820 



SCIENCE 



[N. S. Vol. XXXI. No. 804 



Columbia College 



Mro-TEAK Examination, Februakt 3, 1910 



Astronomy 1 



Answer three questions only in eacli numbered 



group 

 1, o. Define : celestial sphere, declination, hour- 

 angle. 

 1, 5. Describe the ecliptic circle and explain why 



we always see the sun in that circle. 

 1, e. What visible phenomena are produced by the 

 earth's axial rotation? 



1, d. Prove that the altitude of the celestial pole 



is everywhere equal to the latitude. 



2, a. Explain sidereal and solar time. 



2, b. Why does the vernal equinox occur on or 

 about March 21? 



2, c. Explain the reason for time-difTerenees be- 

 tween different places on the earth. 



2, d. In an ordinary horizontal sundial, what is 



the angle of elevation of the gnomon, and 

 why? 



3, a. If a small round steel ball is dropped from a 



tower, will it reach the earth at a point 

 directly under the point from which the 

 ball was allowed to fall? 



3, 6. If not, where will it reach the earth, and 

 why? 



3, c. How is the length of the earth's radius de- 

 termined ? 



3, d. What is the " torsional constant " and how 



is it determined for any given torsion bal- 

 ance? 



4, a. Why is summer hotter than winter ? 



4, 5. In the northern hemisphere, is summer longer 



or shorter than winter? Why? 

 4, c. Explain tropical and sidereal years. 



4, d. Explain the supposed relation between the 



age of the Great Pyramid in Egypt and the 

 precession of the equinoxes. 



5, a. Explain the aberration of light. 



5, 6. What are the four constituent parts of a 



date? 

 5, c. What is the leap-year rule in the Gregorian 



calendar ? 



5, d. How does the apparent angular velocity of 



the moon on the sky compare with the 

 sun's, and why? 



6, o. How is the moon's distance from the earth 



ascertained. 

 6, 6. Explain two lunar librations. 

 6, c. What are occultations, and how are they used 



to determine terrestrial longitudes? 



6, d. Demonstrate Kepler's law of areas under the 



action of a central force. 



7, a. Define sidereal period of a planet. 



Synodic period of a planet, 



Conjunction. 

 7, 6. Derive formula for computing the sidereal 



period from the synodic period. 

 7, c. Explain the connection between the visibility 



of a planet and its synodic motion. 

 7, d. Why does the synodic period approach 365 



days as a limit for the outermost planets 



of the solar system ? 



■* THE DEFINITION" OF FORCE 



To THE Editor of Science : Professor Henry 

 Crew, in his presidential address before the 

 American Physical Society,' comments un- 

 favorably on the definition of force given by 

 me in a letter in Science of December 24, 

 1909, viz., " Force is a pull or a push, some- 

 thing that causes or tends to cause either mo- 

 tion or a change in the velocity or direction 

 of motion." He expresses a " fear " that this 

 definition is used by " not a few students of 

 physics." 



An elaboration of the definition, given 

 many years ago by Professor I. P. Church, is 

 as foUows: 



A force should always mean the pull, pressure, 

 rub, attraction (or repulsion) of one body upon 

 another, and always implies the existence of a 

 simultaneous equal and opposite force exerted by 

 that other body upon the first body, i. e., the 

 reaction. In no case should we call anything a 

 force unless we can conceive of it as capable of 

 measurement by a spring balance, and are able 

 to say from what body it comes. 



That " a few students of physics " use this 

 definition ought not to be the cause of " fear " 

 to any professor of physics; on the contrary, 

 it should be a source of gratification. It is 

 safe to say that nine tenths of all those stu- 

 dents of physics who have occasion after 

 their college days to make use of their physics 

 are going to be either engineers or mechanics, 

 and in that case they will have to learn this 

 " standard defiiiition of the engineer." It is 

 well for them to learn it while they are young. 



Professor Crew gives as " the one perfectly 

 correct, competent and complete description 

 of force " the " rate of change of momentum," 

 and he credits Galileo and Newton with hav- 

 ing thus defined it. I can not find, however, 

 in the quotations he gives from Galileo and 



' Science, April 8. 



