DISTANCE AND DIMENSIONS OF THE, SUN. 413 



sun's distance will be greatly reduced as the result of this work; and 

 yet there are some grounds for anxiety lest the photographic data 

 prove as intractable and inconsistent as those derived from contact- 

 observations. Time only can positively settle the question. 



One of the best methods of determining the solar parallax is based 

 upon the careful observation of the motions of the moon. It will be 

 recollected that the first suspicion as to the correctness of the then 

 received distance of the sun was raised in 1854 by Hansen's an- 

 nouncement that the moon's parallactic inequality led to a smaller 

 value than that deduced from the transit of Venus a conclusion cor- 

 roborated by Leverrier four years later. It seems at first sight 

 strange, but it is true, as Laplace long since pointed out, that the 

 skillful astronomer, by merely watching the movements of our satel- 

 lite, and without leaving his observatory, can obtain the solution of 

 problems which, attacked by other methods, require tedious and ex- 

 pensive expeditions to remote corners of the earth. Our scope and 

 object do not require us to enter into detail respecting this lunar 

 method of finding the sun's parallax ; it must suffice to say that the 

 disturbing action of the sun makes the interval from new moon to 

 full a little longer than that from full to new ; and this difference de- 

 pends upon the ratio between the diameter of the moon's orbit and the 

 distance of the sun, in such a manner that, if the inequality is accu- 

 rately observed, the ratio can be calculated. Since we know the dis- 

 tance of the moon, this will give that of the sun. The results ob- 

 tained in this way, according to the most recent investigations, fix the 

 solar parallax between 8.83" and 8.92". 



There is still another lunar method, mentioned in the synopsis ; 

 but its results are much less reliable subject, that is, to a much larger 

 probable error, though not at all contradictory to those just given. 



But the method by which ultimately we shall obtain the most ac- 

 curate determination of the dimensions of our system is that pro- 

 posed by Leverrier, making use of the secular perturbations produced 

 by the earth upon her neighboring planets, especially in causing the 

 motions of their nodes and perihelia. These motions are very slow, 

 but continuous ; and hence, as time goes on, they will become known 

 with ever-inci'easing accuracy. If they were known with absolute 

 precision, they would enable us to compute, with absolute precision 

 also, the ratio between the masses of the sun and earth, and from this 

 ratio we can calculate ' the distance of the sun by either of two or 

 three different methods. 



1 One method of proceeding is as follows : Let M be the mass of the sun, and m that 

 of the earth ; let R be the distance of the sun from the earth, and r that of the moon ; 

 finally, let T be the number of days in a sidereal year, and t the number in a sidereal month. 

 Then, by elementary astronomy, 



M : m = - : T l; whence R 3 = r 3 f 1 -) (-) 

 T 3 t 2 ' VtV w 



or, in words, the cube of the sun's distance equals the cube of the moon's distance, multiplied 



