Cant Find User Without Id Error In Rails

The first step to constructing out the appliance on this manner will probably be to create a Post mannequin and associated resources. We might want to switch these resources, however utilizing the scaffold command will save us a while and vitality because it generates a shape we will use as a beginning point. Logging is a vital component to understanding the conduct of your applications. Your logs comprise crucial files of software operations consisting of database queries, server requests, and errors.

With correct logging, you usually have comprehensive, context-rich insights into software utilization and performance. In this post, we'll stroll by means of logging alternatives for Rails purposes and investigate some premiere practices for creating informative logs. We may additionally present you methods to additional increase the usefulness of your logs utilizing the Lograge library. The Rails framework makes it straightforward to create safe purposes impervious to many sorts of attacks. Some of that is completed by means of the use of a secret token to safe a session with a browser.

Making all of the helper features reject Step values pressured me to replace all of the decision websites and make the codebase prepared for the brand new schema. If there's a consumer with corrupt knowledge in y x xour set, the user.save! Secondly, in manufacturing you could have quite a few users, which suggests the database would take a very very lengthy time to migrate, probably retaining your software offline for all of the time. Finally, as your software adjustments over time, you would probably eliminate or rename the User model, which could trigger this migration to fail.

Some recommendation means that you just outline a User mannequin inside the migration to circumvent this. For even larger safety, Elle Meredith advises us to circumvent facts migrations inside ActiveRecord migrations absolutely and construct out momentary facts migration duties instead. Rails provides to the issue by tightly coupling your mannequin API to the schema, and inspiring you to make use of this API instantly from controllers and views.

Since the whole software is then coupled to the schema, any change to the database ripples because of the whole codebase until you discover a option to include the change. Fortunately, there are methods to work spherical this and carry out the migration in incremental steps. The replace motion updates user's password with legitimate tokens and redirects to the sign_in_path.

We need to configure our mailers earlier than we accomplished this action, for a consumer to obtain an e mail and reset the password. Before we configure the mailers, let's create the views by operating the command contact app/views/password_resets/edit.html.erb. As you add complexity to your Rails applications, you'll probably work with a number of models, which characterize your application's enterprise logic and interface together with your database.

You're right, your instance is a great technique to unravel N+1 queries problem. Many folks that started out working in rails do not realize what some techniques truly do and what happens. Abstraction layer that, they could use solely in trivial problems. This is verydummy solution, however when a person use yet one different overseas key or add yet one different situations to affiliation then he should add it right here also. But should you wish to make use of it you should realize exacly what you would like do.

Just copy paste some snippet from net is not foremost practise. Reviewing log records is a good approach to be tipped off to inefficiencies in your code and to right them earlier than your software goes into production. If you're engaged on a brand new app, even your creation dataset could commence out small and your app will appear to be it's operating fine. However, as your creation dataset grows, Rails issues like this will likely trigger your software to run slower and slower. This JSON partial will probably be utilized by our controllers at any time when we're handling authentication. It accommodates the user's JWT token which is taken into account sensitive, so it would be the partial solely ever will get rendered for the present user.

Later down the road, we'll create a partial for consumer profiles which can be public-facing. In order for Devise to make use of the jbuilder template we simply created, we'll want to create a pair jbuilder views in Devise's template folders. We're solely going to be applying two of Devise's endpoints in our API, registration and logging in. We'll want to make some adjustments to our controllers to authenticate with JWT's since Devise makes use of session authentication by default. This signifies that you're applying sq. bracket notation to learn a property from an object, however the item is missing, or nil, and thus it doesn't help this method.

Since we're working with sq. brackets, it's possible that we're digging via hashes or arrays to entry properties and one factor alongside the best approach was missing. This might appear when you're parsing and extracting facts from a JSON API or a CSV file, or simply getting facts from nested parameters in a controller action. Because facts is king, we collected, analyzed, and ranked the highest 10 Ruby errors from Ruby on Rails applications. Rollbar collects all of the errors for every venture and summarizes how persistently every one occurred.

