A Treatise On Attractions Laplaces Functions And the Figure of the Earth
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To find these let xyz be the co-ordinates to any element of the mass, rdw be the polar co-ordinates to the same. Then the mass of this element = pr^dndwdr, JJL = cos 0. Also The terms are here arranged as Laplace's Functions. (See Art. 39, Ex. 4. ) r= radius of any stratum =a\l + e (- ^ 2 Jh (Art. 77) ; [ r 4, 1 f a . '. Pr*dr = - p Jo 5J r d. R 5 -j da 4 d. A 5 efl 2 +T- [;- c?a 3 = o- (a) + ^ (a) - /* 2 suppose ; -A = ^ (a) '^ - /^ 2 {- ^* + (1 - & ^s 2 a) Also C - cr (a), neglecting the smal...l term -\Jr (a). O 108 FIGURE OF THE EARTH. XT r / N f a d. A 5 e, 5, , N / m\ . Now y]r (a) = I p j da ~ a
To quickly assess the difficulty of the text, read a short excerpt:
To find these let xyz be the co-ordinates to any element of the mass, rdw be the polar co-ordinates to the same. Then the mass of this element = pr^dndwdr, JJL = cos 0. Also The terms are here arranged as Laplace's Functions. (See Art. 39, Ex. 4. ) r= radius of any stratum =a\l + e (- ^ 2 Jh (Art. 77) ; [ r 4, 1 f a . '. Pr*dr = - p Jo 5J r d. R 5 -j da 4 d. A 5 efl 2 +T- [;- c?a 3 = o- (a) + ^ (a) - /* 2 suppose ; -A = ^ (a) '^ - /^ 2 {- ^* + (1 - & ^s 2 a) Also C - cr (a), neglecting the smal...l term -\Jr (a). O 108 FIGURE OF THE EARTH. XT r / N f a d. A 5 e, 5, , N / m\ . Now y]r (a) = I p j da ~ a
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