The Influence of Cell Size, Part 2
The Influence of Cell Size, Part 2
The Bee World – January, 1934 – Pages 2-5
THE INFLUENCE OF CELL SIZE.
(With Illustrations and Table of Data by M. Baudoux, Tervueren, Belgium).
In April last we published a description by M. Baudoux of his work on the enlargement of the bee by the use of large-cell foundation (THE BEE WORLD, XIV, p. 37). Through his kindness, we are now able to supplement this general account with a Table, giving the average dimensions of bees reared in comb of the various sizes, and with illustrations of the bees (from No. 1, 650; to No. 9, 1050).
The data in the Table are the averages of a large number of observations – the work on which it is based was begun in 1891 – and deserve close study. The Table appeared in L’Apiculture Belge of November in a slightly different form, some of the items not being carried to the third decimal place as in the copy placed at our disposal. We have taken the liberty of omitting the column cubic content of a sq. dm. of comb, since it can be obtained instantly from the comb thickness by moving the point. The smoothness with which the data plot on squared paper against cell-number per sq. dm. or any other of the quantities that may be selected, is an assurance-if, in face of M. Baudoux’s careful and ingenious methods of work, any were needed-that the results are to be relied upon.
As regards the separate items. Span (distance between the tips of the expanded wings) is equal to twice the length of the fore wing plus the distance between the wing roots (headed wing root distance). Thorax is the depth (or width-M. Baudoux informs us that they are equal) of the thorax, as measured by the thoraxmeter (see THE BEE WORLD, XIV, p. 38). Tongue gives a series of values which are intended to be illustrative of the gain to be expected from the use of large cells; the actual values will vary with the strain of bee used. [We may add: This will be so with other quantities-for example, wing length. All varieties of bee are not geometrically similar.] Body length, wing width and thickness of the comb need no comment. Cell width is measured as the distance between two parallel edges. The cubic content of a cell is of interest, in that comparison of it with the values for the drone comb approximately confirms Mullenhoff’s results (announced some 50 years ago) that the drone cell has a volume double that of a worker cell. The ratio for M. Baudoux’s cases lies between 1,823 and 1,938. Weight at emergence is somewhat higher than the normal weight of a field bee when “empty”; it is, at the author reminds us, the only weight that can be used for exact comparative purposes, since older bees’ weights vary so much with the state of their alimentary canal.
The item volume of sac calls for more comment. M. Baudoux considers that the maximum load taken by a bee when robbing, or visiting a large supply of syrup provided for experimental purposes, is carried partly in the stomach; and that the bee can regurgitate the stomach contents at will. The honey sac alone, he states, is unable to contain the whole of the loads sometimes measured, for there would not be room for them in the abdomen. The figures he gives in this column therefore represent, not the maximum possible load of the bee of that size, but the volume of the honey sac only; and are based on the diameter of the anterior part of the abdomen, less the double thickness of the body-wall (taken as 0.2 mm. in all). We understand, however, that experiments with the sacmeter and actual measurement of full sacs have confirmed the values given, in a general way.
In connection with measurements of the tongue length, M. Baudoux in 1926 raised the question (L’Apiculture Rutionelle, December, 1926) whether measurement of the tongue under the microscope really gives a correct idea of its length when in use, seeing that it is a very extensible organ. His glossometer is designed to give values more nearly representative of the practical possibilities of the tongue. He makes due provision (as he recognised to be necessary in the same journal, January, 1927) for avoiding the errors due to surface tension, which draws the fluid up the sides of any surface wetted by it-and is of assistance to bees when they are working on flowers with deep corolla-tubes.
M. Baudoux finds that the size of the drone cells built by bees of a given series always bears a constant ratio to the size of the worker cells. There areas are as 50:31, or 1.61 approximately.The drone cells in the Table therefore are arranged in increments of 31. M. Baudoux, in his notes on the Table in L’ Apiculture Belge, calls attention to the fact that the interval between measurements of the bees of one series and those of the next is larger for the larger bees. This is natural; for 50 is a larger fraction of 650 than it is of 1050. If, however, the quantities are compared by plotting all the data against some length-for example, the cell width-it will be found that the increase of nearly all the quantities is even and regular throughout the series (see below).
If big bees are merely small bees whose every dimension has been multiplied in the same proportion, and if the materials of which they are constructed are in every way similar for the corresponding organs, then we ought to find that any two measures of length bear a constant ratio to one another, whether the bee be large or small. That this is the case is easily seen by plotting against some length, as suggested above. The span, wing root length, lengths and widths of wings, length of body, and the cell width, all plot as very nearly straight lines against any one of their number; and if one of them be divided by another (say, body length by wing length), the result is a quantity which is the same (or nearly so) for all the different sizes of bees. The comb thickness does not however conform to this rule, for reasons which must remain for future consideration.
