12 Mr. John W. Gordon [Feb. 17, 



the march of a company of soldiers across a field, part of which — the 

 darkened portion — is covered with grass and affords good foothold, 

 while the light part represents ice across which it is possible to march 

 only with a shortened step. Now assume that the men receive direc- 

 tions to march shoulder to shoulder and straight ahead. The first 

 step will carry the line forward in unbroken formation parallel with 

 itself into the position shown by the second line of men in the 

 diagram, but upon the second step the man of the first file on the 

 left will step short since he steps upon ice. In order to observe the 

 shoulder to shoulder rule he must advance his right shoulder, and for 

 the same reason his right hand man must retire his left shoulder. 

 Upon the third step both the first and the second file men will step 

 short, keeping step with one another, and the second man will have 

 to advance his right shoulder to keep touch with his right hand man, 

 thus completing the half -turn which he commenced by retiring his 

 left shoulder when his left hand man fell behind. At the next step 

 the third man will execute the same evolution, and so, gradually, a new 

 line will form itself upon the ice, breaking off at a definite angle from 

 the hue of the original formation. When the farther edge of the ice 

 is reached all these evolutions will be repeated in inverse order, with 

 the result, shown in the diagram, that the column which has passed 

 over the ice marches thereafter, when the farther grass is gained, in a 

 new direction branching away from the unchanged direction of the 

 column which has never left the grass. It is obvious, without detailed 

 discussion, that the extent of the deviation — the angle of refraction — 

 depends upon the change of step at the two boundaries where grass 

 and ice meet, and if the matter were investigated it would be found 

 that the mathematical rule which determines this angle is the rule 

 commonly known as the law of sines, by which the refraction of light 

 is calculated. 



To pass from this imaginary march to the analogous case of the 

 progress of a beam of light is quite easy. The successive ranks in 

 the formation, which represent equal distances measured in steps from 

 an original position, or zero line, correspond to wave fronts in a beam 

 of light. The step, which lengthens or shortens according to the 

 nature of the medium traversed, corresponds to the wave length of 

 light ; and the grass and ice, which offer more or less impediment to 

 the column, correspond to transparent media of varying optical 

 density. If we assume that the step of the marching man is shortened 

 when he passes from grass to ice in the proportion of Ij : 1 we shall 

 have a precise equivalent, so far as the mathematical theory is con- 

 cerned, of a wedge of glass in an atmosphere of air. The diagram 

 then illustrates what would happen to a beam of light transmitted 

 through the field of an optical instrument if that field Avere occupied 

 by a fragment of glass having the sectional formation shown by the 

 diagram. 



Herein lies the principle of which the microscopist takes advan- 