We do that by grouping errors in response to fingerprinting. Basically, we group two errors if the second is only a repeat of the first. This provides customers a pleasant overview as opposed to an overwhelmingly huge dump like you'd see in a log file. This new account is saved as component to your Firebase project, and may be utilized to determine a consumer throughout each app in your project, despite how the consumer indicators in. In this demonstration, I will present learn how to make a "destroy" motion for deleting mannequin information from the database. Unlike the "new/create" and "edit/update" assets that use kind submissions to generate POST and PATCH requests, we use a hyperlink with a wonderful choice to generate a DELETE request to the online server.

In this tutorial, you may construct on an present Rails software that gives customers information about sharks. This software already has a mannequin for dealing with shark data, however you may add a nested useful resource for posts about particular person sharks. This will permit customers to construct out a wider physique of ideas and opinions about particular person sharks.

Attempting once more to deploy the app, and this time the construct succeeds. Excitedly, we go to our stay app and are quickly greeted with an software error message that reads, "We're sorry, however some factor went wrong". Everything was working in development, so we're unsure what's occurring in production.

To discover out, we choose to open Papertrail and search our logs for any request with a 500 status. Rails' database migration mechanism permits you to create guidelines to immediately add and take away database tables and rows. Since the information that include these migrations are named in a sequential fashion, you'll be ready to play them returned from the start of time to convey an empty database to the identical schema as production.

This is hence an ideal system to administer granular differences to your application's database schema and keep away from Rails problems. This nonetheless will induce a cluster which could not operate. Authentication system Description Auto login Log in with out consumer operation. When auto login just isn't available, Single Sign On login shall be displayed if SSO is available, and log in with e-mail tackle shall be displayed if it isn't available. To not be unfounded, let's draw up a functional instance of an easy schema for an easy "Twitter clone" application.

The aim right here is simply to not be unique however to have the ability to narrate to sorts exact away. TheViewer isthe consumer who views the feed of different user's tweets. We created a separate sort for a "current user" since it might expose properties in any different case inaccessible on "general" users.

Throughout our software as if we have been utilizing Devise with out JWT's, permitting us to entry the present consumer and checking if a user's signed in utilizing the identical syntax.authenticate_user! Can even be used the identical approach as a before_actionfilter, permitting us to reject requests the require authentication utilizing the acquainted Devise syntax. Next, let's examine the consumer of the logs, who is perhaps you; r it is perhaps a person in your team, in operations, or in client support.

And these customers can be in several time zones, have completely totally completely diverse expertise of the application, or have completely totally completely diverse talent levels. Logs meant for metric gathering might have a totally completely totally completely diverse message format than logs meant for debugging server failures. With Rails and Lograge, you've got quite a few flexibility in creating and producing logs in a format that works finest in your needs. You might even create customized logs to view information for distinct actions in your application. Rails works with a number of log ranges so you'll regulate your logging situated in your environment. U2F augments password-based authentication applying a hardware token that shops cryptographic authentication keys and makes use of them for signing.

The consumer can use the identical token as a second component for a number of applications. It can grant defense in opposition to phishing through the use of the URL of the online net site to lookup the saved authentication key. The trouble with returning a generic error message for the consumer is a User Experience matter.

A legit consumer may well really feel confused with the generic messages, thus making it tough for them to make use of the application, and may well after a number of retries, depart the appliance as a consequence of its complexity. The choice to return a generic error message may well possibly be decided headquartered on the criticality of the appliance and its data. For example, for essential applications, the workforce can choose that underneath the failure scenario, a consumer will at all times be redirected to the help web page and a generic error message shall be returned.

Every time Rails templates a view or partial, it has to open and shut the file. Remember the partial that we positioned contained in the iterator? It created a state of affairs the place our server is having to perform—because there are quite plenty of events—thousands of file reads on each request. As a result, the time it's taking to render the template is making a backlog of requests that point out. Searching for Page Not Found errors making use of PapertrailUsing catch-all routes for dynamic navigation might be useful deal with these situations in a clear and concise manner. What's central to recollect on this example is that folks strive to entry a web page that doesn't exist, not a useful resource that doesn't exist.