From geometrical principles, one would expect that under these conditions the weight of the bee would vary as the cube of her length or other linear dimension. Very surprisingly, this is not so. The weight of the bee is proportional to her length, not to her (length). This is most unexpected; as M. Baudoux states, it must mean that the enlarged bee is not as solid as the bees of the smaller series. M. Baudoux, we understand, intends to test this point. His results will be awaited with much interest.
This matter of the specific gravity of the bee, and its decrease with increase of size, is not only of theoretical interest. If we suppose that the head, thorax and abdomen share alike in the lightening process, we shall-if we continue to enlarge the bee-arrive finally at an insect which cannot fly as fast or lift as great loads as smaller bees. Big wings demand big muscles to move them; as far as can be seen, the mass of the flight muscles must increase as the cube of the wing length. If the weight of the body increases in this proportion, the bee will continue to be an efficient flyer; but if-as is the case with M. Baudoux’s bees-it does not, then one of two things must be happening. Either the bee will have less flying muscle than she needs to work her long wings; or the flying muscles will make up a greater proportion of her total weight. In either case, theory would indicate that very much enlarged bees should be less efficient nectar-carriers. That the limit (where this begins to occur) has not yet been reached is shewn by the excellent practical results which M. Baudoux obtains.
M. Baudoux finds that the sp. gravity of his bees is about 0.525-a little more than half that of water. This agrees well with the usually received value for insects (0.5), and with that calculated from Armbruster’s figure for the volume of a bee (195 cmm.). This would give sp. gr. 0.525 if the bee weighed 102 mg. Actually, most field bees weigh less than this when “empty,” and their sp. gr. will often be nearer 0.4.
[It may be noted that the weight of insects reared in a state of nature does actually conform fairly closely to the cube law. Weighing and measurement of a large number of bees, wasps and related insects, also of Syrphid flies of various sizes, has shown that the weight varies approximately as the cube or the 3.5 power of the wing length. (The latter result is probably due to the insects being unduly heavy with eggs or a full colon). Even wasps or bumble bees of different sizes-the nearest approach in nature to the bees reared by M. Baudoux-follow the same law. It may be remarked that all these insects also have the thorax weight a more or less definite percentage of the body weight; for good flyers, with few exceptions, about 40 to 55%. This includes legs and leg muscles, of course. Poor flyers that use their big legs a great deal, such as the digger wasp Ammophila, have a high thorax percentage weight; but when allowance is made for this, it is some guide to flying power. The drone’s thorax, for example, habitually accounts for more than half of his weight.
It might be thought that, by ensuring that the colony had ample stores, any stinting of the larvae could be prevented, and so their weight increased; but we think it likely that the beekeeper will not be able to intervene here. The nurses will most probably go on giving the grubs, not what they could eat if allowed, but what they are considered to need!
In this connection it is worth while comparing v. Rhein’s work on the rearing of giant workers by feeding them lavishly with older-worker larval food in roomy artificial cells (THE BEE WORLD, XIV, p. 141, December, 1933). His largest specimen weighed 175 mg. at emergence. If its weight followed the same laws as that of M. Baudoux’s series of bees, it would correspond to bees reared in cells 450-500 per sq. dm. It is probable, however, that this is not the case. A comparison of v. Rhein’s figures of a giant and a normal worker shows that the abdomen of the giant is 1.6 times longer than that of the normal bee at the same pupal stage; and that its thorax is only about 1.14 as wide (at most). This probably means that a good part of the abnormal weight is due to the development of the ovaries and spermatheca which is a feature of such giants; so that the giant would (it of normal worker construction) be little if at all heavier than the bees reared in 650 comb by M. Baudoux. That is to say, the unexpectedly light weight of the bees we are considering may be unavoidable, if they are to remain workers and not become half-queens. The nurses may be obliged to stint them in order to prevent development of queen organs and probably also queen instincts. If they did not do this, the use of very large cells would probably result in the rearing of bees which produced an unusual proportion of laying workers or were otherwise abnormal. So far, there appears to be no risk of this; for M. Baudoux’s big bees have proved themselves most efficient honey-producers, and show no sign of queenlike indolence.]
We understand that M. Baudoux welcomes criticism, as long as it is of a constructive nature, and offered by persons who have tried, or are prepared to try, the large cell foundation for themselves. We are convinced that this method of improving the bee deserves to be considered very seriously.
