A. MATHEMATICS AND ASTRONOMY. 41 



which it appears that the line of central totality passed 

 through Northern Italy and Southern Spain. Our author 

 lias sought, by a very careful discussion of the observations 

 at command, to determine the precise northern limit of visi- 

 bility of the total eclipse ; and, by comparing the observa- 

 tions with the tables of Hansen, to deduce some positive 

 addition to our knowledge of the secular changes in the 

 orbit of the earth and moon. He expresses his results by 

 an equation which shows that we need but one more sim- 

 ilar eclipse in order to arrive by means of a second such 

 equation at more correct elements of the lunar orbit. Pub- 

 lication of the Royal Observatory ', Milan, No. 10, 1875. 



STUDIES UPON THE DIAMETER OF THE SUN. 



As the extensive work of Father Rosa upon the solar 

 diameter is likely to provoke much further investigation of 

 this subject, notwithstanding all that has been done by 

 Auwers, Wagner, Newcomb, and many others, we quote the 

 following conclusions to which he has been led, as published 

 in the posthumous work recently edited by Father Secchi. 

 First, the body of the sun must be considered as composed 

 of two masses nearly independent of each other, viz., of a 

 solid nucleus enveloped by a gaseous matter. The expres- 

 sion "solid nucleus" can even be applied to the central por- 

 tion of a gaseous mass whose condensation is such that it is 

 necessary that it should be nearly independent of its en- 

 velope. Second, the deformations of the photosphere are not 

 due directly to the force of gravity. Third, the continuous 

 force, that which especially deforms the photosphere, is con- 

 nected with that which produces actual secular movements 

 of the centre of gravity of the sun as demonstrated by Le 

 Verrier. Fourth, the vertical diameter of the sun experiences 

 an annual variation or a semi-annual period, such that it is 

 greater when the sun is north of the equator. Fifth, the 

 mechanical theory of the sun's motions demands that its 

 centre of gravity should describe, in its apparent movement, 

 a great circle of the celestial sphere. The centre of figure, 

 according to Airy, describes a parallel circle, lying north- 

 ward therefrom. Sixth, it results evidently from the two 

 preceding sentences that the plane of the ecliptic is not par- 

 allel to that which cuts the photosphere into two symmet- 



