444 



SCIENCE 



[N. S. Vol. XXXVIII. No. 978 



medical students to quail. The author as- 

 sumes thorough knowledge of algebra, geom- 

 etry and trigonometry, including particularly 

 the vectorial significance of linear direction. 



Physical optics is avoided entirely, since 

 " no thorough elementary knowledge of that 

 intricate subject can be obtained in the short 

 time allotted to the student for studying op- 

 tics." It is questionable whether this truth 

 warrants the pedagogic loss involved in ig- 

 noring the wave theory of light. Elementary 

 knowledge may be correct so far as it goes, 

 but without involving intricacies. Children 

 are taught in the grammar-school some of the 

 conclusions resulting from the Newtonian 

 theory of gravitation, but without any refer- 

 ence to the difficulties overcome in its estab- 

 lishment. The wave theory of light is now 

 about as well established as the theory of 

 gravitation. To assume it at the outset of a 

 course in elementary optics is common 

 enough to-day. For the college student this 

 assumption is probably accompanied quite 

 generally with the promise that he who perse- 

 veres will in time be provided with adequate 

 foundation for the faith which is accepted 

 without question at the outset. In deducing 

 and applying the elementary formulas of op- 

 tics the use of wave fronts is found to sim- 

 plify demonstrations that are equally possible 

 without them. Wave fronts and rays are quite 

 inseparable instead of being mutually exclu- 

 sive. The judicious teacher will be apt to 

 guide himself by convenience and economy in 

 reaching a decision as to a choice of methods 

 of demonstration. 



In text-books on optics there is unfortu- 

 nately no definite consensus thus far in re- 

 gard to the conventional assumptions to be 

 applied in the development of theory. From 

 the stan-dpoint of the teacher and the manu- 

 facturer certain conventions may be useful 

 which are unsatisfactory to the advanced stu- 

 dent of theory. In every case they should be 

 as simple as possible, so as to be really helpful. 

 For the elementary student, and even the ad- 

 vanced student, probably the most trouble- 

 some snare is the minus sign. Mr. Percival 

 says (p. 22) : " We have adopted the usual con- 



ventions that directions from left to right are 

 considered positive, and those from right to 

 left negative." Similarly, upward is positive; 

 downward, negative; counter-clockwise angu- 

 lar rotation is positive, clockwise, negative. 

 This seems like simplicity itself; but in its 

 application the elementary student of optics 

 finds himself soon confused. In many cases 

 mere magnitude is all that needs considera- 

 tion, and to introduce additionally the ele- 

 ment of direction, especially rotational di- 

 rection, merely increases the chances of mis- 

 interpretation. For example, the deviation, 

 D, which a prism of refracting angle A im- 

 poses on a beam of homogeneous light sent 

 through it is commonly expressed in terms of 

 A and the angles of incidence, <^, and emerg- 

 ence i/', by the formula, 



D=z<p-\-^ — A. 



Mr. Percival expresses this in words by say- 

 ing (p. 43) : " The total deviation is equal to 

 the difference between the angles of emerg- 

 ence and incidence less the apical angle of the 

 prism." A glance at the diagram is enough 

 to satisfy any student of geometry that the 

 former expression is correct. The author re- 

 quests the reader to note that <^ is measured 

 clockwise and i/' counter-clockwise; but the in- 

 troduction of this convention is here wholly 

 unnecessary and misleading. 



The formula for a thin lens in air is one of 

 the most important in optics. Let us assume, 

 as standard form, a bi-convex lens, with re- 

 fractive index, n, radius of curvature r^ on 

 the side of incidence, and r„ on that of emerg- 

 ence. Let this lens receive light from a 

 radiant at distance u, and converge it to a 

 conjugate focus at distance v. The relation 

 existing is expressed by the equation, 



u V \n n) 



(1) 



The conventional assumptions involved are: 



1. Irrespective of direction, the radius of 

 curvature is positive for a convex lens sur- 

 face, and negative for a concave lens surface. 



2. Irrespective of direction, the curvature 



