SCIENCE. 



345 



locities and mean vis viva. This is the foundation of 

 Maxwell's theory of the equality of mean vis viva in the 

 molecular movements of different gases at equal tempera- 

 tures, and of Pfaundler's discovery that in estimating the 

 heat of dissociation, the mean should be taken between 

 the temperatures of incipient and of comnlete dissociation. 



2. The projectile force, which produces flight or cy- 

 clical motion against any central acceleration or. retar- 

 dation, is equivalent to the mean acceleration or retar- 

 dation multiplied by one-half the time of flight or cyclical 

 motion. 



3. The velocities of wave motion in elastic fluids, and 

 of cosmical and molecular orbital moti on, can all be ex- 

 pressed by the common formula v = y/ 2 gh. 



4. Every periodic vibrating or orbital motion can be re- 

 garded as the sum of a certain number of pendulum 

 vibrations. {Fourier's theorem) 



5. The distance of the centre of oscillation from the 

 centre of relative stability is at two thirds of the length of 

 a linear pendulum, or at the square root of four tenths of 

 radius in a rotating sphere. 



6. The acceleration of any force, which is uniformly 

 diffused from or towards a given centre, varies inversely 

 as the square of the distance from the centre. 



7. Times of revolution under the action of such forces, 

 vary as the three halves power of the distance ; distances 

 vary as the two thirds power of the time. 



8. Centres of inertia, or nodes, in a vibrating elastic 

 medium, tend to produce harmonic nodes. 



9. The mutual inter-actions of cosmical, molecular or 

 atomic bodies are proportioned to the respective masses ; 

 actions which are considered with reference to a single 

 active centre vary directly as the mass and inversely as 

 the square of the distance. 



10. In elastic atmospheres the densities decrease in 

 geometrical progression, as the height above the surface 

 increases in the arithmetical progression. 



11. Living force, or vis viva, is proportional to the 

 product of mass by the square of the velocity. 



12. The distance of projection against uniform resis- 

 tance is proportioned to the living force. 



13. In condensing nebulae, the velocity of circular or- 

 bital revolution is acquired by subsidence, from a state of 

 rest, through one-halt of radius. 



The following additional propositions may be readily de- 

 duced from the foregoing. 



1 4. Mean vis viva may be represented by the vis viva of 

 centres of oscillation. 



15. The force of planetary projection should be referred 

 to perihelion ; the force of incipient subsidence, to ap- 

 helion. 



16. In synchronous orbits, the mean velocity of rectili- 

 near oscillation is to the velocity of circular orbital oscil- 

 lation as twice the diameter is to the circumference. 



17. The acceleration or retardation of a centripetal 

 force varies as the fourth power of the velocity of orbital 

 revolution. > 



18. In cyclical motions, the resultant of all internal 

 forces must be in equilibrium with the resultant of all ex- 

 ternal forces, at the expiration of each half cycle. 



19. The modulus of cyclical motion is equal to the 

 product of mean acceleration by the square of the time of 

 a half cycle. 



20. The sum of all external forces may, therefore, be 

 represented by a velocity which is equivalent to the 

 mean or resultant internal force acting for one-half of 

 the cyclical time. 



21. The influence of a central force which acts at the 

 extremity of a linear pendulum is nine times as great 

 upon the centre of oscillation, as its influence upon the 

 centre of suspension. 



22. The limiting vis viva of wave propagation is five- 

 ninths of the mean vis viva of the oscillating particles. 



23. In condensing nebulae, rupturing forces which are 

 due to central subsidence may be. represented by frac- 



tions in which the denominator is one greater than the 

 numerator. 



24. In synchronous rotation and revolution, the nucleal 

 radius varies as the three-fourths power of the limiting 

 atmospheric radius. 



25. The variation in mean vis viva of gaseous volume 

 is to the variation in vis viva of uniform velocity as 1 is 

 to 1.4232. 



26. The mean thermal and mechanical influences of 

 the sun must be in equilibrium. 



27. The collisions of particles, in subsiding towards a 

 centre of force, tend to form belts at the centre of linear 

 oscillation. 



28. The limiting velocity between tendencies to aggre- 

 gation and tendencies to dissociation is to the velocity in 

 a circular orbit as the ratio of the circumference of a 

 circle to its diameter is to the square root of two. 



29. In explosive, as well as in cyclical motions, equili- 

 brium must be established between internal and exter- 

 nal forces. 



30. Apsidal and mean planetary positions must also be 

 controlled by like tendencies to equilibrium. 



31. Undulations in an elastic medium maintain the 

 primitive velocity which is due to their place of origination. 



32. When two or more cyclical motions are combined, 

 they must all be modified by the tendency to conserva- 

 tion of areas. 



33. In expanding or condensing nebulae, the conserva- 

 tion of areas maintains a constant value for the modulus 

 of rotation. 



34. Instantaneous action between different masses or 

 particles, by mere material intervention, is impossible. 



35. In synchronous motions about different centres, 

 the mean distances from the centres of motion vary as 

 the cube root of the masses or other controlling forces. 



36. Constant velocities, in a homogeneous elastic me- 

 dium, represent constant living forces. 



37. The time of acquiring orbital velocity, at Laplace's 

 limit of possible atmosphere, is to the time of acquiring 

 " nascent " or dissociative velocity at the nucleal limit, as 

 the d ameter of a circle is to its circumference. 



These laws are applicable in all branches of radio- 

 dynamics, viz.: photodynamics, thermodynamics, elec- 

 trodynamics, cosmodynamics, chemical physics, hydro- 

 dynamics and pneumatics. 



COMET C, 1 88 1. 



At 3 A. M., of the 14th instant, a comet was observed at 

 Ann Arbor by Mr. T. M. Schaeberle, an amateur astronomer, 

 who has the privilege of the University Observatory. 



Mr. Henry M. Parkhurst, of Brooklyn, whose recent cal- 

 culations on comet B, 1881, proved to be very accurate, has 

 published in the New York Herald the following observa- 

 tions on Mr. Schaeberle's comet : 



" The position of the new comet on the 20th instant at 2h. 

 46m., Washington mean time, was : — Right ascension, 5I1. 

 54m. 58s.; North declination, 40 degrees, 40 minutes. This 

 shows a motion of 29 minutes per day — an increase of 7 

 minutes — showing that the comet is not so distant as I had 

 hoped. I have not succeeded in reconciling my two posi- 

 tions with that telegraphed for the time of discovery. To 

 satisfy the right ascension given the comet must have al- 

 ready passed its perihelion and be moving in such an orbit 

 that it will pass between the earth and sun within a fort- 

 night, and be no more seen in this hemisphere. The in- 

 creased brightness this morning tends to support this idea. 

 Yet it may not have reached its perihelion ; in which case 

 it may be visible for a month longer. I shall be compelled 

 to wait for a third accurate observation before I can deter- 

 mine the orbit more exactly. In any event the comet is 

 coming directly toward the earth, and it will become much 

 blighter than at present, so that it will probably be visible 

 to the naked eye as soon as the moonlight ceases to inter- 

 fere. It is now about 12 degrees southeast of Capella, the 

 bright star in the northeastern sky at 3 o'clock in the morn- 

 ing." 



