The Philosophical magazine; a journal of theoretical, experimental and applied physics . ) , # ^ rf|_^„,„ ,,,^ By the insertion of this value of p\, equation (37) is changed VJl. L d(]^ ^ dq^, dq^ J^ dt ^ As many equations of this form arc obtained as the given vari-ables q^, 72, r/a, &e.; and the work can be supi)lemented by eli-minating from them the inditerminate coefficients. It is tlius shonn in a general way how the equations which Mr. F. P. Purvis on Amslcrs Planimeter. 11 serve for the determination of the virial can be formed with theemployment of any variables; and with this I think
The Philosophical magazine; a journal of theoretical, experimental and applied physics . ) , # ^ rf|_^„,„ ,,,^ By the insertion of this value of p\, equation (37) is changed VJl. L d(]^ ^ dq^, dq^ J^ dt ^ As many equations of this form arc obtained as the given vari-ables q^, 72, r/a, &e.; and the work can be supi)lemented by eli-minating from them the inditerminate coefficients. It is tlius shonn in a general way how the equations which Mr. F. P. Purvis on Amslcrs Planimeter. 11 serve for the determination of the virial can be formed with theemployment of any variables; and with this I think I may onthe present occasion be satisfied, without entering upon specialapplications of the equations—which may be of very variouskinds, andj hence, would lead to extended discussions. II. On Amslers Planimeter. Bij F. P. Pukvis, Esq.^ THE following is a simple and thoroughly general explana-tion of the action of this perplexing little , for simplicity and greater generality, that the instru-ment consisted simply of the straight bar A 13, of length /, car-. rying a pencil at each end, A and B ; and suppose any lines A a,B b were traced out by these pencils : we will consider how thearea AabB may be expressed in terms of / and the motion ofsome point in the line A B. Let the motion from A B to a /9 represent an elementarymotion of the bar, the centre of it C moving from C to 7, andthe bar turning about y through the angle dO; let dns= thenormal distance from y to A B : this motion may be consideredto take place in two parts:—1st, the motion of AB parallelto itself into the position xy ; 2nd, the motion of AB about itscentre into the position a/3; the required area A«/SB is, inthis elementary motion, equal to the area (^Idn), sincethe area yux = the area y ^y, and the areas Kux and B/3?/are negligible with respect to Idn, being the product of two in-finitesimal quantities, while Idn is the product of one infinitesi-mal quantity (comparable with ea
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