June 27, 1901] 



NA TURE 



207 



Stress — Its Definition. 



The important word stress, denoting a fundamental conception 

 in dynamics, is one as to the meaning of which no haziness or 

 doubt ought to be permitted by the scientific community. 



In your review of Prof. Gray's " Physics," the reviewer criticises 

 the use made of the word in question, and makes the statement : 

 " .Strictly a stress is measured by the force applied per unit of 

 area ; it has the dimensions of force divided by the square of 

 a length. . . ." 



No authority is quoted to justify this statement. Does such autho- 

 rity exist ? On collating the statements regarding the meaning 

 to be attached to the word in some of the most authoritative works 

 in the language, I have found a considerable want of agreement. 



Going back to Rankine, who is credited with having intro- 

 duced the word stress as a technical term into mechanics, we 

 find the following paragraph in his paper " On Axes of Elasticity 

 and Crystalline Forms " (1S55) : 



" In this paper the word Strain will be used to denote the 

 change of volume and figure constituting the deviation of a 

 molecule of a solid from that condition which it preserves when 

 free from the action of external forces ; and the word Stress 

 will be used to denote the force, or combination of forces, which 

 such a molecule exerts in tending to recover its free condition, 

 and which, for a state of equilibrium, is equal and opposite to the 

 combination of external forces applied to it." 



Again, in his " Applied Mechanics '' (i860), we find, in § 86 : 



' ' Stress, its Nature ami Intensity. — The word Stress has been 

 adopted as a general term to comprehend various forces which 

 are e.xerted between contiguous bodies, or parts of bodies, and 

 which are distributed over the surface of contact of the masses 

 between which they act. The Intensity of a stress is its amount 

 in units of force, divided by the extent of the surface over 

 which it acts, in units of area. " 



Then, in § 87, Rankine classifies three kinds of stress, 

 <l) Tlirtist or Pressure (2) Pull or Tension, and (3) Shear, or 

 Tangential Stress. 



Further, in j§ 96 : " Internal Stress in General. — If a body 

 be conceived to be divided into two parts by an ideal plane tra- 

 versing it in any direction, the force exerted between those two 

 parts at the plane of division is an internal stress,^'' 



Clerk Maxwell, in "Matter and Motion," Art. 37, says: 

 ■"The mutual action between two portions of matter 

 receives different names according to the aspect under which 

 it is studied, and this aspect depends on the extent of the 

 material system which forms the subject of our attention. 



" If we take into account the whole phenomenon of the 

 action between two portions of matter, we call it Stress. This 

 stress, according to the mode in which it acts, may be described 

 as Attraction, Repulsion, Tension, Pressure, Shearing Stress, 

 Torsion, cic." 



Again, in Art. loi. — " Stress. 



" The next step in the science of force is that in which we 

 pass from the consideration of a force as acting on a body, to 

 that of its being one aspect of that mutual action between two 

 bodies, which is called by Newton Action and Reaction, and 

 which is now more briefly expressed by the single word Stress." 



Thomson and Tait's "Natural Philosophy " (1S67), Art. 65S 

 <referring to the theory of elastic solids). "... the forces 

 called into play through the interior of a solid when brought 

 into a condition of strain. We adopt, from Rankine, the term 

 stress to designate such forces, as distinguished from strain 

 defined to express the merely geometrical idea of a change of 

 volume or figure." 



Thomson (Kelvin) in the 9th edition of the " Encyclopaedia 

 Britannica," article "Elasticity": Mathematical Theory, 

 Chap. i. " Def. A stress is an equilibrating application of 

 force to a body." 



Tait, in "Newton's Laws of Motion" (1S99), Art. 45 : 



' ' A pair of equal and oppositely directed forces, acting in 

 one line, is a particular case of what is now called a Stress. 

 The stress along a stiff rod (necessarily the same across every 

 transverse section) may be either a Thrust or a Tension, that 

 along a string or chain can be a Tension only. [But the term 

 stress, in its widest signification, means any system of equili- 

 brating forces.]" 



" In a fluid the stress at any point is generally what is called 

 Hydrostatie Pressure., whose characteristic is that the stress is 

 the same across a small given plane area. ... In all these 

 cases the stress is measured by the amount per unit area of the 

 surface on which it is exerted." 



