Mechanism of the HeavensJ. Murray, 1831 - 621 pages |
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Page 12
... functions of the distance only . All the forces in nature are functions of the distance , gravity for example , which varies inversely as the square of the distance of its origin from the point of its appli- cation . Were that not the ...
... functions of the distance only . All the forces in nature are functions of the distance , gravity for example , which varies inversely as the square of the distance of its origin from the point of its appli- cation . Were that not the ...
Page 15
... function of x , y , z ; hence , R & r = R , Su 2 √ ( ) ' + ( - ) ' + ( - ) ' ; and if Sy R , λ = δι 2 δι 2 δι + + Sx бу then R , & r becomes Adu , and the equation of the equilibrium of a particle m , on a curved line or surface , is ...
... function of x , y , z ; hence , R & r = R , Su 2 √ ( ) ' + ( - ) ' + ( - ) ' ; and if Sy R , λ = δι 2 δι 2 δι + + Sx бу then R , & r becomes Adu , and the equation of the equilibrium of a particle m , on a curved line or surface , is ...
Page 17
... functions by the gradual variation of some of their elements , which had previously been regarded as constant . In ... function may be illustrated by problems of maxima and minima , of which there are two kinds , one not sub- ject to the ...
... functions by the gradual variation of some of their elements , which had previously been regarded as constant . In ... function may be illustrated by problems of maxima and minima , of which there are two kinds , one not sub- ject to the ...
Page 18
... function expressing the curve , remains the same ; but in the other case , the form of the func- tion whose maximum or minimum is ' required , is variable ; for , let M , N , fig . 16 , be any two given points in space , and suppose it ...
... function expressing the curve , remains the same ; but in the other case , the form of the func- tion whose maximum or minimum is ' required , is variable ; for , let M , N , fig . 16 , be any two given points in space , and suppose it ...
Page 22
... function : but the equations Xdt = d'y da ; Ydt = ; Zdt = dt dt still subsist ; and therefore also equation ( 6 ) . d2z ' 9 dt ' Now however , there are not enough of equations to determine x , y , z , in functions of t , because of the ...
... function : but the equations Xdt = d'y da ; Ydt = ; Zdt = dt dt still subsist ; and therefore also equation ( 6 ) . d2z ' 9 dt ' Now however , there are not enough of equations to determine x , y , z , in functions of t , because of the ...
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Common terms and phrases
A₁ action angle ascending node attraction axes axis B₁ becomes c'mv centre of gravity centrifugal force co-ordinates coefficients comets computed conic sections consequently cosines curve density depending determined differential direction disturbing forces dR dR dt dt earth eccentricity ecliptic elements epoch equal equilibrium equinoxes expression fixed plane fluid functions give hence inclination indefinitely small integral Jupiter latitude mass mean anomaly mean distance mean longitude mean motion moon moon's move nearly observation omitted orbit of Jupiter oscillations parallax particle perigee perihelion periodic inequalities perturbations planets preceding equation preceding values radius vector ratio regard rotation satellites Saturn secular inequalities secular variations sidereal sine spheroid square substituted surface system of bodies terrestrial theory tion true longitude Uranus velocity whence zero