Mathematical Tracts on the Lunar and Planetary Theories: The Figure of the Earth, Precession and Nutation, the Calculus of Variations, and the Undulatory Theory of Optics |
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Page 14
... manner , we find the accelerating force perpendicular to Gm ' m ' 3 EM2 + ME2 2 ( E + M ) 3 ° 7'1⁄2 = 12 2 3 ME sin 2 w , liby ? or m ' 12 • • 2.2 sin 2w , ጥ 2` ( M + E ) 2 ' r ' * ' which , for the same reason , is too small to be ...
... manner , we find the accelerating force perpendicular to Gm ' m ' 3 EM2 + ME2 2 ( E + M ) 3 ° 7'1⁄2 = 12 2 3 ME sin 2 w , liby ? or m ' 12 • • 2.2 sin 2w , ጥ 2` ( M + E ) 2 ' r ' * ' which , for the same reason , is too small to be ...
Page 16
... manner as in ( 9 ) , we suppose this force applied to M in the opposite direction , we have , for , the whole disturbing force on M , in direction of the pro- njection of the radius vector , a , far ? MG EG 1 m ' - Gm'cos 0-0 ' 13 1 + ...
... manner as in ( 9 ) , we suppose this force applied to M in the opposite direction , we have , for , the whole disturbing force on M , in direction of the pro- njection of the radius vector , a , far ? MG EG 1 m ' - Gm'cos 0-0 ' 13 1 + ...
Page 22
... manner , putting u for in equation ( c ) , we have d2 ( ) dt - S. - P 0 : 94-1-4-9 = d d и de ds du Now dt de dt u2 d Ꮎ de dt = - ( u da ds S du ) ✓ T h2 + 2 из ( And = d2 dt de S • H d dt de = u2 h2 + 2 [ d ds u ᏧᎾ . dt ds И S de T ...
... manner , putting u for in equation ( c ) , we have d2 ( ) dt - S. - P 0 : 94-1-4-9 = d d и de ds du Now dt de dt u2 d Ꮎ de dt = - ( u da ds S du ) ✓ T h2 + 2 из ( And = d2 dt de S • H d dt de = u2 h2 + 2 [ d ds u ᏧᎾ . dt ds И S de T ...
Page 26
... manner to find the value of s . hrob 313 -1 Proceed 37. But , in order to carry on this process with facility , it is necessary to establish some rule with regard to the comparative value of small quantities , so that , fixing upon some ...
... manner to find the value of s . hrob 313 -1 Proceed 37. But , in order to carry on this process with facility , it is necessary to establish some rule with regard to the comparative value of small quantities , so that , fixing upon some ...
Page 53
... manner . Thus , y is the longitude of the node , if the second term did not exist , and B the longitude of the Sun , when 00. ( ca. ) . Now , during the description of a portion only of the orbit , we may , without material error ...
... manner . Thus , y is the longitude of the node , if the second term did not exist , and B the longitude of the Sun , when 00. ( ca. ) . Now , during the description of a portion only of the orbit , we may , without material error ...
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Common terms and phrases
analyzing plate angle angular velocity attraction axis bright co-ordinates coefficient common light Consequently cos² crystal curve different colours differential direction displacement distance disturbing force dR dR dt dt dt Earth ellipticity equal equation expression extraordinary ray front ƒ² glass Hence integration intensity investigation length longitude lunar lunar precession motion multiplied nearly Newton's rings node nutation ordinary ray parallel particles perigee perihelion perpendicular plane of incidence plane of polarization plane of reflection precession principal plane produced PROP proportion quantity radius vector refraction rhombohedron rings shew sin² spheroid suppose surface theory tion undulation vibration vt-x wave
Popular passages
Page 257 - We have, every reason,' he observes, ' to think that a part of the velocity of sound depends upon the circumstance that the law of elasticity of the air is altered by the instantaneous development of latent heat on compression, or the contrary effect on expansion. Now, if this heat required time for its development, the quantity of heat developed would depend...
Page 257 - Now, if this heat required time for its development, the quantity of heat developed would depend upon the time during which the particles remained in nearly the same relative state, that is, on the time of vibration. Consequently, the law of elasticity would be different for different times of vibration, or for different lengths of waves ; and therefore the velocity of transmission would be different for waves of different lengths. If we suppose some cause which is put in action by the vibration...
Page 306 - ... we easily arrive at this simple hypothesis explaining the whole : Common light consists of undulations in which the vibrations of each particle are in the plane perpendicular to the direction of the wave's motion. The polarization of light is the resolution of the vibrations of each particle into two, one parallel to a given plane passing through the direction of the wave's motion, and the other perpendicular to that plane ; which...
Page 198 - In planetary theory the adopted ratio of the mass of the Earth to the mass of the Moon is...
Page 229 - ... intensity of either. These intervals of silence and greatest intensity, called beats, will recur every second, but if the notes differ much from one another, the alternations will resemble a rattle ; and if the strings be in perfect unison, there will be no beats, since there will be no interference. Thus by interference is meant the coexistence of two undulations, in which the lengths of the waves are the same ; and as the magnitude of an undulation may be diminished by the addition of another...