210 MR. POND ON THE NEW ZENITH TELESCOPE 



It SO happens, that a small star of about the fifth magnitude, having nearly the 

 same zenith distance towards the south that y Draconis has towards the north, passes 

 the meridian between 20 and 30 minutes in time after it. It is the different modes 

 of employing this star in combination with y Draconis, as a means of determining the 

 various smaller equations, which I now wish to explain. 



The angular distance between the two stars will be determined with this instru- 

 ment in the usual manner, by observing them on the same night, and in the same 

 position of the instrument ; which distance in this case is the sum of the zenith 

 distances of the two stars : but if, on the next or some following night, y Draconis be 

 observed, and after its passage the instrument be turned half round, and the other 

 star observed, then the difference of the measure, as read on the micrometer, will be 

 the difference of the zenith distances of the two stars. Thus, the sum being ascer- 

 tained on one night, and the difference on another, these sums and differences will be 

 independent of any change that may happen to the instrument from one night's ob- 

 servation to another ; and the zenith distance of each star respectively may be de- 

 duced from these data. Whatever may be the superiority of this method of observation 

 in ascertaining the zenith distance of the principal star, it is inconsiderable compared 

 with the powerful assistance it affords in determining, with almost unlimited pre- 

 cision, the value of the small equations which necessarily become the subject of in- 

 vestigation. 



Let it be supposed that the two stars have precisely the same zenith distance, the 

 one to the north and the other to the south, then it is evident that if after the obser- 

 vation of one the instrument be turned half round, the micrometer wire will be placed 

 in the exact position for bisecting the second star in its passage ; but if the two stars 

 have not exactly the same zenith distance, the micrometer wire will require a corre- 

 sponding alteration. The distance between the two positions of the wire I call the 

 subsidiary angle. It is to the properties of this angle that I wish to direct attention. 



Whoever considers the nature of this angle, will perceive that it is measured by a 

 very small motion of a micrometer screw, and therefore may be obtained with great 

 precision : moreover, that any equation which may become the subject of considera- 

 tion will be doubled in its effect on this subsidiary angle, and quadrupled when 

 each star is affected equally by the same equation*. 



This property of the subsidiary angle may be illustrated by observing, that the 

 new instrument stands about seventy feet north of the principal meridian instru- 

 ments of the Observatory. This produces in the zenith distance of each star a corre- 

 sponding variation of about three quarters of a second ; but the subsidiary angle will 

 be altered by double that quantity, or a second and a half. It is probable that this 



* Suppose the subsidiary angle equal 1' 00" when the aberration is nothing, and that the maximum of this 

 equation is equal to 20"'5, then the extremes of the subsidiary angle will be 0' 19" and 1' 41", the difference 

 of which is l' 22", or quadruple of 20"'5, the equation to be investigated. 



