402 KRETZ. 



will give the position of the star with respect to the scale, since 

 the micrometer is so arranged, that the head will show increas- 

 ing numbers, when the threads are made to move in a direction 

 opposite to increasing numbers on the scale. , To measure the 

 plate, then, the following operations were always performed : 



Set the plate correctly in the holder, /. e., so, that the meas- 

 ured coordinates will coincide approximately with right ascen- 

 sion and with declination. This is done by first making the line 

 joining the central star with its trail (or third image) parallel to the 

 cylinder, and then turning the plate through 90°, in such a way 

 that the trail shall be to the idgJit} Then will the hour angle in- 

 crease toward the left on the plate, and the direction of a circle of 

 declination will be perpendicular to the scale. Read the gradu- 

 ated circle on both microscopes, observe for runs,^ and take the 

 temperature. Now measifre the position of each star as fol- 

 lows : Point the microscope on the East Image of the star and 

 read the micrometer ; point at the scale and read twice on the 

 next lower line ; point again on the star and read. Move the 

 microscope so that, the micrometer standing approximately at 

 the same point as before, the wires bisect the West Image. Re- 



J Note. — It will be seen that this method of oi-ientation involves an error due to 

 the curvature of the path of the central star on the plate, which, for high declina- 

 tions, becomes large. For a star which describes a small circle in the sky will trace 

 an arc on the photograph, and if the plate is oriented by the method described above, 

 the cylinder will be made parallel to a tangent to this curve at the middle point be- 

 tween the central star and its trail, and not, as should be the case, at the star itself. 

 It is easily seen that the value of this error in seconds of arc, x/' is 



x" = \d" tan (5 



where d" is the distance in seconds between the central star and its trail (obtained 

 by multiplying the disiance in mm. by an approximate scale value ) and cJ is the 

 declination of that star. If then we move the holder through an angle x'\ the plate 

 will be much more accurately oriented and the least square solution for the con- 

 stants of reduction will be greatly simplified. The sign of this correction will depend 

 on the position of the plate ( whether in the northern or in the southern hemis- 

 phere), and also on the graduation of the plate-holder. In general it can be de- 

 termined from the consideration that the true East and West line passes through a 

 pomt which has an arithmeUcally smaller declination than the trail. In orienting 

 my plates, 1 always applied the above correction. The method is due to Dr. Schle- 

 singer. 



2 See Sect. II, " Runs and Screw Errors." 



(62) 



