Royal Astronomical Society, 309 



Mr. Henderson has here detailed the experiments and investi- 

 gations which he made for the purpose of ascertaining the cause of 

 the anomalies which had been observed in the Cape mural circle, 

 and of detecting the laws by which they are regulated. A similar 

 inquiry by Mr. Sheepshanks and Professor Airy has been already 

 published in Vol. V. of the Society's Memoirs. 



The experiments on which Mr. Henderson grounds his investi- 

 gations are a series of readings at each fifth degree of the limb of 

 the instrument made with each of the six microscopes. The dis- 

 crepancies among the readings indicate that the figure of the limb 

 is that of an oval of small excentricity, and that the centre of 

 motion frequently changes its position. 



A change in the position of the centre of motion occasions va- 

 riations in the readings of the single microscopes, which, however, 

 disappear in taking the means of two or any other number of equi- 

 distant microscopes. 



The oval figure of the instrument requires that corrections should 

 be applied to the readings of the microscopes, in order to obtain 

 the true values of angles which the instrument describes. Angles 

 of 60°, however, as given by six equidistant microscopes, require no 

 correction, they being independent of the effect of errors of division, 

 and of the non-circularity of the instrument. The same holds true 

 with regard to angles of 120° measured with three microscopes, and 

 angles of 180° measured with two. 



Assuming that the necessary corrections may be expressed by a 

 series of the form 



a sin (U + &)-Vb sin (2 U + B) ■*■ c sin (3 U -f C) + &c. 



a, b, c, &c, denoting constant coefficients, A, B, C, &c, constant 

 angles, and U any division of the limb, the observed differences 

 betwixt angles of 60° given by six microscopes, and by three and 

 two, afford data for the determination of «, b, c, &c, and A, B, C, 

 &c. Employing the method of minimum squares, Mr. Henderson 

 finds the correction of the mean reading of two equidistant micro- 

 scopes to be 



5"-523 sin (2 U + 83° 4') + 0"«569 sin (4U-f 16° 46'). 



The correction of the mean reading of three equidistant micro- 

 scopes is 



= l'H71 sin (3 U + 321° 8'). 

 To determine the correction of the mean of six microscopes, an 

 additional pair was required ; but these not being at the Cape Ob- 

 servatory, Mr. Henderson has, from a consideration of the errors 

 of angles measured with two and three microscopes, and corrected 

 by the above formulas, inferred that the probable error of the un- 

 corrected mean of six microscopes is 0"*22. He also found reason 

 to suppose, that of the 720 different sets of divisions to which 

 observations read by the six microscopes are referred, there are, 

 according to the laws of probability, 328 whose errors are under 

 two tenths of a second, and one only whose error exceeds one 

 second. This degree of accuracy, Mr. Henderson remarks, ap- 



