66 



THE AMERICAN MONTHLY 



[April, 



Now, replacing the diaphragm, and 

 looking through the tube, the entire 

 field was visible through the hole, of 

 the exact diameter it had when mea- 

 sured in the ordinary way upon the 

 stage. The distance from the top of 

 the diaphragm to the front of the ob- 

 jective was measured, and subtracted 

 from the working-distance, giving the 

 distance of the object at o from the 

 principal focus o" , and this with the 

 diameter of the field enabled me to 

 construct and measure the angle ao" b 

 and its equivalent / o" l' (fig. 24). 



The draw-tube was then closed, 

 making a tube of about 5}^ inches, 

 and the same series of measurements 

 was made as before. Afer a number 

 of experiments, it became apparent 

 that the uniformity of the size of the 

 field when seen through the dia- 

 phragm and without it, was such that 

 this test need not be repeated, the full 

 illumination of the field-glass of the 

 ocular being entirely reliable evidence 

 that the pin-hole coincides with 0" . 

 The substage and the card-board, or 

 a white disc over the plane mirror, be- 

 ing still useful as giving the white- 

 cloud illumination. 



The following table gives the mea- 

 surements which were made:* 



Objectives. Long tube. Short tube. 



Field. Work. dist. 0" Field. Work. dist. oo<> 



3-inch.. 0.39 1.55 .90 .52 1.95 1.53 



1>^ ".. 0.16 .87 .28 .29 .98 .515 



^ ".. 0.108 .26 .15 .172 .32 .245 



1 " .. 0.13 .97 .33 .195 1.05 .50 



Upon constructing the figures indi- 

 cated by these measurements, one of 

 the first things that will be noticed, 

 is the fact that the principal focus 

 approaches the front of the objective 

 when the tube is shortened, but with- 

 out changing the angle appreciably 

 (see fig. 25). It is as if the angle were 

 . moved toward the objective, its sides 

 including a smaller circle on the front 



* In transferring the measurements from the 

 dividers. I found a loose vernier very useful. 

 It consists of a bit of ivory on which .g-inch 

 being subdivided into ten parts, this scale 

 may be applied to the ordinary scale divided 

 to tenths, so that hundredths are read ofl at 

 once. It can often be used when a diagonal 

 scale could not. 



of the lens. That this is in no pro- 

 per sense a reduction of "available 

 front " will be seen hereafter. 



It might, at first sight, appear that 

 this retraction of the principal focus 

 was due to the combination of two 

 systems in the objective; but it will be 

 seen that it occurs in the single lens 

 of the one-inch objective as well as 

 in the two-system glasses, though not 



Fig. 25 



to the same extent. It is probably 

 the effect, in the main, of the dia- 

 phragm behind the objective, or of the 

 brass mounting of the lens which acts 

 as a diaphragm by interposing be- 

 tween the margin of the back lens of 

 the objective and the edge of the field- 

 glass of the ocular. This, however, 

 deserves a separate investigation, and 

 it is enough to say that the practical 

 result in the lenses measured, was a 

 noteworthy constancy of angle at the 

 principal focus, so that it could be 

 treated as unchanging. Fig. 3 is a 

 protraction of the angles and their 

 relative position in the case of the 

 inch-and-a-half, and it is a fair sam- 

 ple of the result of the other cases. 



The following table gives the com- 

 parison of the angles at the telescopic 

 principal focus, and the microscopic, 

 for both long and short tubes : — 



Objectives. Telescopic P. F. Microscopic. 



Long tube. Short tube. Long tube. Short tube. 



3-inch.. 15° 13>^° 18° 19° 



1>^".. 26° 23 •^° 30° 30° 



^".. 38° 36° 391^° 39>^° 



1 ".. 13° 12K° 21° 21>^° 



In the case of the three-inch ob- 

 jective four separate measurements 

 of field, working-distance, etc., were 

 made with four different lengths of 

 tube, and the results confirmed in the 

 most striking manner the general con- 