Therefore, on the very finish of our routes.rbfile, let's add a catch-all route for any GET requests, sending them to the web page controller's not_found method. Sqlite3 is the default database engine that's initialized in new Rails apps. It's an excellent light-weight engine that helps a big set of the SQL standard—though not all—and wants no further parts or packages to run. That said, its compact nature comes at a price of performance that makes it considerably unsuitable for many creation applications. Nevertheless, it's good to trace how regularly these errors happen.

This results in raised visibility into issues which are affecting your customers or software security, so possible repair them quickly. Otherwise, these error messages will probably be proven to the user, however the engineering and product administration groups will do not know till customers complain to support. Carefully take into account whether or not the additional overhead is price it as you add every gem. Since all content material sorts embrace the Content module, we will add some helper techniques there to assist this annotation.

Method as that might simplify some generic template code. On the has_many facet of the association, we wish to eliminate the related_links affiliation from Step and add it to the suitable content material material types, however preserve the can_have_related_links? API for the time being, with no writing lots of boilerplate. I wished all content material material varieties to assist that API, however solely these with associated hyperlinks to even have a related_links association.

And now, the factories work and all our software code can proceed to work with the brand new mannequin API with no accessing whatever it shouldn't. Making the strategies personal somewhat then elevating an error message means I couldn't generate an explanatory error message any more, however this turned out to not be as tremendous an issue as I'd anticipated. Then, we have to persuade Rails that step.content is one different object, solely it's derived from the identical database file as step. Rails, or particularly ActiveRecord, requires that your mannequin courses are a mirrored image of the database. Their attributes are inferred from the schema and Rails generates strategies to mirror these attributes.

So, altering the schema will change the API of your mannequin classes, and also you need to replace your software appropriately. Next, let's override the create procedure on Devise's SessionController as a way to customise the response conduct of the login endpoint. By default, Devise responds with a 401 standing code when authentication fails, and codecs the error JSON as . We need our login endpoint to reply with a 422 standing code, and the physique to comply with the errors format within the documentation. Once the migration is finished, we ought to have our Users desk created in our database and a User mannequin generated in app/models/user.rb. To exhibit the steps for including a destroy-resource, we'll be making a destroy-resource for a mannequin class representing gadgets in a to-do list.

In addition to including the destroy-resource route and controller action, we'll add "Delete" hyperlinks to the presented index page. Figure 1 illustrates how the modified index web web page will look. The instance initializer proven above masses the lograge-sql library and facilitates Lograge, changing the usual Rails log format. Lograge helps a number of formats, however this configuration makes use of the favored JSON formatter. We've additionally disabled colorized logging—an choice that's beneficial for console outputs however produces messy log files.

You can add customized facts to Lograge logs through the use of the custom_options hook; the instance above incorporates all parameters associated a request. Even of their default format, Rails logs present details that may be very useful in troubleshooting well-known software errors. To bring together a larger quantity of detail, possible add customized logging for Rails. By operating these methods, we create a consumer mannequin with name, e-mail, and password fields and have its schema migrated within the database. Token-based authentication is stateless - it doesn't shop whatever on the server however creates a singular encoded token that will get checked each time a request is made. The most notable big difference between the session-based and token-based authentication is that session-based authentication depends closely on the server.

With API-only purposes so prominent and Rails 5 correct across the corner, some of the most typical strategies of authentication at the moment are transforming into token-based. In this guide, I'll give a brief overview of token-based authentication and the way it really is carried out correct into a Rails 5 API-only application. Remember to add a hyperlink in app/views/sessions/new.html.erb to reset your passwords, replace the file to match the above. Let's create the current.rb class by operating the command contact app/models/current.rb which can permits us to identify Current.user in our views. This generator additionally creates a file in app/views/welcome/ named index.html.erb. By default, Rails renders a view that corresponds to the identify of a controller action.

