120 LECTURES 



Now, by observing tlie instant of the several contacts of the limb of 

 Venus with that of the sun, the exact time in which the centre of the 

 planet traverses the chord will be known. The mean diameter of the 

 sun is 32' 3" nearly, or 1,923". By the known angular velocities of 



the two bodies the time of traversing the diameter becomes known. 

 Calling t the computed time of traversing the diameter, i' the ob- 

 served time of traversing the chord, we shall find the number of 

 seconds in the chord by the proportion t : t' '. : 1,923" : the number of 

 seconds in the chord. By drawing radii from S to E and D we readily 

 find S n and S m from the right-angled triangles S w E and S m D, 

 and hence n mthe perpendicular distance between the chords; that is, 

 we shall know the number of seconds subtended by the line m n, as 

 seen from the earth. We can also compare m n with A B, they be- 

 ing parallel lines in the same plane perpendicular to the plane of the 

 ecliptic. Seen from V, these lines subtend the same angle. Their 

 relative lengths must, therefore, be as their distances. But it is known 

 that •y ?i : V A : : 72 : 28 nearly ; hence, we have 72 : 28 : : iw w : A B. 

 But we have determined the number of seconds subtended by m n as 

 seen from the earth; this proportion, then, gives the number of 

 seconds subtended by A B, seen at the same distance; that is, as seen 

 from the sun. We then have the angular diameter of the earth as 

 seen from the sun. One-half of this is the long-sought element in 

 astronomy, the sun's horizontal parallax. On account of the great 

 importance of this process, and the great interest which always at- 

 taches to the transit of this planet, I have ventured to give the details 

 which are necessary to appreciate the grounds upon which the result 

 rests. It is proper to remark, before leaving this paint, that the two 

 stations A and B cannot well be at the extremities of a diameter, nor 

 will it often happen that the right line joining them will be perpen- 

 dicular to the plane of the ecliptic. But^ what comes substantially to 

 the same thing, the line joining the stations will always be known, 

 and can easily be reduced to an equivalent perpendicular one, so that 

 the accuracy of the final result will scarcely be impaired by this cir- 

 cumstance. 



The only observation of that transit made on the American conti- 

 nent, so far as I am aware, was by Professor John Winthrop, of 

 Harvard University. The transit came on early on the morning of 

 June 6. For the purpose of a favorable station Mr. Winthrop re- 

 paired to St. John's, in New Brunswick. His observations were com- 



