EEROES IN MEEIDTAN TEANSIT OBSEEVATIONS. 45 



"When " is the angle between the axis of one standard and that of the other projected 

 upon it, s the length of the standards and I the length of the frame of the level, the devia- 

 tion X (in seconds of time) of the axis of the level from the horizontal due to the angle a 

 when one standard is vertical is 



s ( 1 — cos n) 

 X = — ^ X 13751. 



In the case of a level now in use by the writer, where s — lO'ô in. and I = 19"2 in., x is 

 equal to 1"08 seconds of time when « = 1°. The error obviously increases as the square 

 of «■, approximately. 



Owing to the imperfect construction of many striding level frames in which the 

 standards are connected to the horizontal bar liy telescoped tubes held by screws, jDassing 

 sometimes through slotted holes, a value of '»' of 1^ is by no means an extreme case. The 

 angles in the frames should he solid tubular castings, or failing tliis the joint should be a 

 close fitting rectangular one, without adjustment movement. The whole difficulty may of 

 course be avoided by keeping the level in adjustment, but the adjustment is usually a tedious 

 one to make and very likely to be neglected. The better plan is to examine the adjustment 

 as frequently as possible, buf in all cases to depend upon the cross level for the complete 

 elimination of the error. 



ITadir observations are of great value as a check on the level and collimation constants, 

 and sliould be employed to a much greater extent than is usual, especially in America. 

 Where two double sets of observations are made, as is customary in longitude work, there 

 should be three complete sets of nadir observations, — one at the lieginning, one at the middle 

 and one at the close of the series. 



The measurement of the level error is a great source of weakness in most longitude 

 work. It should never be forgotten that an error in level is a constant which enters 

 directly into the resulting longitude and that no amount (^f juggling with equations can 

 remedy the evil if the observations be defective. 



Collimation. — The correction for collimation in a well made instrument, especially where 

 a glass reticule is employed, is one of great constancy, and its value, whatever may be the 

 special method adopted for its determination, will usually in the end be made to depend 

 upon the results of the observations in the reversed positions of the instrument. The means 

 by which the wires are illuminated has an important bearing on the constancy of collimation. 

 Where, for example, the intensity of the light is controlled by a reflector in the cube, there 

 is a probability of such changing conditions as to give rise through cross reflections and un- 

 symmetrical illumination, to a considerable variation in the apparent position of the wires. 

 The change in the intensity — it is, however, much better to observe with a constant intensity 

 — should in such cases be eftected from without the instrument, the reflector remaining in a 

 fixed position. Where an instrument is used in a damp atmosphere as on the sea coast, 

 glass reticules should always be employed. 



There is a not uncommon defect in the mounting of object glasses which makes it 

 impossible to maintain a constant collimation value. The lenses are sometimes held in place 

 by three or more screws which pass through slotted holes in the cell. It is next to impos- 

 sible to fix an object glass in its place and quite impossible to hold it there by such a method. 



These notes should not be closed without further reference to personal equation in its 

 direct efiect upon longitude work. While it may be largely neutralized bj^ the interchange 



