260 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. 



10 years account, and the Paris proportion of births, there must be annually 

 born in London 31008 children : therefore, as this number, according to Mr. 

 M.'s calculation, is the produce of 725g03, the present number of the inhabi- 

 tants of London ; so must 280O0, the number of children supposed to be born 

 yearly in the province of Holland and West-Friesland, be the produce of 635485, 

 the present number of the inhabitants of the said province. Notwithstanding 

 Mr. Kersseboom, by his excessive and unprecedented reckoning of the births 

 at a thirty fifth part of the people, has calculated them at 98OOOO ; whereas by 

 the ingenious and learned Dr. Halley's method of calculation, which is so highly 

 approved of by Mr. Kersseboom, that he seemingly would be thought to make 

 it the standard of his calculations, the inhabitants of the province of Holland 

 and West-Friesland do not amount to 29 times the number of the births, 

 which gives room to suspect, that Mr. Kersseboom has introduced this excess, 

 to increase the number of people in the said province of Holland and West- 

 P'riesland. 



A IVater-Level to be fixed to Davis's Quadrant, by which an Observation may 

 be taken at Sea, in thick and hazy Weather, without seeing the Horizon, By 

 Charles Leigh, Gent. N°451, p. 413. 



The sea-quadrant now in use, invented by Capt. Davis, for taking the sun's 

 altitude, is an instrument well known, universally approved, and sufficiently 

 accurate ; this, together with a long use of this instrument, has occasioned 

 such a fondness for it, that it would be no easy matter to dissuade the navigator 

 from the vise of it, to any other. 



It is true, that when the natural horizon is obscured by thick and hazy 

 weather, this instrument, as it now stands, is of no use ; which too often oc- 

 casions melancholy consequences, such as the loss of ships and cargoes, and 

 men's lives. If therefore, to this instrument an apparatus were added, such as 

 an artificial or portable horizon, that could be as effectually relied on, as that 

 of the true or natural; and at the same time plain, easy, and obvious; it would 

 be needless to attempt proving its usefulness. 



The principle on which Mr. Leigh's apparatus is founded, is, " That the 

 surface of all liquids, when free from any external cause, that have a communi- 

 cation with each other, though divided and separated in their surfaces, will be 

 truly in a horizontal plain." 



The quadrant, and its construction, being well known, it is sufficient to no- 

 tice the two sections of two concentric circles, as ab, cd, fig. 3, pi. 7, on which 

 the degrees and minutes are graduated ; e, the common centre, through which 

 goes a brass pin fixed to the apparatus ef, which is an index or radius to the 



