not the first to question glacial motion theories

It was after producing a short note (Croll, 2004) arguing that a thermal ratchet process described in the most recent postings, might help explain at least some forms of glacial ice movement that I became aware of a similar model having been proposed by Henry Moseley as early as 1855 (Moseley, 1855). Curious as to why his intriguing theory seems to have been almost entirely lost from the literature on glacial flow I was compelled to look back at the fascinating debate that occurred on this issue in the years following Moseley’s publication dealing with glaciers. For me the results of this search have been both encouraging, in that I have distinguished company sharing the view that thermal effects may be important in the movement of glaciers, and genealogically quirky. It is though, for the former reason that I thought others might be interested in a summary of the issues that this debate highlighted. Some of these issues, as I will explain, appear to have been misunderstood at the time and a number would seem to be still not satisfactorily resolved today.

MOSELEY AND THE THERMAL MOVEMENT OF LEAD SHEETS:

Henry Moseley would today be regarded as something of a child prodigy. At the age of 17 years, as a pupil at the naval school in Portsmouth, he had his first scientific paper published in the Philosophical Magazine, attempting to measure the depth of the cavities being observed on the surface of the moon. After a distinguished undergraduate career at Cambridge, and having been ordained in 1827, Moseley worked as a curate at West Monkton in Somerset. As was common this did not prevent him from continuing his studies of mathematics and mechanics, and he produced his first book on hydrostatics in 1830. His reputation saw him appointed as the first professor of natural and experimental philosophy and astronomy at the newly established King’s College London. In that capacity he made a number of important contributions to development of practical science and engineering. In 1853 he was with royal patronage appointed to a residential canonry at Bristol Cathedral. While his mind was undoubtedly on other matters he continued his passion for mechanics. He was for example attracted to the phenomenon whereby the lead sheeting on the southern facing roof of the choir chapel at Bristol Cathedral was over time found to move down the slope and end up in the guttering, whereas that on the northern slope suffered no such fate. In 1855 he prepared the article listed below reporting the fact of the descent of a solid body on an inclined plane when subjected to alternations in temperature. Very probably stimulated by the contemporaneous discussions as to the causes of the motions of glacial ice, he attempted to show that the simple formula derived for the movement of a lead sheet might also account for the observed movement of alpine glaciers. It was these rather simple calculations purporting to show that alternations in temperature could also explain the motion of glacial ice that sparked off a controversy that was to run intermittently for the next 15 years. Before addressing Moseley’s contentious application of his theoretical model to glaciers it might be helpful to briefly outline his arguments relating to the motion of a solid sheet.

Figure 1 reproduces Moseley’s diagrams used in his 1855 paper to derive a formula for the descent of a mass due to alternations in temperature. These refer to a “uniform bar AB placed on an inclined plane” which, when “subject to extension from increase of temperature, a portion XB will descend, and the rest XA will ascend; the point X being where they separate being determined by the condition that the force requisite to push XA up the plane is equal to that required to push XB down it.” By invoking simple considerations of equilibrium with the down-slope component of the weight of the sheet, Moseley shows that the point B will have descended by amount u+, given by

eqn (1)  see Figures

In this expression I have used a notation similar to that adopted in a recent independent derivation (see eqn (1) of the posting "thermal ratchet models of glacial motion", which is somewhat different from that employed by Moseley; α represent the coefficient of linear expansion of the solid, T the increase in temperature, l the length of the bar AB, θ the inclination of the rod to the horizontal and θ* the limiting inclination of the rod before kinematic friction will result in sliding under gravity alone. To allow direct comparison with eqn (1) of which relates to a sheet of unit width, it might be observed that

eqn (2) see Figures.

where q is the kinematic friction force per unit area between the rod and the slope, γ is the unit weight of the solid rod, and t is the thickness of the sheet.

