36 KEPORT— 1871. 



calculation, but the principles involTed -would he the same. When the distances 

 and positions of the two components of a binary star have been carefully observed by 

 astronomers for a certain number of years,ithas been found possible in manyinstances 

 to determine the elements of their orbit, its ellipticity, the inclination of its plane 

 to the ecliptic, the time of one complete revolution, the apparent maximum elonga- 

 tion, &c. &c. But the distance of the double star from the earth has hitherto re- 

 mained unknown, because that is dependent upon the real size of the orbit, and 

 observation (without the spectroscope) gives only the ajiparent size of it. Knowing 

 the elements of the orbit we can, indeed, calculate the velocity of either of the 

 stars in the direction of the earth at any moment, relativeli/ to that which it has at 

 any other moment. But the determination of the absolute velocity requires the 

 distance of the stars from the earth to be known. Now a few observations (if per- 

 fectly correct) of the deviation of the ray X supply this wanting element, viz. the 

 actual velocity at the time of observation, and likewise enable us, as I have already 

 explained, to eliminate the proper motion of the double star. This might be some- 

 times difficult, but geometrical considerations, quite in hannony with those now 

 employed by astronomers to determine the other elements of the binary system, 

 would undoubtedly effect this also. 



In what I have written above, I have supposed great precision in the observa- 

 tions- — greater, no doubt, than would be practicable with the optical means no2v 

 in use ; but this makes no difference in the theory of the subject, which for a 

 certain time may be allowed to pass ahead of its practical realization. It will 

 doubtless be remembered that the method of determining the sun's distance by means 

 of a transit of Venus was proposed by James Gregory in his ' Optica Promota,' 

 and by Halley in his ' Catalogus Stellarum Australium,' nearly 100 j'ears before an 

 opportunity offered of testing it by an actual observation. 



On the Nutoscope, an Apjyaratus for slwtuhig Grapliically the Curve of 

 Precession and Nutation. By Professor Chaeles V. Zenger. 



In the case of a rapidly revolving solid body two different cases may occur, the 

 mass of the solid body being quite uniformly distributed around the axis of rota- 

 tion, or, on the contrary, the uniformity being destroyed by the accumidation of 

 matter on one side of the axis. 



In the fii'st instance the centrifugal force will act symmetrically on opposite 

 sides of the solid body in rotation, and be in equilibrium. It then gives rise to 

 the phenomenon of a free axis ; that is to say, the axis of rotation steadily holds 

 its position dm-iug the rotation, because the particles of the body will also have 

 the tendency to retain their position while the motion is going on with sufficient 

 speed. 



These facts may best be shown by Fessel's apparatus, called the gyroscope, in 

 which a cu'cular disk is put in rapid rotation romid an axis freely movable in every 

 direction. 



If there is a force acting only on one side, for instance a weight pressing on the 

 axis, or an impulse given to it, the axis will show a lateral motion, and describes 

 a cone, or at its extremity a circle. 



But if there is on the disk itself an imequal distribution of the mass, which is 

 produced by fastening a small circular disk or sheet of paper with an excentric hole 

 upon the axis, the motion becomes more complicated ; and if the velocity be con- 

 sidered uniform for the short time required for the axis to describe a cirde, there 

 will be an additional lateral motion produced by the adhering paper sheet dis- 

 turbing the motion, and a small ellipse will be described by the end of the axis 

 revolving upon the circle, as is shown in the diagi'am traced on blackened paper by 

 the top of such an apparatus. 



The greater the mass of the disturbing paper sheet, and the more the speed of 

 the motion diminishes, the larger becomes the diameter of the ellipse described by 

 the top, and the more disturbed are its revolutions on the periphery of the circle, 

 both axis of the ellipses becoming much larger. Diminution of the speed origi- 

 nates, instead of the circular motion of the top, a spiral motion, and the effect is 



