156 



MEMORANDA. 



The same result may be obtained from the following pro- 

 portion, both sine and chord being supposed drawn : — 



Proportion. 

 Rad. : -01 Millim. : : secant 4° : chord required. 



Calculation. 



Log. secant 4° = 10 •0010592 



Log. -01 Millim. = 2-0000000 



Subtract Log. Radius = 10 '0000000 



Chord 8° = Num. • 0100244 Millim, 



2-0010592 



The equivalent number '0100244 is the required value of 

 the chord of 8° in fractional parts of a millimetre. This or 

 some other chord having been carefully determined by the 

 instrument-maker, or observer, it should be noted down, as 

 essential for the exactitude of all measurements to be after- 

 wards made. It will save trouble if its logarithm be also 

 recorded. 



Mode of using the Instrument. — Suppose we wish to measure 

 the long axis of an object, such as M N in Fig. III., we so 

 arrange it on the stage that the cross in the field will, when 

 the eyepiece is rotated, touch first the extremity M, and then 

 the other extremity N. The arc A a, traversed by the 



Fig. III. 



pointer, is read off from the brass scale. The chord of the 

 corresponding arc of the imaginary dotted circle is the measure 



