698 



SCIENCE 



[N. S. Vou XL. No. 1037 



pends upon what the word " handmaiden " 

 connotes. If it is used to designate a sup- 

 posed inferiority either in value or respect, 

 or a menial and degrading compulsory service, 

 he justly rebels against the use of this meta- 

 phor. If, on the other hand, divested of all 

 suggestion of inferiority ordinarily concomi- 

 tant with the use of the term servant, the word 

 is only construed to mean a voluntary, honor- 

 able assistance, then, though deploring the use 

 of a figure with such possibilities for false 

 interpretation, he may not seriously object to 

 its use. Mathematics undoubtedly does render 

 incalculable aid to the exact and many other 

 sciences. 



Since mathematics antedates the other 

 familiar sciences, astronomy excepted, its 

 existence is surely not dependent upon their 

 existence, nor can service to the other sci- 

 ences be its sole aim and object. It does not 

 live to serve, alone. It is not a bom slave. It 

 has an existence absolutely independent of 

 any use to which it may be applied. The 

 mathematician has pursued and will pursue 

 his investigations regardless of material profit. 

 The unselfish motive which directs his activ- 

 ities as well as those of other pure scientists 

 is that love of knowledge pure and simple 

 which seeks no reward other than the intel- 

 lectual delight incident to the discovery of 

 unknown truth, for him the revelation of 

 hitherto unseen relations existent in the realms 

 of number and space. However abstract and 

 remote from practical application the truth 

 revealed, matters not. He is not and refuses 

 to be guided by mercenary motives. 



If, however, in the light of popular concep- 

 tions, the standard of appreciation of science 

 be the extent or importance of its application 

 to the exigencies of daily life, mathematics 

 gains rather than suffers from the lowering of 

 the standard. Nevertheless the teacher of 

 mathematics is frequently required by the 

 prospective student to justify the usefulness 

 of his courses. It occurred to me that a very 

 definite and unprejudiced reply to such queries 

 can be obtained from the Encyclopedia Britan- 

 nica, 11th ed. This great work which is a 

 "survey of the field of knowledge" presum- 



ably is impartial. Necessarily only the essen- 

 tials can be given in such a work. We have 

 selected from this book those subjects which 

 have required the symbols of infinitesimal 

 calculus in their treatment. The list is in- 

 tended to be complete, but omissions are prob- 

 able, owing to the haste in covering so many 

 pages. Notice of omissions will be welcomed. 

 Some of the subjects, such as infinitesimal 

 calculus, are obviously mathematical, while 

 the appearance of others, such as clock and 

 sky, may surprise even mathematicians. The 

 list would be far greater if we based it upon 

 a lower subject such as trigonometry instead 

 of calculus. 



The list contains 104 headings which are as 

 follows: Aberration, accumulator, aether, 

 algebra, algebraic forms, amplitude, astron- 

 omy, atmospheric electricity, aurora polaris, 

 ballistics, bearings, Bessel function, bridge, 

 calculating machine, calorimetry, capillary 

 action, chemical action, chemistry, clock, com- 

 binatorial analysis, condensation of gases, con- 

 duction electric, conduction of heat, curve, 

 cycloid, differences calculus of, differential 

 equation, diffraction of light, diffusion, 

 dynamics, dynamometer, earth figure of the, 

 elasticity, electrokinetics, electrolysis, elec- 

 tromagnetism, electrostatics, energetics, 

 Fourier's series, function, fusion, geodesy, 

 geometry, gravitation, groups theory of, gyro- 

 scope and gyrostat, harmonic analysis, heat, 

 Herbart, hodograph, hydraulics, hydromechan- 

 ics, illumination, induction coil, infinitesimal 

 calculus, interference of light, interpolation, 

 lens, light, lighting, logarithm, lubrication, 

 magnetism, magnetism terrestrial, magneto 

 optics, map, maxima and minima, mechanics, 

 mensuration, meteorology, molecule, number, 

 power transmission, probability, quaternions, 

 radiation, radioactivity, series, shipbuilding, 

 sky, solution, sound, spectroscopy, spherical 

 harmonics, spiral, steam engine, stereoscope, 

 stoichiometry, strength of materials, sun, sur- 

 face, surveying, table mathematical, tacheom- 

 etry, thermodynamics, thermoelectricity, ther- 

 mometry, tide, time measurement of, trans- 

 former, trigonometry, units physical, vaporiza- 



