92 MR EDWARD SANG ON THE DEFLECTION OF THE PLUMMET. 



body does not set, the apparent nadir describes a circuit round the true. As the 

 declination decreases, the orbit shows a tendency to form a cusp towards the true 

 nadir, and when the moon or sun comes just to graze the horizon the cusp is 

 formed. When the declination becomes so low that the moon sets, the orbit has 

 a convolution inwards; and as the declination approaches to zero, the two 

 sweeps of the orbit coalesce into an ellipse whose circumference is gone over 

 twice daily. So soon as the moon passes to the south of the equator, what may 

 be called the day part of the orbit takes the place of the night part for the corre- 

 sponding north declination ; so that the same diagrams answer, merely changing 

 the hour marks by 12 hours. 



For all places above 45"^ of north latitude the day is larger than the night 

 part of the curve when the moon is north of the equator. For places on the 

 parallel of 45"^ the two branches of the curve touch each other on the meridian, 

 whatever be the declination, and for places below 45'', the intersection Avith the 

 meridian are, as it were, interchanged. 



For places on the equator, the orbits are always varieties of the hour-glass 

 curve, merging into a simple line when the declination is zero. 



There are two ways in which we may attempt to exhibit these phenomena 

 One is to prepare a spherical level ground to such a large radius of curvature as 

 that the second may be divided into several hundred parts. The motions of the 

 air-bubble will be opposite to those of the nadir point. The other is to direct an 

 extremely powerful telescope to look directly downwards into a basin of mercury, 

 and thereby to examine the motion of the image of the cross wires. But in 

 neither of these ways shall we be able to trace motions exactly like those in the 

 drawings, because actually the disturbances caused by the sun and moon are 

 commingled, while the declinations are continually changing. The complexity of 

 the resulting motions may be exemplified by reducing any one of the drawings 

 to one-third part of the scale, so that it may represent the solar deflection, and 

 by carrying its centre round any of the lunar curves for the same latitude, 

 observing at the same time the distinction between the lunar and the solar day. 



These speculations are interesting, not merely from the singular and unex- 

 pected beauty of the results, but also from their bearings on the higher branches 

 of practical astronomy. They show us that the cross-level of a transit instru- 

 ment is subject to a semi-daily oscillation, amounting at new and full moon to 

 two forty-fifth parts of a second ; and that the surface of the mercury in the 

 collimation trough imitates, as far as it is able, the tidal motions of the sea. 



Let us suppose that, by help of instruments capable of that degree of preci- 

 sion, we are endeavouring to determine the obliquity of the ecliptic true to the 

 fourth decimal part of a second^we place our instruments in the observatory of 

 St Petersburg, in Lat. 59° 56" 30", to observe the sun's meridian altitude at the 