A.D.B.
THE INFLUENCE OF CELL SIZE.
(With Illustrations and Table of Data by M. Baudoux, Tervueren, Belgium).
In April last we published a description by M. Baudoux of his work on the enlargement of the bee by the use of large-cell foundation (THE BEE WORLD, XIV, p. 37). Through his kindness, we are now able to supplement this general account with a Table, giving the average dimensions of bees reared in comb of the various sizes, and with illustrations of the bees (from No. 1, 650; to No. 9, 1050).
The data in the Table are the averages of a large number of observations – the work on which it is based was begun in 1891 – and deserve close study. The Table appeared in L’Apiculture Belge of November in a slightly different form, some of the items not being carried to the third decimal place as in the copy placed at our disposal. We have taken the liberty of omitting the column cubic content of a sq. dm. of comb, since it can be obtained instantly from the comb thickness by moving the point. The smoothness with which the data plot on squared paper against cell-number per sq. dm. or any other of the quantities that may be selected, is an assurance-if, in face of M. Baudoux’s careful and ingenious methods of work, any were needed-that the results are to be relied upon.
As regards the separate items. Span (distance between the tips of the expanded wings) is equal to twice the length of the fore wing plus the distance between the wing roots (headed wing root distance). Thorax is the depth (or width-M. Baudoux informs us that they are equal) of the thorax, as measured by the thoraxmeter (see THE BEE WORLD, XIV, p. 38). Tongue gives a series of values which are intended to be illustrative of the gain to be expected from the use of large cells; the actual values will vary with the strain of bee used. [We may add: This will be so with other quantities-for example, wing length. All varieties of bee are not geometrically similar.] Body length, wing width and thickness of the comb need no comment. Cell width is measured as the distance between two parallel edges. The cubic content of a cell is of interest, in that comparison of it with the values for the drone comb approximately confirms Mullenhoff’s results (announced some 50 years ago) that the drone cell has a volume double that of a worker cell. The ratio for M. Baudoux’s cases lies between 1,823 and 1,938. Weight at emergence is somewhat higher than the normal weight of a field bee when “empty”; it is, at the author reminds us, the only weight that can be used for exact comparative purposes, since older bees’ weights vary so much with the state of their alimentary canal.
The item volume of sac calls for more comment. M. Baudoux considers that the maximum load taken by a bee when robbing, or visiting a large supply of syrup provided for experimental purposes, is carried partly in the stomach; and that the bee can regurgitate the stomach contents at will. The honey sac alone, he states, is unable to contain the whole of the loads sometimes measured, for there would not be room for them in the abdomen. The figures he gives in this column therefore represent, not the maximum possible load of the bee of that size, but the volume of the honey sac only; and are based on the diameter of the anterior part of the abdomen, less the double thickness of the body-wall (taken as 0.2 mm. in all). We understand, however, that experiments with the sacmeter and actual measurement of full sacs have confirmed the values given, in a general way.
In connection with measurements of the tongue length, M. Baudoux in 1926 raised the question (L’Apiculture Rutionelle, December, 1926) whether measurement of the tongue under the microscope really gives a correct idea of its length when in use, seeing that it is a very extensible organ. His glossometer is designed to give values more nearly representative of the practical possibilities of the tongue. He makes due provision (as he recognised to be necessary in the same journal, January, 1927) for avoiding the errors due to surface tension, which draws the fluid up the sides of any surface wetted by it-and is of assistance to bees when they are working on flowers with deep corolla-tubes.
M. Baudoux finds that the size of the drone cells built by bees of a given series always bears a constant ratio to the size of the worker cells. There areas are as 50:31, or 1.61 approximately.The drone cells in the Table therefore are arranged in increments of 31. M. Baudoux, in his notes on the Table in L’ Apiculture Belge, calls attention to the fact that the interval between measurements of the bees of one series and those of the next is larger for the larger bees. This is natural; for 50 is a larger fraction of 650 than it is of 1050. If, however, the quantities are compared by plotting all the data against some length-for example, the cell width-it will be found that the increase of nearly all the quantities is even and regular throughout the series (see below).
If big bees are merely small bees whose every dimension has been multiplied in the same proportion, and if the materials of which they are constructed are in every way similar for the corresponding organs, then we ought to find that any two measures of length bear a constant ratio to one another, whether the bee be large or small. That this is the case is easily seen by plotting against some length, as suggested above. The span, wing root length, lengths and widths of wings, length of body, and the cell width, all plot as very nearly straight lines against any one of their number; and if one of them be divided by another (say, body length by wing length), the result is a quantity which is the same (or nearly so) for all the different sizes of bees. The comb thickness does not however conform to this rule, for reasons which must remain for future consideration.
