672 
8UMMARY OF CURRENT RESEARCHES RELATING TO 
in the centre of this cylinder is a micrometric screw of 50 threads to the 
inch, haying its lower end fixed to the drum-head. The edge of the 
drum-head is divided in the usual way, each division representing 
1/10, 000th inch. The upper row of figures are for measuring convex 
lenses, while the lower are for concaves. 
The upper end of the screw which touches the lens terminates in a 
small polished hemisphere of steel, contact being indicated by the 
formation of Newton’s rings which can be seen through the lens which 
is being measured. 
Only the lower edge of the ring is in contact with the inside of the 
drum-head, and contact at this point steadies the screw. 
The figure shows the instrument in use with a full-sized ring ; hut 
when a small lens is to be measured the full-sized ring is replaced by a 
smaller one, the same screw and drum-head being used in all cases. 
This instrument has three rings, and is practically three sphoro- 
meters. 
Before using the instrument a glass disc 1/2 in. thick, worked on its 
under side to a true plane surface, and having a plano-convex lens 
cemented to its upper side, is placed on the ring ; the drum-head is then 
turned until the hemispherical end of the screw comes in contact with 
the lower side of the glass disc ; the Newton’s rings formed by this 
contact will be plainly seen through the lens on the upper side of the 
glass disc. When this contact is made the index on the drum-head 
should be at zero ; if it is not it can be placed there by means of the 
adjusting screws below the drum-head. 
With regard to the diameters of the rings, if a chord of suitable 
dimensions is chosen the arithmetical computation of the radius can be 
much shortened. Thus — 
Let R be the radius, C the chord, and V the versed sine which is 
measured, then 
If, therefore, we make C = V 8 = 2 • 82843 inch, 
Or C = V 2 = 1 * 41421 inch, 
And if C = 'J ' 2 = *447214 inch, 
e -b( 20T +^> 
As i can be taken out of a table of reciprocals, the computation 
becomes one of mere inspection. 
The above are the diameters of the three rings of this instrument. 
