J. M. Schaeberle—Fleaure of a Telescope Tube. — 375 
the mirror from touching the object-glass of the telescope to 
which it is cemented with a solution of gum arabic. The cen- 
tering is quickly done by shifting the mirror upon the spheri 
cal surface of the lens until the reflected image of the horizontal 
wire is nearly in coincidence with the wire itself. 
n experimenting I have used a piece of plate glass; to test 
the surface of the same before silvering, the image of a distant 
brick wall, reflected obliquely from. the glass surface, was 
examined with the aid of an excellent 23 inch achromatic ; fro 
a number of pieces one was selected which gave a sharp 1 ‘hae 
of both the vertical and horizontal joints for the same focus. 
A beautifully sharp and fine image of the wires will be given 
y such a mirror (silvered on the side toward the object-glass) 
crite less than two inches in diameter.* 
, be the reading when the micrometer wire is in coinci- 
doles with the reflected image of the fixed horizontal wire, the 
telescope being pointed to the vith and let m be the reading 
or any other pointing. Let x be respectively the defle 
tions of the object- and pate es of the tube from the seaterdiie 
these ends would have if ate were no flexur 
L= focal length of objecti 
‘= distance of the object- ola from the line about nach the 
flexure causes it to revolve. acing the sines and tangents of 
very small angles equal to their ares, the linear distance of he 
fixed wire from its reflected image, can be expressed by a very 
simple equation. For we have, 
2 x a m—m 
arq— 7 Y ‘Sa pus therefore 
Letting (j-1)=< ad 
‘=F, we can write 
a =F 
car’ +y' =F’ 
ce” +y"= “ 
etc., etc. 
If f, represents the maximum astronomical meosta determined 
by means of two horizontal collimators, we ha 
* The focal length of the seg used is eet feet, and the wires made 
visible in pei Ae the same way as observations. 
+ The flexure really gives the ine a carved outline: Tn assuming that the 
change in the inclination of the mirror (due to flexure) is equal tos +. (where 
7 can usually be taken equal e distance of the objective from ie 
of the eube, to which the acts : ‘oted) - very small terms are omitted which 
n generally be neglected as inapprecia 
