170 PROFESSOR KELLAND, ON THE 



we obtain, if we write 2 A^~ l for,/ (as), a for U ; 



f &- 1 d% sin — (vt - y/% + a) = ( - Vf&l <p («) dor 



= (— i)>/ sin x ( vt ~ v/ ") rfa ^' 

 and consequently, from the equation above, 



1A{— iy*£ /" sin-^(i^ - y/a)daf l = sin -^ («£ - Va). 



•'A A 



This equation is satisfied (apparently) by making n = 0, A = - , 



and consequently f(%) = — , /(f) = — 2 . 



The case is, however, of too doubtful a character to warrant us in 

 adopting the conclusion. One thing alone I infer from it, that if any power 

 of the distance (not of r) be assumed as the factor, it must be the inverse 

 square. It would require that we should retrace our steps, and investigate 

 the different formulas corresponding to this hypothesis, before Ave could 

 speak positively on the subject. I have only to add to this discussion on the 

 probable coefficient of vibration, that an approximation has been made use 

 of in the value of the distance between the disturbing and disturbed points, 

 as it appears within the circular function. The approximation amounts in 

 fact to supposing the wave elliptical, instead of circular. In the second 

 problem I find that the square of this distance, being substituted within the 

 circular function for the distance itself, leads to precisely the conclusions we 

 have obtained. It is possible, therefore, that the omission of our factor, and 

 the approximation made use of within the circular function, exactly coun- 

 terbalance each other. 



I cannot conclude without repeating my conviction of the importance 

 of results such as those which Professor Forbes has just announced. It 

 appears that the effect of scratching a piece of rock salt, &c. is to alter its 

 power of transmitting heat in such a manner, that heat of a low tem- 

 perature, or dark heat, is transmitted in greater proportions than before. If 



