Reply to Prof. Kelland’s Letter of November 1842. 23 
page writing 8p = éacos§ + 8y cos ¢ + 82 cos fp, which of 
course he would not have done had @p been equalto dy. At 
page 166 he gives é p the value @ z, that is, he supposes the axis 
of x to be the axis of transmission; and a little below he gives 
8 p the value 6 2, that is, he supposes he aais of z that of trans- 
mission; thus deducing the corresponding results from his 
previous investigation in a manner which can only be justified 
by the supposition that the axis of y was not the axis of trans- 
mission. At page 179 he for the fst time really does suppose 
the axis of y to be that of transmission; and this hypothesis is 
introduced exactly as a person would introduce it who had all 
along supposed his previous investigations independent of the 
hypothesis ; his words are, * suppose, then, to fia’ zdeas that the 
wave is transmitted along the axis of y.” Now if this had been 
the hypothesis through the previous part of the paper, why 
was it here necessary to state it for the first time in order to 
fix ideas? ‘The ideas would have been fixed upon it from the 
first. Is it not clear from this sentence, after what is said 
above, that the Professor did not suppose the axis of y to be 
the axis of transmission in the early part of his paper, to which 
only our remarks were directed ? 
2. The Professor says that the quantities we have quoted 
are not all equal to »*, but that the second of them is equal 
to ,?. 
It is at least very singular that no such quantity as 7/ is 
mentioned or alluded to, or its existence implied in the whole 
memoir; which is almost inconceivable if the Professor’s MS. 
had contained it. Now it so happens that the integrals of 
the three differential equations under discussion are written 
down in the middle of page 163, and those integrals are cor- 
rect, only on the supposition that the coefficients are all equal; 
unless indeed we suppose that the transcriber and printer have 
made another mistake. In lines 2 and 13 the author twice in- 
forms us what is the value of n*, the information being neces- 
sary in order to make his readers understand the meaning of 
the integrals, but he makes no allusion to an 7, though, had 
there been such a quantity, information of its value was as 
necessary as in the case of n*. Line 4 of the same page is 
irreconcilable with line 2, unless the author had supposed the 
coefficients all equal. And, had they been unequal, there 
would have been éwo velocities of transmission, a circumstance 
which it would have been absolutely necessary to notice to 
prevent confusion of ideas, when the author at pages 164, 
165, 167, ... speaks of the velocity of transmission. 
3. In the places we have quoted, and some others, the 
equality of the coefficients is implied in such a manner that 
