January. 1911. 



KNOWLEDGE. 



17 



must be done must be settled by the estimated 

 position of the star, or b\' consultini; other previous 

 measures. 



Thus far we have spoken of taking measures of 

 distance b\- adjusting the wires on the stars: and if 

 the micrometer screw-head reads zero when the wires 

 were over each other we should onl\- have to convert 

 the divisions of the reading on the stars into seconds 

 of arc, and the angular distance would be had. It is 

 not without risk of error that we can adjust the 

 screw so as to read 0° when the wires are coincident, 

 and the difference in the expansion of the steel screw 

 and the brass in which it is mounted would soon 

 cause an error in the value of the zero which might, 

 however, be allowed for when ascertained. But it is 

 better to avoid this complication of error by taking 

 measures of the star w ith the moveable wire first on 

 one side of the tixed wire and then on the other. 

 The distance through which the wire is moved will 

 then be double the interval between the stars, and 

 dividing this by two will give the actual interval : 

 which process also has the good effect of halving the 

 error of observation. Thus, it is advisable that the 

 reading of the screw-head should only be approxi- 

 mately zero when the wires coincide. If the 

 readings are taken when the\" increase with the 

 increase of the distance of the w ires thev are called 

 "direct": and when the mo\eable wire is on the 

 other side and they decrease w ith the increase of the 

 distance of the wires, thev are called '' indirect.'' 

 Since the numbers decrease from 100 (or from what- 

 ever may be the reading of the screw-head) on the 

 indirect side we have to subtract the indirect read- 

 ing from 100 and add this to the direct reading. 



To avoid risk of error and for convenience' sake, 

 it is well to adopt the fiction of calling the reading 

 1000 when the wires coincide, that being the usual 

 number of divisions for 10 revolutions of the micro- 

 meter screw. It follows, therefore, that all readings 

 within this distance of the wires a.re positive, and we 

 have only to subtract the smaller reading from the 

 larger to get the double distance of the inters-al 

 measured. 



For instance : suppose that a direct reading 

 embraces one revolution (= 100 divisions) and 15 

 more, making a total of 115 divisions. Add to this 



1000, and write down the result 



1115. The 



indirect reading of the same stars after crossing the 

 wires will also be one revolution (100 divisions) and 

 about 15 divisions over, but as we are reading back- 

 wards from 100 the reading actually is about 85, sav 

 80. (For it is not likely that the wires coincided 

 exactly at 0). On the assumption that coincidence 

 takes place at 1000, we write down 880 as the 

 indirect measure : then J-i-^y ''"— " is the distance of 

 the stars in divisions of the instrument. 



To find the value of the divisions in arc, separate 

 the wires by a known number of revolutions, and 

 note the time that a star on or near the equator takes 

 in passing transit-fashion from one wire to the other. 



Then, since 15" of arc are covered in 1* of time the 

 number of divisions (100 time: the number of 

 revolutions) divided by 15 times t>:; time of passage 

 in seconds will give the number o' divisions which 

 correspond to 1" of arc* 



Seeing that it often happens that : asures have 

 to be reduced under circumstances uni vourable to 

 accurate mathematical thought, it is well :^ resort 

 when possible to mechanical labour-saving expedients. 



One of these available for Double Star w -k is 

 a ■■ Barlow lens," the usefulness of which seims 

 now-a-days to be very little understood. It is an 

 achromatic plano-concave lens which has a powerful 

 magnifying effect, and by inserting such a lens 

 between the object-glass and the micrometer a few- 

 inches inwards from the latter an image is altered 

 in size so that the distance between the two stars 

 can be made to accommodate a certain number 

 of micrometer divisions without fractions. For 

 instance, the magnification of a pair of stars may 

 be so adjusted that 10 divisions correspond to 1" of 

 arc. After finding the value in divisions of a measure 

 we have onh- to move the decimal point, and then a 

 value recorded in seconds of arc presents itself. 

 Should this value not be absolutely correct we learn 

 at anv rate the percentage of the error and appl\- it 

 in writing down the definitive distance. 



The following forms are recommended for use. 

 No. 1 shows the method of entering observations 

 as they are taken, and No. 2 the method of recording 

 the final results for permanent reference : — 



No. 1. TEMPLE OBSE R\'AT() RV. 

 DOUBLE ST.\KS. 



Date: Sept. 6. I'JUyr,/. 

 S 22IS 

 K. A. //- J'.l. Dec. +fiJ //. 



PDsrrujx. 



Wires E. i W. 106' 2 

 90 



Mag. 



DISTANCE. 

 Direct. Indirect. 



Zero error 



Readings. 

 SS'j 

 57-0 



srn 



5S'5 



76-2 



1017 

 1018 



101 7' 3 

 981-3 



982 

 981 



981-5 



230-8 



57-7 

 76-2 



161-5 



Pos. 



Dis. 



( A.B. .}J1-5 

 I A.C. 



I A.B. 1-80 

 A.C. 



A more exact method of obtaining this result is to measure the distance of two stars whose position is \er\- e.\actK known 

 such as certain stars in Pleiades. As to this see Gledhilt's " Double Stars." 



