>r.\ONETIC SFR VF.Y or JAPAN. 101 



wns tnken, tho n/.iiniitli \vns nd justed every tliird observation. Tliis 

 is certainly sufficient ; since, as is well known, a small error in the 

 azimuth causes an error in the dip of a higher order of small 

 quantity. * 



To make the observations that :ire necessary for findinsf the 

 astronomical meridian, all the magnetometric ])ieces of ajiparatus must 

 be (listuMiitled and the theodolite telescope mounted in po.siti(jn. (See 

 I'late A^T, Fi«? 4.) The observations were made as much as possible 

 on stars, since it is idways objectionable to expose such an instrument 

 to direct solnr light ;ind bent. Then, again, there is more chance of 

 instrument'd error when the theodolite is turned into the prime ver- 

 tical, inasmuch as all the declination observations in this country 

 liapjien to be made near the meridian. 



In general, the perfection of observati<in nimed at was to obtain 

 transits of eight conveniently destributed stars across an ap[)roximate 

 meridian, and, by combining these observations, deduce the values of 

 the four unknown quantities, — the clock error, the, two nzirnuth 

 errors, and the collimation error. 



The approximate meridian was found by taking two transits of 

 Polaris, the telescope being reversed by turning the Y's through IcSO^ 

 between the two transits. The mean of the two aziuuiths read was 

 taken as correspond irjg to the instnnt midwny between the noted 



* The following proof, from its simplicity, may be of interest. Let V be the vertical, H the 

 horizontal component, and the dip ; then tan 6 = V H. Ti the plane of the needle makes 

 a small angle a with the magnetic moriilian, the apparent dip ö' is given by the equation 



V V , a» ^ a"- 



tan 9 -Heosa== H" ^^^ ~i + ) - tan 9 + tan», -j 



a - 

 or, (/ (tau'e) ^ - tiin it. ., 



which gives i\ o — — sin 2 9. -p 



If WO put a - 10', which is ro.ighly tho range of the diurnal variation, wo find for the 

 greatest possible value of d^, the utterly insignificant quantity 0"-4. 



