AnalyticalDetermination of the Laws of transmitted Motion. 267 



refracted, in the precise degree which prismatic observations 

 indicate. 



This inquiry, of some difficulty but of the highest interest, 

 whichever way it may turn out, I have been engaged in pro- 

 secuting, and hope soon to be able to bring the results before 

 the public. 



Meanwhile I would observe, with reference to the formula, 

 that in deducing it from M. Cauchy's theory, I by no means 

 intend to affirm that it cannot be deduced on any other prin- 

 ciples. I have, in fact, heard it stated that an equivalent ex- 

 pression may be obtained on less complicated considerations. 

 It must, however, be allowed that no such deduction has been 

 specifically made : and any mathematician who would make 

 it, would be conferring a vast benefit on this branch of sci- 

 ence, if, indeed, it should be found to stand the test of com- 

 parison with exact observations ; if it should not, it will be- 

 come the only course to attempt some further modification of 

 first principles until we can deduce an expression which will 

 represent the law of nature. 



XLIV. On the Analytical Determination of the Laws of trans- 

 mitted Motion. By the B.ev, James Challis, M.A.* 



TN the Report on the Analytical Theory of Hydrostatics and 

 ^ Hydrodynamics which is printed in the second volume of 

 the Transactions of the British Association, I have ventured, 

 under a persuasion that the cause of scientific truth might be 

 benefited, to express some doubt of the accuracy in principle 

 of the received method of determining the nature of trans- 

 mitted motion. The question will be allowed to be an im- 

 portant one by all who have turned their attention to this part 

 of the application of analysis; but as it is somewhat of au abs- 

 truse nature, I fear that what is there said may not be per- 

 fectly understood without further illustration. For this reason 

 1 propose in the present communication to adduce a simple 

 instance, which may serve to exhibit both the received method, 

 and that which, as I conceive, ought to be substituted in the 

 place of it. 



The instance here selected is that of the transmission of 

 motion along an elastic chord fixed at both ends : this will 

 answer the purpose intended as well as an instance of trans- 

 mission of motion in fluids. Let the chord in a state of rest 

 be in a horizontal straight line ; and at any position between 

 the two extremities, let a limited portion, equal in length to 



* Communicated bv the Author. 

 2M 2 



