544 PHILOSOPHICAL TKANSACTION8. [aNNO 1708. 



the neighbourhood of the zodiac, quicker than that of altitude, he apprehends 

 it to be easier to follow the slower motion with the screw, so as to preserve the 

 intersection, than the quicker, and therefore in general to be preferred ; but 

 where it happens otherwise, or the stars lie more conveniently, the inverse 

 method may be pursued. 



It is true, that some degree of dexterity and practice may be requisite in the 

 observer in managing the set screw, so as to keep the object intersected by the 

 wire ; but if fine smooth screws, such as are used for micrometers to astrono- 

 mical quadrants, are adapted to the instrument, as well that commanding the 

 horizontal motion as the vertical, the management will be perfectly easy and 

 familiar to an observer otherwise well practised. It is easy to see, that those 

 stars are to be preferred that are nearest the heavenly body to be observed; 

 and that, caeteris paribus, those in such positions, as rise or fell slowly, are best 

 for determining their altitude ; and those that alter their azimuth slowly, are best 

 for determining the azimuth. 



To avoid intricacy in description, Mr. S. has supposed only 2 wires intersect- 

 ing each other at a right angle, in the focus of the telescope : but, for the sake 

 of getting a medium in such parts of the observations as depend on time, it will 

 be proper to have, not only 3 perpendicular wires, parallel to each other as 

 common, but also 3 horizontal wires ; the proportional distances of which being 

 previously determined by observation, the oblique motions may, in parts not 

 near the pole, be considered as right lines. 



This method is the more valuable as it is entirely free from the knowledge of 

 refractions ; for since the computation gives the real altitude from the time given 

 independent of refractions ; and since the heavenly body is equally affected by 

 refraction, at the same altitude ; the computed altitude of the star will give the 

 real altitude of the heavenly body cleared of refraction, which never enters the 

 question : and since such stars may be chosen as will render the time intercepted 

 short, there is the less chance of a change of refraction, during the time between 

 the middle and last observation ; and therefore this method will be particularly 

 useful in observations near the horizon. 



Observations of this kind may be made on the planets in the day light, by 

 making use of the sun for the first observation, instead of a star ; and waiting 

 afterwards for the appearance of the stars. 



XXVI. Specimen of a New Method of Comparing Curvilineal Areas ; by which 

 many such Areas may be compared as have not yet appeared to be Comparable 

 by any other Method. By John Landen, F. R. S. p. 174. 

 When a body in motion is continually acted on by a variable force, the space 



it has passed over at the end of any given time, it is well known, will be ex- 



