Jtily lO, 1879] 



NATURE 



247 



A third curve is also introduced which represents such 

 a rotation of the system that the planet always shows the 

 same face to the satellite, just as we always see the same 

 face of the moon ; this curve is called the curve of rigidity, 

 because when the motion is of this kind, the system 

 moves as though the planet and satellite were parts of 

 one rigid body. 



It appears from a consideration of these three curves 

 that if the whole momentum of the system be less than a 

 certain amount, then it is not possible to set a given 

 planet and satellite in rotation, so that the planet shall 

 always show the same face to the satellite ; but if this can 

 be done at all, it can be done in two ways, and one of 

 those ways corresponds to a maximum amount of energy 

 of the system, and the other to a minimum. Moreover 

 the configuration of ma.ximum energy is one of dynamical 

 instability and the system may degrade in either of two 

 ways from that state. In one of these modes of degrada- 

 tion the satellite approaches and falls into the planet, and 

 in the other it recedes from the planet. 



Part of the author' s previous papers consists in tracing 

 backwards the moon's motion from its present condition 

 to that configuration of maximum energy ; and it was 

 found that that state corresponded with a rotation of the 

 earth and moon, like the parts of one rigid body, in about 

 five hours. This rapid periodic time of the moon corre- 

 sponds with only a few thousands of miles intervening 

 between the earth's surface and that body. Since the 

 tides on the earth must be subject to friction, it follows 

 inevitably that, if time enough has elapsed since the 

 origin of the moon and earth, the present state must 

 be a degradation of the configuration of maximum energy, 

 which cannot itself be a degradation of a previous state. 

 And therefore it was maintained that this closeness of the 

 two bodies points to the community of their origin. 



In this mode of evolution we see that the rotation and 

 revolution of the two bodies was primitively such that 

 the month and day were of equal length (about five hours), 

 and that in the future they will again come to equality, 

 each being then about fifty of our days long. From this 

 it follows that the system must pass through some phase 

 in which there is a maximum number of planetary rota- 

 tions during one revolution of the satellite, or shortly 

 there must, at some time, be a maximum number of days 

 in the month. Numerical calculation shows that for the 

 earth and moon that maximum number is about 29, and 

 that at present, when we have 27J days in the sidereal 

 month, we have slightly passed that maximum. 



From a further consideration of the figures it appears 

 that if the planet and satellite are set in motion with 

 opposite rotations, the satellite will fall into the planet if 

 the moment of momentum of orbital motion be less than 

 or equal to, or only greater, by a certain critical amount 

 than the moment of momentum of planetary rotation ; 

 but if it be greater by more than a certain critical amount 

 the satellite will approach the planet, the rotation of the 

 planet will stop and reverse, and finally the system will 

 come to equilibrium when the two bodies move round as 

 a rigid body, with a long periodic time. 



If the rate of the planet's rotation be less than that of 

 the satellite' s revolution, so that the sidereal month is 

 shorter than the day (as with the inner satellite of Mars), 

 then the satellite will either approach the planet and ulti- 

 mately fall into it, or will approach the planet and will 

 finally move round the planet at the same rate as the 

 planet rotates. It depends on the nature of the system, 

 as to which of these two cases will be the result. 



The method is then extended to the case where the 

 satellite, instead of being merely an attractive particle, is 

 also a spheroid rotating about an axis perpendicular to 

 the plane of the orbit. In this case the graphical illus- 

 tration is by means of surfaces, there being one surface 

 representing conservation of moment of momentum, and 

 aiiother representing the energy of the system. Each 



point on one surface has a corresponding point on the 

 other surface, and the point on the energy surface must 

 always shde down hill. It is not necessarily the case 

 that the descent should be down a line of greatest slope. 

 Illustrations are given to show that a point on an energy 

 surface may sometimes depart from the bottom of a 

 furrow, or may descend a ridge on the surface. The 

 path to be followed by the point on the energy surface 

 depends on the nature of the tides raised in the two 

 bodies. Thus the solution in this case is not determinate, 

 without some further knowledge of the system. 



MORE NOTES FROM K I LB URN 



THE gas and petroleum-engines make a fair show. 

 The Otto silent gas-engine, however, seems still to 

 hold its own, other constructions having, so far as one 

 can judge from a short inspection at Kilburn, some 

 defect or other, such as noisy working, or a dangerous- 

 looking outside flare of the ignited gas. One striking 

 novelty is shown in this section, namely, an invention of 

 Mr. Dugald Clerk, whereby the gaseous mixture is 

 lighted by a cage of platinum wire, which retains heat 

 enough from one ignition to the next to be efifective for 

 this purpose. It is stated that 400 ignitions have been 

 made in the cylinder of an engine of this type in one 

 minute. There are other distinctive contrivances in this 

 gas-engine, which, by the by, is the manufacture of 

 Messrs. Thomson, Sterne, and Co., and altogether shows 

 great ingenuity. One of the engines exhibited by this 

 firm is described as a "Domestic Motor," of ^horse- 

 power, costing but 15/., and deriving its power from 

 steam generated by the ignition of air and gas. Such an 

 engine seems admirably fitted for private use in labora- 

 tories and small workshops as well as in houses. 



Self-binding harvesters, in which wire is used for the 

 automatic tying-up of the sheaves, are attracting much 

 attention, now that millers have adopted the use of 

 magnets, preferably electro-magnets, to separate any bits 

 of iron wire that may happen to get mixed with the grain. 



The machinery and implements employed in butter- 

 making and cheese-making afford a striking example of 

 the advantages resulting from the application of scientific 

 exactness to a most useful art. The question of tempera- 

 ture in every operation of the dairy is now recognised as 

 of extreme importance. The thermometer reigns supreme 

 in the interesting tent where dairying is shown. The 

 material, the depth, and the diameter of the pans for 

 "setting" milk have been duly studied. Though the 

 processes and instruments exhibited in action are few in 

 comparison with those at the previous shows at Ham- 

 burg and other special gatherings, yet the exhibits of 

 Mr. E. Ahlborn and of the Aylesbury Dairy Company 

 are worth attentive study. We noted especially an in- 

 genious butter- squeezer or presser, which removes in the 

 most effectual way that very variable and often excessive 

 quantity of butter-milk and water and of interstitial air 

 which occur in ordinary butter, even when quite genuine. 

 Not only is liability to change and decomposition much 

 lessened by this operation, but constancy of composition 

 is secured, and we no longer find the proportion of water 

 in fresh butter ranging between 6 and 20 per cent. 



Messrs. F. H. Atkins and Co. show some good models, 

 and examples of their water-filters and other sanitary 

 appliances in connection with water supply. One of their 

 contrivances is specially clever. The surfaces of filtering 

 media of course become rapidly clogged and useless when 

 the water supply is particularly turbid. The vertical sur- 

 faces of Atkins's cloth filters are so arranged as to be 

 capable of rotation against a rotating cylindrical brush, 

 set vertically, and accommodating itself perfectly to the. 

 surface to be cleansed. 



An instructive section of the Kilburn Show is that' 

 devoted to hops. From a paper issued by Messrs. John 



