282 



POPULAR SCIENCE MONTHLY. 



wood forests, he invoked the mammals to 

 yield the sinew from the leg or the scapula, 

 and with this he glued an elastic back upon 

 his poor implement or united two or three 

 horns so as to get his effect, the middle piece 

 giving the columnar resistance, the wings 

 putting to flight the arrow. By and by you 

 approach the hyperborean man and ask him 

 how he is going to have a bow. It is true 

 that he has only brittle driftwood, that glue 

 will not hold in his cold and damp clime, 

 and that materials for arrows are scarce. 

 The result of this is the sinew-backed bow 

 and the harpoon arrow, together the most 

 complicated and ingenious device ever con- 

 trived by a savage mind. The bow wood 

 has one virtue, that of rigidity. By an in- 

 genious wrapping of hundreds of feet of fine 

 sinew thread or braid from end to end along 

 the back with half hitches on the limbs at 

 every danger point the virtue of elasticity is 

 added, and you have one of the most quickly 

 responsive implements in the world. The 

 arrow is quite as cleverly conceived." 



Value of Pure Mathematics. — The presi- 

 dential address of Prof. A. R. Forsyth in the 

 Section of Mathematical and Physical Science 

 of the British Association related to the value 

 of the study of pure mathematics aside from 

 the consideration of any applications that 

 may be made of it. By some, mathematical 

 study is regarded as useful only as it affords 

 means for arriving at results connected with 

 one or other of the branches of natural phi- 

 losophy ; by others, as it may possibly apply 

 to practical issues. To the former class of 

 critics the author cited instances in which 

 the utilitarian bias in the progress of knowl- 

 edge has not been the best stimulus, or in 

 the long run the most effective guide toward 

 securing results ; to the others he maintained 

 that mathematical students are justified in 

 not accepting practical issues as the sole 

 guide by the consideration that such issues 

 widen from year to year and can not be 

 foreseen. Moreover, if such a principle was 

 adopted many an investigation undertaken 

 at the time for its intrinsic interest would be 

 cast aside unconsidered, because it did not 

 satisfy an external test that really had 

 nothing to do with the case, and might 

 change its form of application from time to 

 time. Among instances in which the purely 



mathematical discovery preceded the prac- 

 tical application and was not an elucidation 

 or an explanation of observed phenomena, 

 are cited the principles of conic sections, 

 known to the Greeks two thousand years 

 before Kepler and Newton found in them the 

 solution of the universe ; the methods of 

 analysis by the application of which the dis- 

 covery of the planet Neptune was attained ; 

 the reasoning on the properties of wave-sur- 

 faces by the use of which Sir William Hamil- 

 ton inferred the existence of conical refrac- 

 tion ; and the theory of functions, in which 

 the purely mathematical interest was deemed 

 supreme, which has found application in the 

 investigations of Lagrange and others on the 

 construction of maps ; in investigations on 

 discontinuous two dimensional fluid motion 

 in hydrodynamics ; in the dynamics of a 

 rotating heavy body, in various questions in 

 electrostatics, and in some of the recent 

 advances in physical astronomy. In the field 

 of natural philosophy mathematics will fur- 

 nish more effective assistance if in its sys- 

 tematic development its course can freely 

 pass beyond the ever-shifting domain of use 

 and application. 



Cnriosities of Zoology. — Prof. L. C. Miall 

 observes, in his sectional address at the Brit- 

 ish Association, that zoologists may justify 

 their favorite studies on the ground that to 

 know the structure and activities of a variety 

 of animals enlarges our sense of the possi- 

 bilities of life. Surely it must be good for 

 the student of human physiology, to take 

 one specialist as an example of the rest, 

 that he should know of many ways in which 

 the same functions can be discharged. Let 

 him learn that there are starfishes whose 

 nervous system lies on the outside of the 

 body, and that in other animals it is gen- 

 erally found there during some stage of de- 

 velopment ; that in certain animals the cir- 

 culation reverses its direction at frequent 

 intervals ; that there are animals with eyes 

 on the back, on the shell, on limbs and limb- 

 like dependencies, in the brain cavity, or on 

 the edge of a protective fold of skin ; that 

 there are not only eyes of many kinds with 

 lenses, but eyes on the principle of the pin- 

 hole camera without lens at all (nautilus), 

 and of every lower grade down to mere pig- 

 ment spots ; that auditory organs may be 