User authentication is a elementary function within the safety of net resources. While establishing consumer authentication in a rails program, the devise gem is a well-liked tool. However, at occasions it usually is too great and sophisticated to customise mainly when constructing an easy application.

How To Find Mass Using Density And Volume

The tube is bent into a "U" shape and mounted on an inexpensive piezoelectric speaker. The resonance frequency of the tube is detected by a photointerrupter, amplified, and fed into the speaker; the resulting feedback circuit keeps the glass tube vibrating at its resonance frequency. A peristaltic pump and computer are used to flow samples through the tube and record the resonance frequency of the tube. Detail of the glass tube shows the path followed by a sample inside the tube as it flows into the sensor ("a"), passes the tip of the sensor ("b"), and exits the sensor ("c").

Resonance frequency of the vibrating tube vs. time as a 770 μm diameter glass bead is passed back and forth through the tube eighteen times. Each passage of the bead through the tube results in a momentary decrease in the tube's resonance frequency; this is recorded as a downward peak in the resonance frequency . Each point on the peak (baseline "a," tip "b," and baseline "c") corresponds with the bead's location in above. The height of this peak is used to determine the buoyant mass of the bead . Histograms showing the buoyant mass of another bead weighed thousands of times in two different fluid densities.

In deionized water (density 1.000 g/mL) the bead has an average buoyant mass of 3.69 ±0.12 μg, and in a sodium chloride solution (density 1.046 g/mL) the bead has an average buoyant mass of −4.42 ±0.16 μg. The widths of these distributions—120 and 160 nanograms—provide an estimate of the resolution of our mass measurements. Before using a vibrating tube to weigh a sample, the tube must first be calibrated. We calibrated the sensor shown in Fig 1A using a glass bead of known size and density in a fluid of known density . Fig 1C shows eighteen downward peaks in the resonance frequency of the tube as the bead is pumped back and forth eighteen times through the tube. The height of each peak (72 millihertz; Fig 1D) is proportional to the buoyant mass of the bead .

From this relationship we obtain the calibration constant c2 for this tube sensor in micrograms per millihertz (4.8 μg/mHz) that can subsequently be used to determine the buoyant mass of any object flowing through this tube. Our homemade vibrating tube mass sensors typically have quality factors around 500, which is comparable to that of tuning forks and high enough for precise measurement of the tube's resonance frequency . The four proof-of-concept samples studied here—microbeads, embryos, seeds, and biomaterials—are representative of a wide range of samples that may be analyzed in fluid using vibrating glass tube sensors.

Our technique is very versatile because all objects have fundamental physical properties like mass. Consequently, our mass sensor can be applied to problems as diverse as screening toxic substances, understanding the growth of plants, measuring the degradation of biomaterials, and many others. And unlike imaging-based measurements of size, our mass sensor is insensitive to the shape of the object. Finally, the automation, portability, and low cost of this technique make vibrating glass tubes particularly well suited for applications in the field or in resource-limited settings. The ideal density measurement would directly monitor the mass and volume of each cell within a population with minimal sample perturbation and allow cells to be collected for subsequent measurements.

Toward this aim, we utilized the suspended microchannel resonator to measure single-cell buoyant mass with high precision. The SMR is a silicon cantilever with an embedded microfluidic channel that resonates at a frequency proportional to its total mass, which changes as individual cells flow through the channel (Fig. 1) . Unlike density gradient centrifugation, this technique provides buoyant mass and volume information, measures growth-arrested cells in almost any medium, and does not require density gradient chemicals. With this method we found that cell density increases prior to bud formation at the G1/S transition. To investigate the origin of this density increase, we used the SMR in a second method where relative density changes of growing yeast cells are measured as the cells are sampled by the microchannel.