Moseley goes on to observe that on the basis of Figure 2, also reproduced from Moseley (1855), “when contraction takes place the converse of the above will be true. The separating point X will be such, that the force requisite to pull XB up the plane is equal to that required to pull AX down it. BX is obviously equal to AX in the other.” Hence, by the time the bar has returned to its former temperature, “the point B (Figure. 2) will by this contraction be made to descend through the space”,u- , where

eqn (3) see Figures

On this basis the total descent of “B by elongation and contraction is therefore determined by the equation

eqn (4) see Figures

This process, referred to at the time of its derivation as the “crawling theory” (to distinguish this form of motion from that I believe to be of perhaps even greater importance in many glaciers, I had adopted the terminology “gravity ratchet” (Croll, 2004)), was followed up in early 1869 by a paper, a summary of which was read before the Royal Society in January 1869 (Moseley, 1869a), that described a somewhat more elaborate theoretical model for the motions of a solid body on an inclined plane subject to fluctuations in temperature. In this fairly lengthy, but today difficult to follow discussion, Moseley again established how the combined influences of the gravitational forces acting on the inclined mass of a solid body, together with the effects of shear breaking expansion and contraction forces caused by changes in temperature, are able to account for the downward, incremental, motions of a solid sheet such as the lead on the Cathedral roof. Neither temperature nor gravity acting alone would it was argued be sufficient to cause these motions. Each was found necessary but not sufficient to induce the downward motion. In this important but largely forgotten contribution Moseley reports a simple experiment he undertook in his back garden between 16th February and 28th June, 1858. Since it would appear that this experiment has not been repeated*, and because it was to form the backdrop to the later arguments concerning the motions of glacial ice, the following is a brief description of what he did and what he found.

On a 9 foot plank of specially prepared wood (to be specific Deal) of width 5 inch, he placed an equally long sheet of lead having a thickness of 1/8th inch. To prevent it falling off, the lead sheet was carefully turned over each of the longitudinal edges in a way that would not impede its downward movement by causing it to stick to the plank. The plank with the lead sheet was fixed at an inclination of 18o 32’ to the southern facing wall of Canon Moseley’s house. It was arranged to allow convenient recording, to 1/100th of an inch, of the positions of the bottom edge of the lead “every morning between 7 and 8 o’clock, and every evening between 6 and 7 o’clock”. As confirmation of his explanation for the observations on the movement of the lead sheeting on the Cathedral roof, he found “on the days when the thermometer in the sun varied its height rapidly and much (as on bright days with cold winds, or when clouds were driven over the sun) that the descent was greatest. So remarkably indeed was this the case, that every cloud which shut off the sun for a time from the lead, and every cold gust of wind that blew upon it in the sunshine, seemed to bring it a step down. On the contrary, when the sky was open and clear, and the heat advanced and receded uniformly, the descent was less … It was least of all on days when there was continuous rain. During the night it was often imperceptible.” And as Moseley remarked any night time movement was most probably the result of the sunshine in the spring to summer months experienced before his early morning readings or after those in the evening. The detailed results tabulated (Moseley, 1869b) for the month of May are indeed convincing with regard these overall conclusions. That alternations in temperature acting on a solid having a down-slope gravitational force less than that required to overcome the frictional resistance (the slope required for friction between the lead and the wood to allow gravity alone to cause motion was 22o 30’) seems clear. It is surprising therefore that this experiment does not appear to have been repeated* and the fact of its occurrence largely overlooked in most of the subsequent discussion of the flow of glacial ice.



* This is no longer the case. Over the academic year 2007-08 a pair of UCL undergraduate students repeated the experiments taking quantitative readings of the downward motions of the lead sheet when subject to precisely controlled levels of thermal fluctuations. Their results are reported in Kaimakamis and Patel (2007)

References mentioned in blog:

Croll, James G. A. (2004) “The Movement of Glaciers”, submitted to the J of Glaciology, 2004.
Kaimakamis, A, and Patel, K (2007) Pulsatile motions of solid bodies due to thermo-mechanical action, thesis presented in partial fulfillment of MEng Degree, Dept. of Civil Engng., University College London.

Moseley, Henry. (1855) “On the Descent of Glaciers”, Proc Roy Soc, 7, 1855, 333-342.
Moseley, Henry. (1869a) “On the Mechanical Possibility of the Descent of Glaciers by their Weight only”. Received, Oct. 1868, read before Royal Society, 7 Jan., 1869, reported Phil. Mag., 37, 229-235. Proc. Roy. Soc., xvii, Jan., 1869, pp202-207.
Moseley, Henry. (1869b) “On the Descent of a Solid Body on an Inclined Plane when subjected to alternations of Temperature”, Phil Mag, S.4, 38, August 1869, 99-118.
Moseley, Henry. (1869c) “On the Mechanical Impossibility of the Descent of Glaciers by their Weight only”, Phil Mag., 37, no 208, May, 1869, 363-370.