Sir, I send, herewith, a side view, and section of a Tide and Lunar Rotula of my construction, which exhibits in a more correct manner than any other, with which I am acquainted, the apparent diurnal revolutions of the sun and moon, the mean-time of their southing, the age of the moon, and common, spring, and neap tides, during her conjunctive period with the sun.

In both figures, the same letters of reference are made use of to denote the same parts; in the section, the different wheels are called by their numerals, in order that their relative bearings may be the more readily comprehended.

A A is a circular box, containing the wheel-work and necessary appendages; on the top of this box are two moveable circular plates, the outer one of which, B B, is divided into 24, and the interior one into 29 equal parts; C is a sort of pedestal screwed to the bottom of the box, through the top of which a hole is pierced for the admission of the horizontal axis to which the handle H is attached, to keep it steady, and into the line of pitching with its connectingwheel in the centre. Both these wheels are bevelled, as they turn at right angles to each other. In the section they have twelve teeth each, but any number of teeth will do, provided they are equal numbers, as these wheels are not considered to constitute a part of the train, the purpose of them being merely to transmit motion horizontally to the wheel 53, which is assumed to make one revolution in 24 hours. This is effected in the following manner :-The horizontal axis, turns once round in one day, or 24 hours, having on its interior end one of the before-mentioned small bevelled wheels of 12 teeth; this wheel turns another similar wheel, of the same size and number of teeth, which is made fast to the lower end of the hollow axis of the solar wheel 53, and thereby gives it a motion, in common with the handle, every 24 hours. The solar wheel 53 turning once round its centre in 24 hours,

acts into the teeth of a small wheel of 24 teeth, having a hollow axis, or tube, turning on a stud screwed into the bottom of the frame. On the lower end of this tube, is made fast another small wheel, having 14 teeth revolving in the same period as wheel 24; this 14-teethed wheel takes into the teeth of wheel 32, and makes it revolve once round its hollow axis (on the long wire supporting the globe) in 24 hours, 50 minutes, 27 seconds, 37.5 thds. The tube of this wheel 32, or lunar wheel, is prolonged until it reaches to within a very little of the globe, and across its diameter at the top, is cut a slit, similar to that of a batwing which takes easily into the burner, under part of the black elliptical sort of tide ring, T, that encompasses the globe, andcauses it to turn with it in the abovementioned period. The tube of the lunar wheel is made so as turn tightly on its wheel in order to allow the tide ring, T, and the moon M, to be rectified to any required meridian. This elliptical tide-ring is grooved all round its exterior circumference, and within this groove lies a thin flexible spring ss, which by its peculiar motion exhibits the appearance of the spring and neap tides. This motion is obtained by the following arrangement:-A small tube is inserted in the lunar tube, to which is attached (above) the moon-plate of 29 divisions, and, on its under surface, there is a circular frame furnished with small friction-rollers. These rollers come into conjunction twice in a lunation of 29 days, 12 hours, 44 minutes, with two small semicircular pieces of brass rivetted into the upper surface of the solar wheel 53, and when doing so, they cause the lunar-wheel tube and this bar to have a

small perpendicular motion. By the ascent of the tube, it presses with its horizontal pin P against the underpart of the above-mentioned flexible spring ss, laying in the grooved circumference of the elliptical tide-ring T, until it assumes

*Spring tides happen at the time of new and full moon, to nearly the same extent generally; they cannot happen at any other time of the month, because, at no other time are the sun and moon upon the same or opposite meridians. Neap tides arise trom the action of the moon being opposed by that of the sun, and this happens when the moon is either at the end of her fist or last quarter. Care must, therefore, be taken when putting together the wheel-work, to place the small risings on the upper surface of the solar-wheel directly under the elliptical tide-ring.

the appearance exhibited in the engraving, which is an indication of spring tide. When the spring lies concealed in the groove A, it is an indication of neap tide. This spring is pinned to the upper part of the grooved circle-ring, and by the depth of the slit cut across the lunar tube, it is allowed to ascend and descend with the attached flexible spring with great ease. The 24-hour circle BB turns round with the solar wheel 53, by means of two long through-going pins DD, and the lunar circle of 29 divisions, turns round with wheel 32, by two short pins passing through its plate and the cir cular frame EE. From each of these circular plates arises a stem carrying halls, S and M, representing respectively the sun and moon. The sun is carried, as before stated, round the earth in 24 hours; and the moon, with its accompanying tide ring, &c., every 24 hours, 50 minutes, 27 seconds, 37.5 thds, which is a very near approximation, to the apparent daily motion of the moon and tide.

