instrumental Error of his Horizon- Sector. 93 



the great discordance between the values by the first and se- 

 cond arcs. 



Arc 10' 29" 1° = 0"-65 Temp. 60°. 

 April 1830. Same as last, but the final arc only was 

 read off. 



Arc 9' 33"' 1° = 0"-65 Temp. 60°. 

 The experiments on levels differently mounted (given in Phil. 

 Mag. and Annals, vol. v.), led me to anticipate some of the above 

 discordances. Probably they were increased by the weight of 

 Fortin's level-tube, which might be sufficient, when resting 

 upon the index-bar (which has no apparatus to clamp it to its 

 arc), to depress it gradually. On this account it would have 

 been advisable to have made two sets of observations, one 

 with the telescope elevated, and the other with it depressed. 

 In the former case the weight of the tube would tend to give 

 an arc in excess, and in the latter case in defect. 



(In reply to my inquiries, M. Fortin informed me that he 

 had not ascertained the value of the scale with extreme exact- 

 ness, but that the divisions would be about half-a-second sex- 

 agesimal each.) 



Process of measuring the horizontal inclination of the cylinder. 



There are three methods. One is, to place the upper sur- 

 face of the (supposed) cylinder exactly parallel to the horizon 

 by means of the; proof-level, and then to take it out of its Ys 

 and replace it within them reversed in direction ; the conse- 

 <]uent deviation of the bubble of the sector-level being double 

 the horizontal inclination. Or, if we have previously deter- 

 mined the reversing point of the sector-level, the difference 

 between that point and the one at which the bubble stands 

 when the surface of the cylinder has been rendered horizontal 

 by the proof-level, gives, without reversion of the cylinder, 

 the inclination required. In this method it is not necessary 

 that the proof-level should be strictly parallel to the cylinder, 

 or its plates truly horizontal in the transverse direction ; but, 

 on the other hand, we measure the inclination by the sector- 

 levels which are inferior to that of Fortin. As it is almost 

 impossible to place the cylinder with its upper surface hori- 

 zontal to the fraction of a second, it must be noted which end 

 of the cylinder stood the higliest, and the amount, in the case 

 of the thicker end, must be deducted from the measurement. 



Every visible particle of dust being carefully removed from 

 the cylinder and the Ys, the proof-level was placed upon the 

 cylinder with one side of the bar resting within and against 

 the adjacent arc of the sector, and the opposite side of the bar 



against 



