58 Rev. T. K. Abbott : To what Order 



by (34), (29), and (24) of Part III., is found to have the 

 same value. For the particular case of ^=0 (that is to say, 



the mere integral I dx of each member), the equality is 



proved by (12). 



For the most interesting cases of our physical problem, the 

 solution (13) converges with great rapidity, except for small 

 values of %; and for these the form of the surface is more 

 easily calculated by (2). Numerical illustrations and the 

 working out of the solution corresponding to (13) for the case 

 of b < a are reserved for Part V., which, I am sorry to say, 

 must be set aside for some time. I hope it will appear in the 

 April or May number, and that it, or Part VI., will contain 

 practical illustrations, such as the stationary waves produced 

 by a deeper place, or a less deep place, extending over a con- 

 siderable length of the stream, which is very easily worked 

 out from our solution (40) (48) Part III., for the effect of a 

 single infinitesimal ridge. I hope to pass next to the effect of 

 surface disturbance, with interesting applications to the ques- 

 tion of the towage of a boat in a canal, and the beautiful 

 practical discoveries of Mr. Houston and Mr. Scott Russell 

 referred to at the commencement of Part III. If I succeed 

 in carrying out my intention, this series of Articles on 

 Stationary Waves will end with the investigation of the wave- 

 group produced by a ship moving through the water with 

 uniform velocity, promised at the commencement of Part L; 

 and suggestions for extension in the direction towards the 

 theory of the effect of the wind in generating waves at sea. 



VII. To what Order of Lever does the Oar belong? 

 By Rev. T. K. Abbott, Fellow of Trinity College, Dublin*. 



TO the above question every one who has learned even the 

 elements of Mechanics will reply without hesitation " To 

 the second, the fulcrum being in the water and the resistance 

 acting at the rowlock." I propose to show that the answer is 

 erroneous, and that the vulgar conception of the oar as a lever 

 of the first order is correct. 



In fact, if the supposed answer were correct, it would fol- 

 low — first, that the power would have the advantage over the 

 resistance in the proportion of about 4 to 3 (this being usually 

 about the proportion of the whole length of the oar to the part 

 outside the rowlock) ; secondly, that if we moved the hands 

 nearer to the rowlock we should gradually but slightly dimi- 

 * Communicated by the Author. 



