Method of determining Curvature of Spherical Surfaces. 219 



straight uniformly divided scale, without corrections or 

 calculations of any sort. We shall not attempt to give 

 an account of all the mechanical devices which might 

 be profitably employed in attaining the highest possible 

 accuracy, but shall content ourselves with describing the 

 plan of the method and the elementary geometrical prin- 

 ciples involved in the application of the method to practical 

 measurements. The simple apparatus which we describe 

 has been in use for some months in one of the classes at the 

 Cavendish Laboratory, Cambridge ; the method has been 

 found to interest the students. 



§ 2. The principle of the method may be described as 

 follows : — 



A table turning truly and without shake about a vertical 

 axis is required. For the most accurate work the fit of 

 the vertical spindle in its bearings must be as perfect as 

 in a good lathe-head. The plane of the top of the table 

 is normal to the axis of revolution, and the top carries 

 a straight scale against which slides a carriage bearing 

 the spherical surface (see fig. 1). We shall assume that 

 the scale is so adjusted on the table that the straight line 

 described by the centre of curvature of the spherical surface 

 when the carriage slides along the scale intersects the axis of 

 revolution of the table. The position of the carriage relative 

 to the table-top when the centre lies on the axis of revo- 

 lution will be called the first position. If the table be 

 turned through any angle about the vertical axis when the 

 carriage is in the first position, the only effect of the angular 

 motion is to substitute one part of the surface for another. 

 Hence, if rays from a luminous point fall upon the surface, 

 the reflected rays will be unaffected by the motion. It 

 is not necessary that the rays which enter the eye from 

 the luminous point should have met the surface very nearly 

 normally, or, in other words, that the geometrical image 

 of the point should be observed. It is sufficient to use 

 a pencil of rays whose axis is nearly horizontal and strikes 

 the surface not very obliquely, and to observe the vertical 

 focal line of the reflected pencil. If a vertical line be used 

 as an object, the "image" by reflexion will be a vertical 

 line formed by the vertical focal lines corresponding to 

 individual points of the object. If a microscope be used 

 for observing the image of the vertical line, the proper 

 adjustment of the carriage along the scale can be made 

 with great accuracy. The microscope must, of course, be 

 firmly supported and must be furnished with cross-wires or 

 with a micrometer-scale. In the absence of a microscope, 



