366 



eluding the effect of all the inequalities of the ground within a radius 

 of 6000 feet (or rather more than a mile) around each of the stations, 

 and denoting by x the unknown ratio of the density of the hill to 

 that of the entire globe, these equations are obtained : 



Deflection at South station, . . . = 4-197 x North. 



„ Arthur's Seat, . . . = 0-607 x South. 



„ North station, . . . = 3-710 x South. 



by the solution of which the ratio of the density of the hill to that 

 of the whole earth is as "5245 to 1.* 



By extending the radius of sensible attraction considerably beyond 

 6000 feet, and calculating the effect of the surrounding country in 

 the same manner on the plumb-line at the three stations, this value 

 of the relative density of the globe is somewhat modified. The ratio 

 is then -5348 to 1. 



From direct experiments on the specific gravity of the rocks of 

 Arthur's Seat, Colonel James infers the mean density of the hill to 

 be 2-75 times that of water ; whence the earth's density comes out 



5-14, 

 with a probable error of 0-07. 



3. On the Possibility of combining two or more independent 

 Probabilities of the same Event, so as to form one definite 

 Probability. By Bishop Terrot. 



In this paper the author showed that, a and e being independent 

 probabilities of the same event, the expression a + e — ac, given in 

 the article Probability in the Encyclopaedia Metropolitana as the 

 value of their combined force, was erroneous. For if a-\-e — ae 

 be the probability of the occurrence of the event, then 1 — a + 1 — e 

 — 1 — a • 1 — eor 1 — ae, is the probability of its non-occurrence. 

 Whereas the probability of non-occurrence derived directly from the 

 expression a + e — aeis 1 + ae — a + e. 



It was then shown, that if the ratio only of equally probable cases 

 in two or more probabilities were given, no definite probability could 

 be derived from their composition ; but that if the two given pro- 

 babilities - and - indicate not merely the ratios, but the actual 

 r s 



* The outstanding abnormal deflection of the plumb-line (assumed to be 

 equal at the three stations) amounts to 4''-72. 



