&96 A Reply to Earl Stanhope, on his Defence of 



ship's pen had occasioned his appearing to advance a doc- 

 trine, so opposite to all that had heen demonstrated by Dr. 

 Smith, Dr. Robison, and a host of other mathematical 

 writers ; but his defence of the same in pages 150 to 152, 

 vol. xxviii., precludes any such charitable suppositions in fu- 

 ture. The scientific terms, or rather the " scientific jargon/' 

 of His Lordship, I certainly do not understand, if by that 

 he means, that I am to receive them, in opposition to the 

 authorities above quoted, by whom His Lordship was cer- 

 tainly not " obliged to use" his new terms, for, they have 

 uniformly and consistently used pulses or vibrations for 

 what His Lordship would now for the first time call beats ; 

 and what he would exclusively call beatings they have gene- 

 rally called beats, but have sometimes used beatings as sy- 

 nonymous therewith. 



Before His Lordship took pen in hand on this subject, I 

 well knew that the rate of beating increased along with every 

 increase of the imperfection of a consonance ; but His Lord- 

 ship is the only one I ever heard assert, that it increases 

 " As the imperfection increases " which is no more true, 

 than that the sine of an angle increases as the angle increases, 

 or that gravity increases as the distance decreases. His 

 Lordship refers (page 151,) to an example, and attempts to 

 prove, that the triequal quints DA, one an octave above the 

 other, beat equally quick : let us therefore see what evidence 

 numbers furnish in this case. By referring to my table in 

 page 5, vol. xxx. it will appear, that the two D's vibrate or 

 excite 134*44 and 268*88 complete pulses in the air in one 

 second of time respectively, and the two A's 200*83 and 

 401*66 pulses respectively, and by using these in the proper 

 theorem for the purpose, we get 1*666 beats per second 

 made by the lower, and 3*333 beats per second by the upper 

 of these tempered or tri-equal quints ; the one just double of 

 the other, instead of their being equal as our noble author 

 has maintained ; and thus we see, that no " beating between 

 the two beatings" could in this case happen even in theory, 

 and certainly none in practice could be expected ; for who 

 besides Earl Stanhope ever talked of hearing beatings, be- 

 tween two noises which themselves occur but If and 3^ 



times 



