preferred to long ones ; Euchd shelved or buried " deeper 

 than did ever plummet sound ; " morphology introduced into the 

 elements of algebra ; projection, correlation, motion, accepted as aids 

 to geometry ; the mind of the student quickened and elevated, and 

 his faith awakened by early initiation into the ruling ideas of 

 polarity, continuity, infinity, and familiarization with the doctrine 

 of the imaginary and inconceivable. It is this living interest in 

 the subject which is so wanting in our traditional and mediaeval 

 modes of teaching. Some people have been found to regard all 

 mathematics after the 47th proposition of Euclid as a sort of morbid 

 secretion, to be compared only with the mother-of-jDearl generated 

 in the deceased oyster ; others find its justification, its " raison 

 d'etre" in its being' either the torch-bearer leading the way, or the 

 handmaiden holding up the train, of physical science ; and a very 

 clever writer, in a recent magazine article, expresses his doubts 

 whether it is in itself a more serious pursuit or more worthy of 

 interesting an intellectual human being than the study of chess 

 problems or Chinese puzzles. But this is like judging of architec- 

 ture from being shown some of the brick and mortar, or even a 

 quarried stone of a public building ; or of painting from the colours 

 mixed on the palette ; or of music by listening to the thin and 

 screechy sounds produced by a bow passed haphazard over the 

 strings of a violin. The world of ideas which it discloses or illu- 

 minates, the contemplation of divine beauty and order which it 

 induces, the harmonious connection of its parts, the infinite hier- 

 archy and absolute evidence of the truths with which it is concerned — 

 these and such like are the true grounds of the title of mathematics 

 to human regard, and would remain unimpaired were the plan of 

 the universe unrolled hke a map at our feet, and the mind of man 

 qualified to take in the whole scheme at a glance. 



At the conclusion of the above addrees the reading of the papers 

 commenced. As it would be impossible to give within the hmits 

 at our command an intelligible abstract of the mathematical and 

 some of the physical papers, we shall confine our reports to abstracts 

 of those papers which will be of interest in their condensed form. 



The first paper was the report of the Lunar Committee, read by 

 the Secretary, Mr. W. E. Birt. Since the formation of the com- 

 mittee in 1864, a surface of 100 square degrees has been surveyed ; 

 the outhnes of 433 objects have been laid down on a scale of 200 

 inches to the moon's diameter ; and a catalogue has been prepared, 

 containing notices of important phenomena bearing on the question 

 of either transient or permanent lunar change. The report enters 

 fully on this latter point, and, in conclusion, draws attention to cer- 

 tain diflerences between the photographs employed, particularly one 

 with respect to a certain crater figured by Lohrmann, which is found 



