96 Mr. Hunt on the Itifluence of Light on Plants. 



In the Mecanique Anatytique (part 2. sect. xi. art. 18) the 

 following sentence occurs: — " Lorsque le mouvement com- 

 mence du repos, on a alors p = 0, q = 0, r = 0, lorsque t = 0, 

 done p d x + qdy + rdz sera integrable pour ce moment." 

 The inference in the last clause evidently rests on the ana- 

 lytical theorem, that p d x + q dy + r dz may be considered 

 an exact differential whenever p = 0, q = 0, and r = 0, which 

 I have just shown to be untrue. The assertion of Lagrange 

 has been adopted by subsequent writers, and has occupied a 

 very important place in analytical hydrodynamics, the manner 

 of treating a large class of problems entirely depending on the 

 assumption of its truth. It is remarkable that so unfounded 

 a theorem should have remained so long unquestioned. The 

 omission of it in the last edition of Poisson's Mecanique is 

 perhaps an evidence that that author considered it incapable 

 of proof. The only attempt at a proof that I have met with 

 occurs in the Cambridge Philosophical Transactions (vol. vii. 

 part 3. p. 462), where it is asserted that when u = 0, v ;= 0, 

 and to = for a given value of t (for instance t = 0), the ex- 

 pression u d x + v dy + to dz " may be regarded as a com- 

 plete differential with respect of x, y, z, of an arbitrary func- 

 tion of t." To this I answer, that since u, v and to each 

 vanish when t = 0, we may assume that u dx + v dy + ivdz 



= f (U d x + V dy -f W dz), the quantity in brackets not 

 vanishing when / = 0. If now for / = u d x + v dy + to d z 

 may be regarded as a complete differential with respect to .r, 

 y and z of a function of t only, in the same case U d x -f- V dy 

 + W d z may also be regarded as such a differential. But 

 the latter quantity does not vanish when t = ; which is 

 absurd. The argument of this writer consequently rests on a 

 false assertion. 



I think I have now said enough to show that no confidence 



whatever can be placed in any l'esearches in hydrodynamics 



which depend on the assumption that u d x + v dy -f to d z is 



always an exact differential when the motion begins from rest. 



Cambridge Observatory, Dec. 18, 1843. 



XVII. On the Itifluence of Light on Plants. By Robert 

 Hunt, Secretary to the Royal Cornwall Polytechnic Society. 



To Richard Taylor, Esq. 

 Dear Sir, 



IN the Philosophical Magazine for January is a communi- 

 cation from Dr. D. P. Gardner on the influence of Light 

 on Plants, in which he states that in 1840 I published "the 

 most decided results to the effect, that blue light alone causes 