The meridian circle is fixed to the north pole of the globe by means of a tapped nut, and supports the brazen horizon (encompassing the globe round the equator) having laid down on its surface a variety of places in the world, selected so as to indicate the hour as compared with Britain, as also the tides. These particulars are indicated by the revolution of the sun and moon, and by observing what places are against the stem of each. From the under surface of the horizon, are suspended four wires supporting the cover-plate F, and to the right of the meridian horizon is a small horizon of brass, projecting outwards, being fastened by means of a screw to the meridian circle, and furnished with two small circular holes marked S and M; the one marked S, being for the meridian passage of the sun, and M for that of the moon. From this meridian, a pointer G descends to the surface of the hour-plate, and indicates the time at the place for which it is rectified. The apparatus, as seen in the engraving, is rectified to the meridian of Peterhead, in order to bring the moon and tide on the meridian; but can be very easily rectified to any given place according to the following examples explanatory of its use.

Examples.

1. To find the hour of the day.-This is accomplished, by observing what par ticular hour is immediately under the suspended point g.

2. To find the moon's age.-Observe what number on the lunar circle of divisions, is in conjunction with the sun's stem, the number against it being the day of the moon's age.

3. To find the times of high water at Southing, at the rectified meridian.-The hour on the hour-circle right against the moon's stem will indicate the meridian passage, and the required time of high

water.

4. To rectify the globe. Nothing further is here necessary than to bring the particular place required under the meridian, and mark it; and then the machine is ready for use. But mark first, that you set the moon and tide to their true situation on the days of new and full moor, which is done in the following manner: Observe the time of high water on the day of new or full moon, set the tide-ring to that hour, and the globe to its place in the horizon; or, in other words, suppose it to be high water at any given place, precisely at 12 o'clock on the 12th day of the moon's age, and imagine the highwater mark to extend to the ecliptic in the heavens; it will be found, that the point will be a little more than two hours' distance; the tide-point being before the moon, the machine must be rectified after this manner, and then it is ready for use.

The several particulars indicated by the apparatus, as represented in the engravings, are as follows: Under the suspended meridian pointer, is the hour of 12, that being the hour of the day; opposite the sun's stem is 14 nearly, being the days of the moon's age; and opposite the moon's stem is also 12, being the time of high water, and southing at the rectified port.

A perusal of the description of my tide-dial, given in the Mechanics' Magazine for December 25, 1831, will assist the reader to a still clearer idea of the management of the Tide and Lunar Rotula.

It may be proper to mention, that Mr. Ferguson made a machine which exhibited part of the particulars here

described, by adding only two wheels and one pinion to a common clock movement. The numbers of the teeth were 57 and 59, because in 57 apparent daily revolutions of the moon, there are in round numbers 59 revolutions of the

;

sun and a wheel or pinion turning once round in eight hours, having 19 teeth, turned them both. But there are two objections to this arrangement: first, there is a mechanical objection to two wheels having different numbers of teeth, because the spaces between the teeth, not being in proportional ratios to each other, the line of pitch cannot be exactly effected, and a jarring is thus occasioned, the effects of which are transmitted to the hands or circles driven by the wheel or wheels, so that the exact time of new, first quarter, full, and last quarterly moon, cannot be cor rectly ascertained. Secondly, the num bets 57 and 59, lead to a very serious error in a very short period of time. For, if the wheel with 57 teeth turn once round in 2 hours, that with 59 will revolve in 24 hours, 50 minutes, 31 seconds, 39-249; and comparing these rates with the true average time, the error will stand thus :

which, being subtracted from the true period, 24 hours, 50 minutes, 28 seconds, 2. will be found to produce an error of 35 seconds per day, or 21-2 minutes per annum; which is 63-6 minutes in three years, or three hours in the course of 83 years behind the true time; thus causing the wheel-work to exhibit half tide, when it should be full tide, &c. To obviate the first-mentioned objection, and to reduce the error of the second, has been my principle object in the construction of the apparatus before described. My improvements will be illustrated by the following considerations. I find by calculation, that were the sun and moon exactly in conjunction with each other, they would be within about 7 minutes of being so. again after 768 apparent diurnal revolu tions of the sun, and 742 revolutions of the

The moon's apparent diurnal revolution an.o ants to 24 hours, 58 minutes, 282 seconds.

moon. Now, if there were two wheels, the one containing 742 teeth, and the other 768, and both were driven by a wheel of 742 teeth, the wheel 742 would make one revolution in 24 hours, 50 minutes, 27 seconds, 376 thds. ; but these numbers being too high to be put into practice, they are susceptible of the following fractional reduction: 53x14