How To Find Mass With Density And Volume Example We found that the density increase requires energy, passage through START, function of the protein synthesis regulator target of rapamycin , and an intact actin cytoskeleton. In conjunction with these density measurements, FACS analysis and bud emergence data suggest that this density change is independent of DNA replication and may result from several START-dependent events. In this work, we demonstrate a simple and inexpensive sensor capable of weighing microgram-sized objects in fluid.

Like the SMR, this sensor uses a change in resonance frequency to weigh an object in fluid with high precision. But unlike the SMR, this sensor can weigh samples with a large range of sizes and is extremely simple to fabricate. Our sensor consists of a short length of glass tubing bent into a "U" shape and attached to an inexpensive speaker that vibrates the glass tubing at its resonance frequency. The resulting sensor shown in Fig 1 costs about US $12 in materials and can be made in under 10 minutes. Additionally, by weighing samples in fluids of different densities, we can also use our sensor to measure the volume and density of samples in fluid.

The SMR reads out real-time changes in relative cell density via the direction of change in buoyant mass as synchronized and growing cells flow through the cantilever. A cell with a density greater than that of the fluid appears as a positive buoyant mass, and a cell with a density less than that of the fluid appears as a negative buoyant mass (Fig. 6). This single-cell technique enables the timing and detection of density changes in biological samples as they occur in growth media.

It has a higher time resolution than current gradient-based approaches and does not involve a subsequent gradient fractionation to define the density distribution . This method may also be applied to cells transitioning to lower density by decreasing the fluid density to below that of the cells' initial density. When a sample passes through the vibrating tube sensor, its buoyant mass is recorded as a brief peak in the plot of resonance frequency vs. time (e.g., Fig 1C and 1D). Once a peak is located, the height of the peak can be measured and converted to a corresponding buoyant mass value using the sensor's point mass calibration described below.

Alternatively, a custom Python program can be used to fit the raw frequency measurements to an analytical equation of expected peak shape derived from Dohn et al. The resulting buoyant mass measurements were recorded and processed using a moving window average filter with a window size of five data points to slightly reduce noise in the plots of buoyant mass vs. time. Additional details about signal processing are provided in S6 Fig. Where mo is the absolute mass of the object, ρo is the density of the object, and ρf is the density of the fluid filling the channel. Stated in words, an object's buoyant mass is equal to its real mass minus the mass of an equivalent-volume amount of fluid.

If the object's density is greater than the fluid's density, then the object has a positive buoyant mass and its passage through the vibrating tube will be recorded as a momentary decrease in the tube's resonance frequency . If the object's density is less than the fluid's density, then the object has a negative buoyant mass and its passage through the tube will result in a momentary increase in the tube's resonance frequency . Finally, if the object's density equals the fluid's density, then the object will have zero buoyant mass and its passage through the tube will have no effect on the resonance frequency of the tube . Note that while the vibrating tube sensor is sensitive to an object's buoyant mass, it is not affected by buoyant forces because the object being measured is confined to the tube and cannot sink or float vertically. Thus, the orientation of the vibrating tube with respect to gravity has no effect on its measurements. Measurements of an object's fundamental physical properties like mass, volume, and density can offer valuable insights into the composition and state of the object.

However, many important biological samples reside in a liquid environment where it is difficult to accurately measure their physical properties. Since all objects have these physical properties, this sensor has immediate applications in a wide variety of different fields including developmental biology, toxicology, materials science, plant science, and many others. To determine the density of an irregular solid in pellet form, add approximately 40 mL of water to a clean and dry 100-mL graduated cylinder.

Place the cylinder on an analytical balance and tare. Add approximately 10 pellets, and record the new volume after the addition. The mass is only the pellets, as the rest have been tared.

Make at least two additional sets of mass and volume measurements to calculate an average value of the density. The density for zinc was measured for three different samples. Note that, since the measurements were made in a graduated cylinder, which is less precise than a volumetric flask, the density has lower degree of precision. In order to address this limitation and to measure an uninterrupted cell cycle, we continuously sampled from split cultures of elutriated G1 yeast cells that remained in media for both measurements.

