DETERMINATION OF THE OPTICAL POWER OF A TELESCOPE. 5 



660. In most cases, however, the approximation indicated by the 

 optical power is not exceeded, or even attained, especially in the case 

 of moving images, or of observations which cannot be repeated at 

 will ; any practical miscalculation will be avoided if we assume that 

 an object-glass of 16 centimetres diameter can measure at least i". 



On the other hand, a divided circle 80 cm. in diameter, of good 

 construction, gives 2" directly, when read by a vernier, and the com- 

 plementary part with a less error than i"; a circle of this diameter is 

 therefore comparable with a telescope of 16 cm. aperture. 



In these conditions the ratio of the diameter of the circle to that 

 of the object-glass is equal to 5. This ratio ought not to change it 

 we desire to maintain the same concordance between the two organs 

 for any given limit of accuracy. 



This rule being admitted, it is interesting to examine what is the 

 absolute degree of approximation obtainable in reading verniers. 

 The value of an angle of i" is 0*0000048 ; on a circumference of 

 80 cm. in diameter it corresponds to a length of 0*002 mm. This 

 is the limit which the errors of the graduation must not exceed, 

 unless we make a special examination of the divisions of the circle. 



661. It frequently happens that we have to determine the 

 rotation which a movable system spontaneously undergoes about its 

 axis in the course of an experiment. 



Such, for instance, is the case of a magnetised needle suspended 

 in a cup about a vertical pivot, or of a dip needle movable about a 

 cylindrical axis which turns in a plane, or of the beam of a balance 

 oscillating about a knife-edge, or of any apparatus suspended by one 

 or more wires. It is not possible to provide these objects with 

 verniers, which move along a circular division, for we ought to avoid 

 all friction, and verniers are only really useful when they can be 

 placed in contact with the scales. On the other hand, a telescope 

 mounted on the movable arrangement would needlessly increase the 

 weight. 



The simplest plan is to provide the apparatus with a very 

 movable index in the shape of a long pointed needle, which moves 

 over a divided scale. The needle should then be sighted in a 

 plane perpendicular to the circle ; in any other direction it would 

 be projected on a division different to the first, and what is called 

 the parallax error would be produced. 



This latter error is sometimes avoided by dividing the circle on a 

 plate of silvered glass ; the movable index being placed above, it is 

 viewed so that its image is covered, and the corresponding division 

 is read off. 