742, and 32 × 24768-which are the numbers of the teeth in the wheels which I have inade use of in my ma-` chine, in the manner before described. My period of 24 hours, 50 minutes, 27.6 seconds, differs only about 6 dec. of a second in an apparent diurnal revolution, or 4 minutes per annum, or 35 minutes in 83 years nearly, before the true time, while in the same period, Mr. Ferguson's numbers are liable to an error of nearly 3 hours. By making use of the numbers which I have calculated for this machine, the error will be reduced one-sixth in the period of a second, and its accompanying small error would be hardly observed on the dial of a common clock, though it were to go for seven years without cleaning. The advantages of my apparatus for all common practicable purposes, are

therefore obvious.

Yours, &c. Duke street, Liverpool, Sept. 13, 1831.

E. HENDErson.*

HYDRAULIC DYNAMOMETER.

Sir, In addition to the few unworthy plans for dynamometers, which you did me the honour to publish recently, I beg to submit another, which has since occurred to me.

In

It is known to your readers, that a body whose specific gravity differs from that of water, will, if it be immersed in that element, either sink in it or remain at the surface with only a portion of its bulk above it; in the first case, the den-. sity of the body exceeds, and in the latter it falls short, of that of the water. the first case also, the body can be kept just below the surface by a weight counteracting it, whose magnitude is the difference between the absolute weight of the immersed body, and that of an equal bulk of water; in the latter, by a weight equal to this difference pressing directly upon the body.

The law is universal for all fluids, that ́ if depths be taken in arithmetical pro

gression, the densities will be in geometrical progression; and, therefore, the heaviest substance with which we, at least, are acquainted, will, if plunged into an abyss of the element of sufficient depth, such, for instance, as the sea, continue to descend until it come to a position, where its own density is the same as that of the fluid, and there it will remain at rest.

My plan is this:-If the body, thus immerged, be connected with a cord supposed without weight, and going over a fixed pulley with, and forces be in succession applied to draw up this weight, a variation will exist in their intensity in every successive stage, or position of the body in its ascent, and the limit of these forces will be contained hetween, nothing, and the difference between the weight of the body, and that of an equal bulk of the fluid.

Further, if additional forces be applied until the body is completely drawn from the water, it is manifest that the scale of forces obtained will be increased, and its limits will be contained between,-nothing and the absolute weight of the body.

Hence, a theoretical dynamometer of powers from nothing to any extent proposed

The whole of this theory, however, is not entirely practicable, although part of it may be said to be so. I have adduced the case of the descent of the body in the fluid, until it rests only to render the theory more complete and better understood. That part of it which relates to the body at the surface is the one to be considered; the contrivance which it suggests, may, I think, be best illustrated by a diagram.

AB is a cylinder of wood, having a small weight of metal at C, the middle of its base to keep it vertical; this cylinder and weight attached should be of bulks and substances, such that when left in the fluid, they may either remain at rest just below the surface, or have only a small tendency to descend. CDE is a cord or line attached to the cylinder by knots at the ends of smail cords, radiating from equidistant points on the periphery of the upper plane A, the cord CDE going round the groove of a fixed pulley at D. It will be readily seen, that by this means we obtain the measure of forces applied at E, to counterpoise the

cylinder in each of its positions, whether they be those exerted by inert matter, or the muscular energy of animals. His a curved rack fixed on the extremity of the short arm K G of the lever L G. The extremity K of this lever is made to traverse on an arc Z Z, whose centre is K, and to indicate the amount of the forces applied at E, by this means:at a point a on the rope, the distance of which from C is not less than the depth CB of the cylinder, is fixed one end of a chain whose length is equal to the depth C B; the links on this chain take into the cogs the curved arc; the lever made of a light material should turn somewhat stiffly on its centre K, and it will then have no propensity of itself to move from the position into which it may be drawn, by the force, either when that force is exerted or relaxed.

The rest of the scheme will now be obvious the use of the lever being to read off the forces exerted by the graduations or the arc to a nicety.

I did think of troubling you with a few remarks on dynamometers in general, and on the great variety of instruments already in existence, which though not nominally, are yet, in effect, nothing but dynamometers for various purposes; and to make some remarks on the objections, to which the present plan may be open, with suggestions of the way in which they may be, at least partially obviated. As, however, this communication has extended much further than is perhaps proper, I must beg to reserve my remarks for another occasion. Yours, &c.