Buoyant mass and volume growth rates increase during the cell cycle, and the coefficient of variation for volume is greater than that observed in buoyant mass (Figs. 5 and S2–S4). The distributions widen as the culture loses synchrony and cell size variation emerges. Although the smaller sample size prevented accurate density calculations, this approach offers a powerful means to observe growth dynamics in synchronized cell populations.

To measure the density of a sample of material, both the mass and volume of the sample must be determined. For both solids and liquids, a balance can be used to measure mass; however, methods for determining volume are different for solids and liquids. As liquids can flow and take the shapes of their containers, glassware such as a graduated cylinder or volumetric flask can be used to measure the volume of a liquid. The volume of an irregularly-shaped solid can be measured by submersion in a liquid — the difference in volume caused by addition of the solid is equal to the volume of the solid. To validate our technique with a diverse range of biological samples, we used vibrating tube sensors to monitor the mass of individual plant seeds during imbibition and germination.

Seed imbibition, or water uptake, is used in agriculture as a metric of seed health and quality . Seed germination is a change in seed metabolism when imbibition starts; germination culminates with the elongation of the embryonic axis that penetrates the seed coating. The imbibition of seeds is accompanied by a rapid leakage of cellular materials and the rate of this leakage is decreased as the tissues become hydrated . If water uptake by the seed is too rapid, the seed tissue might experience injury, and if the seed enters an anaerobic state, the seed might experience accumulation of toxic chemicals such as ethanol. Both situations can encourage undesirable seed dormancy and delay germination .

In summary, seed imbibition and germination are important phenomena in plant research, and quantitative measurements of these phenomena would be valuable in a wide range of botanical and agricultural fields. Magnesium ribbon with a thickness of 250 μm (98% pure; MiniScience Inc., Clifton, NJ) was used as a model biomaterial in our degradation rate measurement studies. Roughly 1 mm sized pieces of magnesium were cut from the ribbon. The samples were polished before measurement using 600, 800, and 1200 grit silicon carbide abrasive papers to remove the native oxide layer. Each magnesium sample was then immersed in simulated bodily fluid (phosphate-buffered saline ) with adjusted pH and passed back and forth through the vibrating tube sensor every 30 seconds until the piece had fully degraded. Flow through the sensor was controlled using the servomotor as described previously.

The resulting buoyant mass measurements are shown in Fig 4. The yeast strains used in this study are listed in Table 1. Cells were grown in YEPD at room temperature (21 ºC).

Cells were synchronized with 5 μg/mL alpha factor at 0 and 90 min, for a total arrest of 120 min, with the exception of cells synchronized by the 120-min hydroxyurea (10 mg/mL) or nocodazole (15 μg/mL) treatment. An equal volume DMSO mock-treated culture was a control for the nocodazole measurements. For cdc28-as1, cells were arrested with 1-NM-PP1 (5 μM) for 3 hr.

For the density measurements on growth-arrested cells, cells were washed via vacuum filtration at 120 min and concentrated in phosphate buffer to ∼108cells/mL. We observed no change in cell volume resulting from suspension in phosphate buffer. We compared the original sample volume distribution to that of cells collected from the SMR waste and directly observed the SMR's preferential selection of small particles. Accurate measurements of cell size are fundamental to understanding the cell cycle and to identifying cell type and cell state. The key to cell cycle control is the concentration of critical regulatory proteins, which is defined not only by expression levels, but the volume of the cell.

Furthermore, cell volume is coupled to mass and energy requirements that control cell division and survival. Changes to rates of mass and volume accumulation may be correlated with cell cycle position and can be measured as variations in cell density. The density of a substance can be used to define the substance.Water is unusual because when water freezes, its solid form is less dense than liquid water, and thus floats on top of liquid water. Raw resonance frequency data from repeated measurements of a single polyethylene microbead in water (from the right-hand distribution of measurements in Fig 1E). After zooming in to the filtered data , peaks corresponding to individual measurements of the microbead are visible.