From geometrical principles, one would expect that under these conditions the weight of the bee would vary as the cube of her length or other linear dimension. Very surprisingly, this is not so. The weight of the bee is proportional to her length, not to her (length). This is most unexpected; as M. Baudoux states, it must mean that the enlarged bee is not as solid as the bees of the smaller series. M. Baudoux, we understand, intends to test this point. His results will be awaited with much interest.
This matter of the specific gravity of the bee, and its decrease with increase of size, is not only of theoretical interest. If we suppose that the head, thorax and abdomen share alike in the lightening process, we shall-if we continue to enlarge the bee-arrive finally at an insect which cannot fly as fast or lift as great loads as smaller bees. Big wings demand big muscles to move them; as far as can be seen, the mass of the flight muscles must increase as the cube of the wing length. If the weight of the body increases in this proportion, the bee will continue to be an efficient flyer; but if-as is the case with M. Baudoux’s bees-it does not, then one of two things must be happening. Either the bee will have less flying muscle than she needs to work her long wings; or the flying muscles will make up a greater proportion of her total weight. In either case, theory would indicate that very much enlarged bees should be less efficient nectar-carriers. That the limit (where this begins to occur) has not yet been reached is shewn by the excellent practical results which M. Baudoux obtains.
M. Baudoux finds that the sp. gravity of his bees is about 0.525-a little more than half that of water. This agrees well with the usually received value for insects (0.5), and with that calculated from Armbruster’s figure for the volume of a bee (195 cmm.). This would give sp. gr. 0.525 if the bee weighed 102 mg. Actually, most field bees weigh less than this when “empty,” and their sp. gr. will often be nearer 0.4.
[It may be noted that the weight of insects reared in a state of nature does actually conform fairly closely to the cube law. Weighing and measurement of a large number of bees, wasps and related insects, also of Syrphid flies of various sizes, has shown that the weight varies approximately as the cube or the 3.5 power of the wing length. (The latter result is probably due to the insects being unduly heavy with eggs or a full colon). Even wasps or bumble bees of different sizes-the nearest approach in nature to the bees reared by M. Baudoux-follow the same law. It may be remarked that all these insects also have the thorax weight a more or less definite percentage of the body weight; for good flyers, with few exceptions, about 40 to 55%. This includes legs and leg muscles, of course. Poor flyers that use their big legs a great deal, such as the digger wasp Ammophila, have a high thorax percentage weight; but when allowance is made for this, it is some guide to flying power. The drone’s thorax, for example, habitually accounts for more than half of his weight.
It might be thought that, by ensuring that the colony had ample stores, any stinting of the larvae could be prevented, and so their weight increased; but we think it likely that the beekeeper will not be able to intervene here. The nurses will most probably go on giving the grubs, not what they could eat if allowed, but what they are considered to need!
In this connection it is worth while comparing v. Rhein’s work on the rearing of giant workers by feeding them lavishly with older-worker larval food in roomy artificial cells (THE BEE WORLD, XIV, p. 141, December, 1933). His largest specimen weighed 175 mg. at emergence. If its weight followed the same laws as that of M. Baudoux’s series of bees, it would correspond to bees reared in cells 450-500 per sq. dm. It is probable, however, that this is not the case. A comparison of v. Rhein’s figures of a giant and a normal worker shows that the abdomen of the giant is 1.6 times longer than that of the normal bee at the same pupal stage; and that its thorax is only about 1.14 as wide (at most). This probably means that a good part of the abnormal weight is due to the development of the ovaries and spermatheca which is a feature of such giants; so that the giant would (it of normal worker construction) be little if at all heavier than the bees reared in 650 comb by M. Baudoux. That is to say, the unexpectedly light weight of the bees we are considering may be unavoidable, if they are to remain workers and not become half-queens. The nurses may be obliged to stint them in order to prevent development of queen organs and probably also queen instincts. If they did not do this, the use of very large cells would probably result in the rearing of bees which produced an unusual proportion of laying workers or were otherwise abnormal. So far, there appears to be no risk of this; for M. Baudoux’s big bees have proved themselves most efficient honey-producers, and show no sign of queenlike indolence.]
We understand that M. Baudoux welcomes criticism, as long as it is of a constructive nature, and offered by persons who have tried, or are prepared to try, the large cell foundation for themselves. We are convinced that this method of improving the bee deserves to be considered very seriously.
A.D.B.