ME.MOIUS OF THK NATIONAL A<A1H:MV OK S( 'I KNCHS. 43 



Tho U>rin iiiiifriiiruratinn has two distinct mwiuiiiffs, namely, tiie ratio of the dimension of tiic 

 imuKPs to that of tin- ohji'ct nieasiuod at n;jiit an^'hfs to thh axis, and a concspoiidiii},' ratio in th«' 

 dinrtiouof tilt' axis. The liist \vc may call tlu^ transverse ina;,'iiifi''ation and dcsi|,'nat.- .1/; tho 

 other may bo called the loii-jitndinal matrnitication and desi};nated /..- 



From the tilth e(|iiatioii on ]ia},'e H' we may write at e the value for the. lirst species of 



magnilieation. It is e(iual to 



•V = "o*-J/ (c) 



The lonjiitudiual magnification is obviously eiiiial to the ratio of the displacement of the imaj^e 

 alon-,' the axis to the corresimndintr displacement of the i»bie<t. From this definition and equa 

 tion {d) we find 



''- . 1 -de cv - '^o'' c',' 

 (I i„ 



From those two oiiuations we find 



This law explains why the depth of fieldin microscopic vision seems so small, and also why an 

 object under the microscope appears so much flatter when mounted in a medium of hifjh refractive 

 jtower, tor in this case /;„ is {greater than unity. 



A consideration which is of niueh iini)ortance is the relation of the directions of the wave 

 surfaces. This relation is readily determined for the points a and x,. In Fij;. 3 let j) and 

 p' be the points x„ and .ri, respectively, then, since by definition p' corresponds to p we need 

 make no restiictions as to the value of the anjjles of inclination of the oblique wave surfaces. 

 Call these angles (po and <p, respectively, then, it' pq is small, we have, as before, 



Po q>h = q'q', 



and 



an<l tinally, since p'q' is the image ofpq 



From these eiiuations we read at once 



qq' = pq sin ipo 

 q'q', = p'q' sin cp, 



pq 

 P'q' 



sin (7j, , • , , 



. -^ = A'A) (g) 



sm <po 



IV — TO FIND THE VALUES OF THE CONSTANTS IN EQlATION (d). 



There are two cases presented in practice: First, when all the constants of the optical system 

 are given, and, second, when we can only depend upon measurements as applied to the system 

 as a whole. We shall consider these two cases in turn. 



Case 1. — All the constants of the system being known compute c"a+i by making c' equal to zero 

 in etiuations (a) ; the value of m is one divided by /u in this computation. 



To find A' we either assume the value of Jo and thence compute Ji and A, or, assuming the 

 value of A-, compute .Iq and xi . 



For the first method make c'= -— in (a); the resulting value of Ca+1 equals , and, substi- 

 tuting these values of c' and 6-*+, in (b), remembering that (n+(ic') is one divided by //* we find 

 the reciprocal of A- at once. The .-solution is therefore comi)lete. 



If A- is assumed, we compute c"»+, and u as before, then 



whence we lind .;„ from (<() by making c^, , = when x„ = \ 



