TOL. IX.] PHILOSOPHICAL TRANSACTIONS. 1^7 



Then in the triangle NRT, fig. 8; Toises Feet 



. , TNTR = 7^° '25' 40'/ The sideNR 7122 2 



^^\TNR = 67 21 40 Hence NT 4822 4 



Finally, in the triangle NTV; 

 /NTV = 83° 58' 40'/ The side NT 4822 4 



"^^^tTNV = 70 34 30 Hence NV Iii6l 4 



Now adding the distance between Malvoisin and Sourdon, viz. 68359 O 



To the distance between Sourdon and Amiens 1 1 l6l 4 



The whole will be the distance between Malvoisin and Amiens 79520 4 

 Having thus measured the particular distances between Malvoisin, Mareuil, 

 Sourdon, and Amiens, he proceeds to examine the position of each of these 

 lines of distance in respect of the meridian, or to deduce the length of the 

 meridian intercepted between the parallels of Malvoisin and Amiens, which was 

 thus done: — In Sept. 1669, from the top of the hill Mareuil, marked with G 

 in fig. 7, from whence may be seen Clermont on one side, at I, and Malvoisin 

 on the other side, at E, he took the meridian, and with a quadrant the angles 

 of declination from this meridian ; and he found — 



The angle EGs in fig. 7? the dec. of EG from the merid. westw. 0° 26' O" 

 The angle GI9, the declin. of GI from the meridian eastward 1 9 o 

 The angle INV, the declin. of IN from the meridian eastward 2 9 10 

 The angle VN|3, in fig. 8, the dec. of NV from the merid. westw. 18 55 O 

 So that in all these 4 triangles, EGs, GI9, INV, VN|3, there are two angles 

 known, (for the angles at £, at 6, at V, at j3, are right,) and a side, viz. EG, GI, 

 IN, NV ; whence he concludes. 



The length of the meridian Gf to be . . . . 31894to i.Oft. 

 of the meridian I& ........ 17560 3 



of the meridian NV I8893 3 



of the meridian N|3 IO559 3 



And hence the length of the whole meridian « (3 



between the parallels of Malvoisin and Amiens to be 78907 3 



Though these lines, which make up the meridian, are not in strictness a curve, 

 but in reality the side of a polygon circumscribed about the circumference of the 

 earth ; yet the difference between those lines and a true curve is only 3 feet for 

 a degree, which he observes is scarce worthy of notice, as he afterwards proves. 

 The length of the meridian between Malvoisin and Amiens being thus stated, 

 his next business is, to enquire what answers to it in the heavens, comparing 

 those meridian distances already measured, with minutes and seconds there. 

 These were taken by an instrument, whose limb was an arch of ^ of a circle, 

 of 10 feet radius. The star in the knee of Cassiopeia was that he pitched on, 

 from whence to measure the minutes and seconds of a degree in the heavens. 



