\Q6 PHILOSOPHICAL TRANSACTIONS. [aNNO 1705. 



him ; but it will be still better to have two observers, one of whom being in a 

 boat must, at the time he takes the angle subtended by some 2 objects on the 

 shore, make a signal to the other observer, who, being placed at one of the ob- 

 jects as a station, must at the same time observe the angle subtended by the boat 

 and the other object. By this means, 2 angles in a plain triangle being given, 

 with the distance between the 2 objects, as a base, the whole triangle, and the 

 situation of every part of it, will be given likewise. By such observations as 

 these, provided the boat be at rest during the time of making them, and they be 

 made carefully with good quadrants, though without the assistance of telescopic 

 sights, the situation of places may be easily determined to 20 or 30 feet on every 

 3 or 4 miles. 



Besides the use of Hadley's quadrant in surveying, it may on some occasions 

 be very advantageously employed in piloting ships into harbours, the great rea- 

 diness with which it may be used, making it a very convenient instrument for 

 this purpose: but that this may be done to the greatest advantage, it will be ne- 

 cessary to have a proper provision made for it on the charts, by.expressing on them 

 the angles subtended by given objects, by means of which, with the bearings, a 

 ship may be enabled to know her situation with great exactness. The well 

 known property of the circle, that angles in the same segment are equal to each 

 other, may be often very conveniently applied on this occasion : for if, through 

 any 2 given objects, we describe several segments of circles, in which those ob- 

 jects shall subtend the angles of* 120°, QO", 80°, 70°, &c. respectively, we shall 

 then know immediately, on finding the 2 objects subtend any one of these angles, 

 that we are situated somewhere in the circumference of the corresponding seg- 

 ment ; and the bearing also from one of the objects being known, our precise si- 

 tuation will be determined with great accuracy. 



Mr. M. makes an application of this method, to the case of the mouth of the 

 Humber, where the Spurn Lights are placed, to direct ships in entering the har- 

 bour. The present inconvenient and indeed dangerous situation of the two 

 lights at the mouth of the Humber, says he, commonly called the Spurn Lights, 

 must probably soon make it necessary to remove them; for the ground, on which 

 they formerly stood, is now so far washed away, as not to leave sufficient room 

 to erect them at a proper distance from each other; and fresh ground being 

 grown up to the southward, so as to make the point above a luile distant from 

 them, ships are frequently thereby liable to be deceived. In case therefore these 



* The number and frequency of these segments, as well as the magnitude of their respective 

 angles, must be determined, according to the particular circumstances of the occasion, on which 

 they are applied: 1 have mentioned no greater angle than 120°, as there are few cases in which this 

 will not be sufficient; and indeed it is the greatest that Hadley's quadrant, the only instrument fit 

 for this purpose, will easily admit, according to the present construction of it. — Orig. 



