Septembek 26; 1913] 



SCIENCE 



445 



is considered positive for a wave front propa- 

 gated toward or from a real focus; and nega- 

 tive if from a virtual focus. 



Another form commonly seen is, 



in -I) 



(---)■ 



(2) 



The assumptions now involved are: 



1. The direction from lens toward radiant 

 is positive; its opposite is negative. 



2. Curvature concave toward the radiant is 

 positive; its opposite is negative. 



If it is assumed additionally that the radi- 

 ant is at the right of the lens, Mr. Percival's 

 convention is expressed in Eq. (2). 



The conventions connected with Eq. (1) 

 have long been in common use. A converging 

 lens is commonly called positive; a diverging 

 lens, negative. Of late years Eq. (2) has been 

 increasingly coming into use, for analytical 

 reasons. The teacher of optics is free to take 

 his choice; and this is apt to be influenced, in 

 part at least, by ease of application. In a 

 text-book published about twenty-five years 

 ago by a pair of highly respected American 

 college teachers of physics the deduction and 

 discussion of Eq. (2) is given; but at its close 

 they add the remark : " The equation is more 

 simple in application if, instead of making the 

 algebraic signs of the quantities depend on 

 the direction of measurement they are made 

 to depend on the form of the surfaces and the 

 character of the foci." The conventions given 

 in connection with Eq. (1) are then expressed. 

 The present writer has tried both sets of con- 

 ventions with his students; and with the re- 

 sult that pedagogically Eq. (1) is found much 

 preferable. On examining thirty text-books 

 in his library he finds Eq. (1) used in sixteen 

 of them; Eq. (2) in thirteen; and both in one 

 of them. 



Mr. Percival seems to select the position of 

 the radiant as origin, for in his diagrams he 

 places this at the left, or negative, side of the 

 lens or mirror; but this is not always done by 

 him. He makes a distinction (p. 49) between 

 the convention applied in finding a general 

 formula and that applied in using a formula, 

 saying, " when using the formulae it will gen- 



erally be found convenient to regard the direc- 

 tion of the incident light as the positive di- 

 rection." The ordinary student, expecting 

 uniformity and consistency, will be apt to 

 stumble here, especially if he consults Edser's 

 excellent book " Light for Students," and 

 finds (p. 28), that "when the direction of 

 measurement is opposite to that in which the 

 incident light travels, the distance is positive." 

 In this connection it should be noted that both 

 Edser and Percival use the same form, ex- 

 pressed in Eq. (2). The positive direction for 

 this equation may thus be either rightward, 

 or leftward, or in the direction of propagation, 

 or opposite to this direction, according to pref- 

 erence. The student probably has no prefer- 

 ence, but wants definite information. After 

 reversing his minus sign, and then re-reversing 

 it a sufficient number of times, his mental con- 

 dition becomes undesirable, to say the least. 



Taking the equations as they are found in 

 Mr. Percival's volume, he illustrates them by 

 the solution of numerical problems, and in a 

 number of cases additionally by graphic 

 methods. The discussion of Gauss's cardinal 

 points for a thick lens, or system of lenses, is 

 perhaps scarcely full enough to enable the stu- 

 dent to acquire very satisfactory working 

 knowledge of the subject. Its application to 

 the optics of the human eye is well illus- 

 trated both numerically and graphically. 



An appendix is added in which a number of 

 topics of practical importance are treated 

 mathematically, without any attempt to avoid 

 or disguise the notation of calculus. Medical 

 students, for the most part, may naturally be 

 disposed to accept the results without master- 

 ing the details of demonstration. 



There are a few obvious typographical errors 

 that will probably be corrected in a future 

 edition. Despite the uncertainties about 

 linear and angular direction, the book is 

 clearly written, and by one who has evidently 

 had good experience in dealing with students. 

 It is worthy of commendation to those for 

 whom it was intended. 



W. LeConte Stevens 



Lexington, Va., 

 September 2, 1913 



