4.32 Introduction to the Sixth Section 



, . (F+» (/-«*'/' + «*//' 

 ~ (F+d)(f+f'-d) + (d-f')f 

 _ Off_ 

 (F+J)C/H 



(F+s)(/+/'-d)+(<'-./')/' 



Tlience the magnifying power for parallel rays,, or 

 m= F </4-/ ; -«0 OI . ( Wlt h sufficient accuracy) = — 4- — — • 



I have supposed - = 6, and found the magnifying powers 

 = 66-03; 106-75; 128-61; 181-93. By this method any de- 

 cree of accuracy may be obtained by taking into the account 

 the thickness and curvature of the glasses ; which, however, 

 in this case, would be entirely unnecessary. Up to the 21st 

 of April 1820, I have alternately used the middle powers; 

 but from the 22d of April I have exclusively employed the 

 highest power of 182. 



2. The Level of the Horizontal Axis. 

 This level is so constructed that it can be placed exactly in 

 a plane with the axis, which renders the small cross level 

 which is commonly used, superfluous, and greatly contributes 

 to the accuracy in levelling, as the air -bubble does not sensi- 

 bly change its place, if the plane passing through the axis and 

 the level sensibly deviate from vertically. The value of the 

 parts of the scale was determined by fixing the level to Gary's 

 circle, and observing its changes by the microscopes. By 

 three sets of such observations a change of the bubble of 

 one line (Paris) was found 



= 2 // -196 therm. + 5°-0 Bessel. 



2"-120 ... -|- 13°-6 Argelander. 



2"-175 ... + U°'G — — 

 Mean = 2"-164. Although the air-bubble in each of these 

 sets was gradually moved four inches, there never appeared a 

 trace of irregularity of curvature, as there never appeared an 

 error of one second which might be ascribed to this cause. 



3. Figure of the Pivots. 

 The examination of the horizontally of the axis instituted 

 at each reversion of the instrument, has proved that the pivots 

 somewhat deviate from the figure which they ought to have. 

 This examination was repeated each time in the two opposite 

 horizontal positions of the instrument, from which it followed, 

 that being directed to the north, the level was 0-194 line 

 more to the westward than when turned to the southward : 

 this quantity is the mean of the following 62 observations 

 from the 17th March 1820 to 1st July 1821. 



Position 



