VOL. IX.] PHILOSOPHICAL TRANSACTIONS. IQ5 



and 8^ lines, the astronomical radius; the -j- of this radius the universal foot; 

 the double of which radius might be called the miiversal toise or fathom, which 

 would be to the Parisian toise as 881 to 864 ; the quadruple might be called the 

 universal perch, which is equal to the length of a pendulum for two seconds. 

 And the universal mile might contain 1000 of these perches. 



M. Picard describes the manner of taking the distance between Sourdon and 

 Malvoisin, with the triangles, and the stations from whence he observed his 

 angles. This distance is 68,343 toises and 2 feet; and the measures of the 

 triangles, 1 3 in number, were as follows. 



In the first triangle ABC, (fig. 7), to find the sides AC, BC. 



Toises Feet 



rCAB = 54° 4' 35^ Measured side AB 5663 O 



Angles <ABC = 95 6 55 Hence is found AC 11012 5 



CACB = 30 48 30 And BC 8954 O 



In the 2d triangle, ADC, to find DC and AD. 



rDAC = 77° 25' 50'^ Given AC IIOI2 5 



Angles ^ADC = 55 o 10 Hence DC 13121 3 



CACD = 47 34 O And AD 9922 2 



In the 3d triangle, DEC, to find DE, CE. 



rDEC = 74° 9' 30' The side DC 13121 3 



Angles ^DCE =40 34 O Hence DE 8870 3 



CCDE=65 16 30 And CE 12389 3 



In the 4th triangle, DCF, to find DF. 



fDCF = 113° 47' 40'^ ThesideDC 13121 3 



Angles <DFC= 33 40 Hence DF 21658 

 CFDC = 32 32 20 



In the 5 th triangle, DFG, to find DG, FG. 



f DFG = 92° 5' 20'' The side DF 21658 O 



Angles ^DGF = 57 34 Hence DG 25643 o 



CGDF = 30 20 40 AndFG 12963 3 



In the 6th triangle, GDE, to find GE. 



The Angle GDE = 128° 9' 30^' The sides DG 25643 o 



And DE 8870 3 



Hence GE 31 8970 O 

 So then, the line of distance between Malvoisin and Sourdon being divided 

 into three parts, viz. EG, GI, IN, the part EG is already found, as above. 

 In the 7th triangle FGH, to find GH. 



CFGH = 39° 51 0'/ The side FG 12963 3 



Angles <FHG = 91 46 20 Hence GH 9695 



(HFG = 48 22 30 



C C 2 



