182 . THE AMEEICAN MONTHLY [August, 



In my use of tliis instrument I found the diBbrence lietwcen 

 water and liomogeneous fluid to be some six divisions of the rack- 

 har, and between the homogeneous fluid first referred to and an 

 other it was one division. It was extremely difficult to observe 

 such a small difference in the dim light about the tube. But a 

 more serious objection was in the fact that when the adapter 

 screwed " home" the slit was " fore-and-aft," and and as I used 

 a ^ objective (not having a i-inch) in racking up to get the right 

 focus when the fluid was in the field, the glass slips projected 

 backward, caught under the body of the microscope, and with a 

 little more upward motion would have been broken. Professor 

 Smith's illustration, as given in the report referred to, provides, 

 however, for this, as the " concave" is there made near one end 

 of its slip and not in the middle. I have another microscope with 

 a rifle-screw for the coarse adjustment and with a ^ or i^ inch 

 ol)jective the refractometer could not he used on it. It seemed to 

 me that the principle involved in Prof. Smith's device could be 

 applied in a readier manner. A little consideration by any one 

 acquainted with the simpler optical principles of the action of 

 lenses will show him that the concave acts by itself as a plano- 

 concave lens, and that when the concavity is exactly filled to the 

 plane surface with a substance having the same refractive index 

 as the glass, it is virtually restoring the material that made the 

 slip at first before the concave was ground out, a plane glass slip 

 with parallel faces. Now the simple method adopted by oculists 

 in determining whether a spectacle glass is concave or convex is 

 to hold it 1 8 inches or two feet from the face and view through it 

 any rectangular object lo or I3 feet distant. If when thus view- 

 ing such an object the glass be moved from side to side or up and 

 down, it will be found that in the case of a concave lens the ob- 

 ject (part of a window sash) will be seen to move with the lens, 

 while with a convex glass it will appear to move in a direction 

 opposite to that given to the lens. A glass with plane parallel 

 surfaces gives no apparent motion to the object when moved itself. 



Experiment in this way with the first homogeneous immersion 

 fluid did not restore the refractive property to the concavity filled 

 with it, but in order to neutralize the concave action still left, a 

 convex lens of 40 inches focus had to be placed in flat contact 

 with the slip. Measurement of the focal length of a convex lens 

 is done by projecting the image of a distant object upon any suit- 

 able surface, the distance between the; lens and the image thus 

 formed being the focal length. But it is impossible to measure in 

 any such way the strength of a concave lens, as it has only a so- 

 called negative focus and causes only a virtual image. The ocu- 

 list in order to determine the strength of a concave lens places in 

 apposition with it, successively, convex lenses of different focal 

 lengths until he finds one that exactly neutralizes the refractive 

 power of the concave lens, and when two lenses, one negative or 

 concave, the other positive or convex, are placed together and 