Zooming in further on one pair of peaks shows the ∼2 millihertz height of these peaks (corresponding to a buoyant mass of ∼3.7 μg for this microbead). The peaks come in pairs because the particular vibrating tube sensor used for this measurement had a tuning-fork shape with two vibrating "U"-shaped lobes . Additional measurements of the buoyant mass of single zebrafish embryos in water, obtained using our vibrating glass tube sensor. We then hypothesized that mass measurements from vibrating tubes can give insights into the health of organisms. Previous work with the microfluidic SMR mass sensor showed that single cells undergo predictable changes in mass during normal development and reproduction .

Thus, any deviation from the normal growth trajectory can be used as a signal for abnormal development or the emergence of an illness in a cell. On the other end of the size spectrum from cells, measurements of human body weight provide some of the most fundamental insights in the health and growth of a person. We hypothesize that the same relationship between mass change and organism health applies for organisms throughout the size spectrum from cells to humans. As an object passes through the vibrating tube sensor, the shape of each resulting peak in the tube's resonance frequency is a function of the vibrational mode and amplitude of the tube.

In this work, the tubes are vibrating at their primary vibrational mode, meaning that the amplitude of vibration is highest at the tip (the bottom of the glass "U") and lowest at the base (the top of the "U"). However, as the object rounds the tip of the tube (point "b" in Fig 1B), the vibrational amplitude at the tip is the highest, so the object has a maximum effect on the tube's resonance frequency here (point "b" in Fig 1D). As the particle leaves the tube (point "c" in Fig 1B) the tube's vibrational amplitude in this region decreases again, so the resonance frequency of the tube returns to baseline (point "c" in Fig 1D). General mathematical expressions for predicting this peak shape for any vibrational mode were derived by Dohn et al.

This linkage between mass and membrane growth is central to how the cell coordinates growth with division and may have an important role in the signal for cell cycle progression. The density measurement techniques may be generalized to other cells and subcellular particles, and future technology developments aim to acquire single-cell mass and density measurements at once and with only the SMR. Because the differences in density could be artifacts of the different treatments or the cell cycle arrests, we sought to determine if cell density varied during an unperturbed cell cycle. For this purpose we measured the buoyant mass, volume, and density of G1 cells isolated by centrifugal elutriation, resuspended in media for synchronous cell cycle progression, and formaldehyde-fixed overnight.

Although fixation artificially increases cell density (Fig. 3A), the relative density throughout the time course (Fig. 4A) agrees with our previous observations and others' . Cell density was correlated with cell cycle position by comparing the cell density with the percent of budded cells (Fig. 4A, numbers in brackets). The density is relatively low in elutriated G1 cells, increases to near maximum during late G1 and S-phase entry , and then decreases through mitosis. The recorded cell density does not return to its minimum at the end of the first cell cycle because of the time course's resolution, loss of synchrony, or a possible elutriation effect on the initial selection. Buoyant mass and volume continue to increase throughout the time course as the cells grow and the population adjusts from the elutriation's size selection (Fig. 4B). The cantilever vibrates in and out of plane with an amplitude of a few hundred nanometers.

The number of single-cell measurements was maximized by adjusting the sample concentration. A more detailed description of the instrument and its operation is available in ref.12. The frequency shift as cells flow through the microchannel is position-dependent, and the maximum frequency shift, which is proportional to the recorded buoyant mass, occurs when the cell is at the cantilever tip. The frequency returns to baseline upon each cell's exit from the cantilever. Now, Karen needs to take some measurements of her ring to figure out if its density matches that of gold.

First, she uses the balance to measure the mass of the ring, which is 1.35g. To do this, Karen fills a graduated cylinder with 100 milliliters of water and then drops in the ring. Karen measures the new volume of the water, 100.5 milliliters, and then subtracts 100 milliliters. She's left with 0.5mL, which is equal to 0.5 cubic centimeters, the volume of her ring.