NO. 1652, VOL, 64] 



Love, in " Theoretical Mechanics" (1897), Art. 122, defines 

 the stress at a point A across a plane interface passing through 

 A, as the force per unit area exerted across a small area whose 

 centroid is A. 



From the preceding quotations there would seem to be a 

 double ambiguity in the present usage of the word stress. 



Firstly, it may be used to denote the whole mutual action 

 between two portions of matter, A and li, say, in which case 

 it would be specified by stating the force or system of forces 

 exerted either by A upon B, or by B upon A ; or it may be 

 used to denote the force per unit area exerted by A upon B. 

 The latter is clearly less widely applicable (torsional stress, e.g., 

 cannot be reckoned per unit area), and corresponds to what 

 Rankine calls intensity of stress, or what is by some teachers 

 appropriately named unital stress. 



Secondly, the term stress may be defined as in the " Elasticity " 

 article in the Encyclopaedia to bean " equilibrating application 

 of forces," or, as by Maxwell, to be the complete phenomenon 

 including the "Action and Reaction" of Newton's Third Law 

 of Motion. 



To my mind there can be no doubt as to the greater usefulness 

 of the latter definition, even though the former may be more con- 

 sistent with some of Rankine's statements on the subject. It will 

 be noted that in my quotation from Prof. Tait's work there seems 

 to be a vacillation between the two meanings (what is meant 

 there by " stress across a transverse section," or " stress across 

 a small plane area" ?), though he explicitly adopts the former 

 alternative; and in the paragraphs of "Thomson and Tait " 

 immediately following that quoted above there seems to be a 

 similar shifting of ground in applying the term, while Maxwell's 

 use of the word is consistent with his clear definition. This in 

 itself argues strongly for the Maxwellian use of the word. 

 Besides, the " equilibrating application" definition would seem 

 to leave us in the lurch when we wish to name the internal 

 forces of bjdies not in equilibrium. And all who have had 

 much experience in teaching dynamics to beginners must appre- 

 ciate the help which the word in its Maxwellian sense ali'ords in 

 getting the student to see the difference between reaction and 

 equilibrant, and to stop asking one such conundrums as " If 

 action and reaction are equal, why does a body move?" And 

 of course it is precisely the beginner for whose benefit we should 

 take the trouble to be consistent in the use of words. 



Let me conclude by ofl'ering the following suggestions for 

 what they are worth : — 



(i) Let the word "stress" be defined and used as in Maxwell's 

 " Matter and Motion." 



(2) Let " unital stress" or "unital stress at a point across a 

 plane" be used as defined in §122 of Love's "Theoretical 

 Mechanics." R. F. Muiuhead. 



Glasgow, June 4. 



I HAVE to thank the Editor for his courtesy in allowing me 

 to see Mr. Muirhead's interesting letter. I quite agree that the 

 meaning attached to the word "stress" by eminent writers 

 during the fifty years from the time of Rankine to the present 

 day has varied. At the same time, I observe that the only two 

 definitions of the " measure of stress " which are quoted are of 

 recent date, and both state clearly that a stress is measured by 

 the force per unit area, though I find this same definition in 

 Thomson and Tait, 1867 edition. Art. 661, a few lines below 

 the quotation given by Mr. Muirhead. I think, then, I may 

 claim sufticient authority for my statement, "Strictly a stress 

 is measured by the force applied per unit of area," and for the 

 doubt which I expressed as to the desirability of introducing 

 the word "stress" as practically synonymous with "force" in 

 a discussion of Newton's second law of motion. 



While I share Mr. Muirhead's regret at the limitation thus 

 imposed on the meaning of a general term " stress " as indicat- 

 ing the mutual action between two bodies, I hardly think his 

 suggestion to distinguish between "stress" and "unital 

 stress" will meet the case. Re\ie\ver. 



Hybrid Oochromy, with a Note on Xenia. 



In a note on " Telegony, Xenia and Hybrid Oology,"' which 

 appeared in Natural Science (vol. xiv. p. 394, 1899), I intro- 

 duced the last-mentioned term to denote a singular phenomenon 



1 Xl the request of the editor I have altered the term hybrid oology to 

 hybrid oochromy, which 1 agree is in many ways betler, except that it would 

 seem to refer to the coloration of the e^g t ) the exclusion of its micro- 

 scopic s 



