 Jo When P and Q have been thus found by quadratures, for all values of t, and any particular value of x, by integration by parts on the plan of § 134, we readily find, without farther quadratures, or integrations, expressions for the seven other formulas...  Proceedings of the Royal Society of Edinburgh - Pagina 361door Royal Society of Edinburgh - 1907Volledige weergave - Over dit boek
 | William Thomson Baron Kelvin - 1910 - 581 pagina’s
...wt -}- Q sin at ...... ...... (196) ; where rt rt P=l dqc.QScoq<f>(M,z, q)\ and Q=| dqsin co Jo Jo When P and Q have been thus found by quadratures,...exponential form for </>, given by (137), we find P = {RS} dq cos uqe-™? ; and Q = {RS} /— f °° dq sin aqir™* ............ (198), V g Jo where m — £#/(#... | |
 | William Thomson Baron Kelvin - 1910 - 588 pagina’s
............... (196); where rt n P=\ dqcoawq<f>(a;, z, q); and Q= I dq sin taq<f> (x, z, g)...(197). Jo ' Jo When P and Q have been thus found by quadratures,...in (189), (190). 151. Let us first find P and Q for t=,x,. Using the exponential form for <f>, given by (137), we find and Q={RS} V— Pd? sin wge-""•... | |
 | William Thomson Baron Kelvin - 1910 - 588 pagina’s
............... (196); where re rt P=l dqcos mq<f>(x, z, q); and Q=l dq sin a>q<f>(x, z, q)... (197). Jo Jo When P and Q have been thus found by quadratures,...in (189), (190). 151. Let us first find P and Q for t = oo. Using the exponential form for <f>, given by (137), we find P = {RS} /—jTdq cos aqe—™?... | |
 | Royal Society of Edinburgh - 1907 - 630 pagina’s
...<at . . . (196): where P = I <]q cos <oq<f>(x ,z,q); and Q = / dq sin <og<t>(x , z , <?) (197). JD JQ When P and Q have been thus found by quadratures, for all values of f, and any particular value of x, by integration by parts on the plan of § 134, we readily find, without... | |
 | 1907 - 858 pagina’s
.... . (1%) ; where P= I dq co* caq<f>(.i; ., q) ; Jo ' . (197). and Q=l (]q*mcoq(f)(:r, z, q) «. i) When P and (Q have been thus found by quadratures, for all values of t, and any particular value of a; by integration by parts on the plan of § 1)54, we readily find, without farther quadratures, or... | |
 | Sir Joseph Larmor - 1929 - 596 pagina’s
...(196); where f* f* • " P=\ dq cos(oq<f>(x, z, q)', and Q = I dq sin <aq<f> (x, z, 5). ..(197). Jo Jo When P and Q have been thus found by quadratures,...in (189), (190). 151. Let us first find P and Q for t = oo . Using the exponential form for <j>, given by (137), we find P = {ES\ /— ("dq cos »j«—... | |
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