Page:Popular Science Monthly Volume 52.djvu/296

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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 contrived by a savage mind. The bow wood has one virtue, that of rigidity. By an ingenious 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 presidential 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 philosophy; 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 knowledge 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 practical 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 discovery of the planet Neptune was attained; the reasoning on the properties of wave-surfaces by the use of which Sir William Hamilton inferred the existence of conical refraction; 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 furnish more effective assistance if in its systematic development its course can freely pass beyond the ever-shifting domain of use and application.

Curiosities of Zoölogy.—Prof. L. C. Miall observes, in his sectional address at the British Association, that zoölogists 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 possibilities 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 generally found there during some stage of development; that in certain animals the circulation 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 pinhole camera without lens at all (nautilus), and of every lower grade down to mere pigment spots; that auditory organs may be