Review of Mathematical Researches. 1 2 1 



contractions which we daily and liourly exercise, how few are voluntary in 

 the strict sense!* Nor is it very easy to separate the latter from those 

 which derive their character of voluntariness from the mere circumstance 

 that they are not inconsistent with, or might be suspended by our will or 

 desire. Perliaps the readiest mode of ascertaining them may be to select 

 those which certainly do take place, without any efficient desire, and thus 

 to arrive at the others by what our neighbours call " la voie d'exclusion." 



It may seem at first sight, with reference both to what has been already 

 advanced, and to what remains to be said, that the nervous connections of 

 muscles have been overlooked ; but a little reflection will shew that our 

 remarks upon the action of muscles, apply equally to the nerves which 

 excite those organs. A change in the nerve supplying a muscle, must 

 undoubtedly take place before the latter can act in obedience to the stimu- 

 lus of desire, or of any other of the causes to be mentioned hereafter. 

 When we speak of muscular contraction as following immediately upon 

 desire, we by no means wish to intimate that the muscle contracts without 

 a prior affection of its nerves, and indeed of that part of the central nervous 

 organ with which they are connected ; — we mean only that desire is the 

 last state of consciousness, or that which is immediately prior to that series 

 of organic phagnomena, which constitute nervo-muscular action. 



The motions independent of desire, may be arranged under the following 

 heads : — 



J. Motions immediately consequent upon certain organic conditions, 

 without sensation. 



2. Upon simple internal sensations. 



3. Upon external sensations. 



4. Upon emotions. 



5. Upon a vague principle called imitation. 



6. Upon habit. 



(To be concluded.) 



• It might perhaps obviate confusion, to characterize such motions as volitional. 



REVIEW. 



Mathematical Researches, Parts I. 11. III. By G. B. Jerrard, A. B. 

 1832, 4, 5. Strong, Bristol. 



Such is the unattractive title by which the author sends forth his spe- 

 culations on a refined and ditficult subject ; a subject on which it is no- 

 torious that the ablest mathematicians have so lost their labour, that many 

 may be deterred from reading, by a persuasion that the task is hopeless. It 

 is not quite accordant with the plan of this Journal to enter on tiie abstruse 

 parts of analysis j nor can we afford much space at present. Nor are we 

 apprehensive that Mr. Jerrard needs our praise j as the talent disi)layed in 

 these unpretending tracts is such as will sooner or later be acknowledged. 



No. 2.— Vol. I. K 



