A. MATHEMATICS AND ASTRONOMY. 55 



M, at any moment, t. Let Ax be a variable line that, start- 

 ing always from A, remains during the whole time, T, equal 

 and parallel to the velocity, v, and pointing in the same di- 

 rection. Finally, let 

 ab be the arc de- 

 scribed by X during 

 the interval T; that 

 is to say, ah will be 

 the hodograph of 

 the velocity, v. 



Conceive now any 

 mass so distributed along ah that the density at the point x 

 shall be in the inverse ratio of the force which solicits the 

 point M, or of the acceleration of the first order. 



It can now.be shown that the centre of gravity, C, of this 



AB 



mass lies on the chord AB, and that the ratio -^^ is equal 



to the duration T. We may, therefore, consider the line AC 

 in lenirth and direction as the mean of the velocities which 

 the projection of M upon the chord AB acquires during the 

 time T.Bull. Acad. Sci. of SL Petersburg, 1874, 258. 



THE SOLAR SPOTS AND PROTUBERANCES OF THE SUN FROM 



1871 TO 1875. 



Father Secchi, in giving a review of his observations on 

 the solar spots and protuberances for the past four years, 

 states that they extend over about fifty-two rotations of the 

 sun upon its own axis (or solar days). The average number 

 of protuberances observed each day, which was about fifteen 

 in 1871, was reduced to from four to ten in 1870, the average 

 of the whole period being about ten, and the progressive dim- 

 inution being very regular. The area covered by the protu- 

 berances was reduced in a similar proportion, viz., from fif- 

 teen to five. In 1871 the average number of groups of 

 spots was about twenty-five, which number Avas reduced to 

 six or seven in 1875. The surface covered by the spots has 

 diminished to ten in 1875, being ninety in 1871. It is evi- 

 dent that the solar activity, as far as manifested by the 

 quantity of spots, corresponds to the activity presented by 

 the protuberances. The parallelism is not absolute, how- 

 ever, nor could this be expected, since certain protuberances, 



